Report Study on Joint Replenishment

Description
CPFR seeks cooperative management of inventory through joint visibility and replenishment of products throughout the supply chain.







ABSTRACT




Title of Document: JOINT REPLENISHMENT AND SUPPLY CHAIN
ACTIONS IN THE RETAIL GROCERY INDUSTRY:
TWO ESSAYS

Pamela S. Donovan, Ph.D., 2006

Directed By: Dr. Curtis Grimm,
Dean’s Professor of Supply Chain and Strategy,
Logistics, Business & Public Policy
Dr. Philip T. Evers,
Associate Professor,
Logistics, Business & Public Policy


This study investigated supply chain management practices in the retail
grocery industry from two perspectives. First, the operational performance objectives
were examined by developing and testing a periodic review, joint replenishment
model and heuristic. Joint replenishment policies, designed to coordinate the
ordering of multiple items, can reduce inventory costs by synchronizing
transportation and replenishment decisions (Cetinkaya and Lee, 2000). A fully
specified model was developed taking into account the cost disadvantage of over-
declared shipments. Based on the performance of the Full model, a Truck heuristic
was proposed to fill a truck with each order. By varying the model parameters, the
study demonstrated the large impact transportation costs had on total inventory costs
and the viability of the Truck heuristic, even for moderate differences in

transportation rates. A simulation study tested violations of the demand normality
assumption and found the Full model suboptimized the order interval and base stock
levels under non-normal demand conditions. The result was a 2 percent cost increase
over the expected costs in the Full model. The primary cost drivers were positive or
negative deviations from truckload shipments and higher than expected demand
during the order interval and replenishment period.
The second essay examined the strategic objectives of the retail grocer using
the Schumpeterian perspective to relate supply chain actions, market-based actions,
and firm performance in a longitudinal study. A structured content method was used
to code articles reporting on supply chain and market-based activities. The study
found that higher levels of supply chain and market-based actions, a source of
competitive advantage, resulted in higher sales growth. Unexpectedly, firms engaged
in a broad range of supply chain activities realized a decline in sales, suggesting that a
more narrow focus on specific supply chain programs provided greater financial
benefits to firms in the retail grocery industry. An exploratory study using cluster
analysis found grocery retailers used a variety of strategies. Larger firms were more
likely to focus on market-based strategies and realized the largest sales growth.
Smaller firms, on the other hand, tended to choose balanced or supply chain-focused
strategies, while still realizing average sales growth.













JOINT REPLENISHMENT AND SUPPLY CHAIN ACTIONS IN THE RETAIL
GROCERY INDUSTRY: TWO ESSAYS.



by


Pamela S. Donovan




Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park, in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2006










Advisory Committee:
Professor Curtis Grimm, Co-Chair
Professor Philip Evers, Co-Chair
Professor Martin Dresner
Professor Jeffrey Herrmann
Professor Angelisa Gillyard



















© Copyright by
Pamela S. Donovan
2006
ii
Acknowledgements
I would like to thank Dr. Curt Grimm, Dean's Professor of Supply Chain and
Strategy, University of Maryland, and Dr. Phil Evers, Associate Professor, University
of Maryland, for guiding this research project. Their expertise was invaluable during
each step of the process from narrowing the scope of the research to theoretical
development and analysis. I am particularly grateful to Dr. Grimm and Dr. Evers for
keeping me focused and on track, which was much more important than I would have
thought. I would also like to thank my committee; their suggestions and insight
throughout the process greatly improved this research.
I would like to extend special thanks to Mr. Ken Miller, Miller's Food Market,
Inc., for his support of this research with inventory data and insight to industry
practices. Mr. Miller and his store manager, Rusty Christman, were very helpful in
explaining the ordering practices used by independent grocery retailers.
I am also grateful to Dr. Bill Cunningham, Professor of Logistics
Management, Air Force Institute of Technology, who kept in touch over the past 10
years and encouraged me to seek this degree.
Finally, I am deeply thankful for my family's support and understanding.
They made it possible for me to commit the time and energy necessary to succeed in
this program. I particularly want to thank my husband for helping with the more
tedious tasks related to data entry.

iii
Table of Contents
ABSTRACT................................................................................................................... i
Acknowledgements .......................................................................................................ii
Table of Contents .........................................................................................................iii
List of Tables................................................................................................................ vi
List of Figures ............................................................................................................viii
Chapter 1. Introduction........................................................................................... 1
1.1. Overview of the Retail Grocery Industry.............................................. 2
1.2. Competition in the Retail Grocery Industry.......................................... 3
1.3. Supply Chain Management in the Retail Grocery Industry.................. 4
Chapter 2. Joint Replenishment with Transportation Costs.................................... 7
2.1. Introduction........................................................................................... 7
2.2. Literature Review of Joint Replenishment Inventory Policies.............. 8
2.3. Joint Replenishment Inventory Model Development.......................... 14
2.3.1. Model Assumptions and Notation.......................................... 14
2.3.2. Base (R, T) Policy.................................................................. 16
2.3.3. Full (R, T) Policy ................................................................... 18
2.3.4. Comparing Models: A Numerical Example.......................... 24
2.3.5. Truck (R, T) Heuristic............................................................ 27
Chapter 3. Joint Replenishment Methodology and Experimental Design............ 30
3.1. Model Sensitivity and Model Selection .............................................. 30
3.2. Model Calculations ............................................................................. 31
3.3. Test Problem Description.................................................................... 33
3.4. Discriminant Function Analysis.......................................................... 38
3.5. Simulation Study................................................................................. 41
3.5.1. Data Collection....................................................................... 42
3.5.2. Simulation Model................................................................... 44
3.5.3. Model Measurement............................................................... 46
Chapter 4. Joint Replenishment Results and Discussion...................................... 48
4.1. Discriminant Function Analysis (DFA) .............................................. 48
4.2. Simulation Results............................................................................... 56
4.3. Discussion and Managerial Implications ............................................ 58
4.4. Future Research................................................................................... 59
4.5. Limitations .......................................................................................... 61
iv
Chapter 5. Supply Chain Actions in the Grocery Industry................................... 63
5.1. Introduction......................................................................................... 63
5.2. Theoretical Foundations: Competitive Dynamics.............................. 65
5.3. Supply Chain Activities ...................................................................... 66
5.4. Supply Chain Actions.......................................................................... 69
5.5. Hypotheses Development.................................................................... 70
5.6. Supply Chain Strategies ...................................................................... 73
5.7. Research Setting.................................................................................. 75
Chapter 6. Supply Chain Actions Data Collection and Methodology.................. 77
6.1. Structured Content Analysis ............................................................... 77
6.2. Data Sources........................................................................................ 78
6.3. Data Collection: Action Articles ........................................................ 80
6.3.1. Supply Chain Action Categories ............................................ 80
6.3.2. Market-Based Action Categories ........................................... 82
6.3.3. Extracting data from BCRC................................................... 83
6.3.4. Reliability............................................................................... 85
6.4. Data Collection: Firm-Level Data...................................................... 87
6.4.1. Extracting data from Market Scope ....................................... 88
6.4.2. Firm Names and Parent Corporations .................................... 89
6.4.3. Associating Articles with Parent Corporations ...................... 91
6.5. Model Specification and Variables ..................................................... 91
6.5.1. Dependent Variables .............................................................. 93
6.5.2. Total Supply Chain and Market-Based Actions..................... 93
6.5.3. Supply Chain Action Diversity .............................................. 94
6.5.4. Control Variables ................................................................... 95
6.6. Exploratory Analysis of Market-Based and Supply Chain Actions.... 98
Chapter 7. Discussion – Supply Chain Actions.................................................. 105
7.1. Panel Data Regression Results.......................................................... 105
7.2. Cluster Analysis Results.................................................................... 110
7.2.1. Cluster Analysis A and B..................................................... 111
7.2.2. Cluster Analysis C................................................................ 118
7.2.3. Performance and Descriptive Attributes .............................. 120
7.2.4. Changes in Firm Strategies .................................................. 122
7.3. Discussion ......................................................................................... 124
7.4. Future Research................................................................................. 126
7.5. Limitations ........................................................................................ 127
Appendices ................................................................................................................ 129
Appendix 1. Derivation of Full (R, T) Policy .......................................... 129
Appendix 2. Comparing Models: Full (R, T) and Truck (R, T) Policies 131
Appendix 3. Visual Basic Module in Excel 2003 .................................... 133
v
Appendix 4. Grocery Item Demand Characteristics ................................ 158
Appendix 5. Supply Chain Actions Source Publications......................... 162
Appendix 6. Supply Chain Actions.......................................................... 163
Appendix 7. Market-Based Actions ......................................................... 164
References ................................................................................................................. 166
vi
List of Tables
Table 1. Joint Replenishment Models in the Literature ............................................... 9
Table 2. Notation........................................................................................................ 16
Table 3. Transportation Rate Schedule ...................................................................... 20
Table 4. Numerical Example Parameters................................................................... 25
Table 5. Inventory Model Comparison for Numerical Example ............................... 26
Table 6. Numerical Example Problem Set ................................................................. 29
Table 7. Model Comparison with Varying Cost Parameters ..................................... 29
Table 8. Problem Factor Levels ................................................................................. 34
Table 9. Item Demand Characteristics ....................................................................... 34
Table 10. Test Problem Results – Sub-Sample.......................................................... 35
Table 11. Group Membership – Percent Cost Increase Over Full Model.................. 40
Table 12. Discriminant Analysis Significance Tests ................................................. 49
Table 13. Analysis A Classification Matrix – Cut-off = 0.1%................................... 50
Table 14. Analysis B Classification Matrix – Cut-off = 0.5%................................... 51
Table 15. Analysis C Classification Matrix – Cut-off = 1.0%................................... 52
Table 16. Analysis A Discriminant Loadings ............................................................ 53
Table 17. Analysis A Descriptive Statistics............................................................... 54
Table 18. Simulation Output – Inventory Costs......................................................... 58
Table 19. BCRC Articles by Year.............................................................................. 78
Table 20. BCRC Categories....................................................................................... 81
Table 21. Market-Based Actions in the Literature..................................................... 82
Table 22. Number of Grocery Retailers and Average Market Share by Year ........... 90
Table 23. Descriptive Statistics.................................................................................. 92
vii
Table 24. Pearson Correlation Coefficients ............................................................... 92
Table 25. Aggregate Action Categories ................................................................... 101
Table 26. Clustering Variables and Descriptive Statistics ....................................... 102
Table 27. Action Categories as a Percent of Total Firm Actions............................. 103
Table 28. Regression Models for Growth as Dependent Variable........................... 106
Table 29. Generalized Least Squares ....................................................................... 108
Table 30. Analysis A&B 3-Group Solution – Characteristics and Performance..... 115
Table 31. Analysis C – Group Action Profile .......................................................... 121
Table 32. Analysis C – Group Attributes and Performance Summary.................... 122
Table 33. Summary of Results ................................................................................. 124
viii
List of Figures
Figure 1. Shipment Rates with Phantom Freight ....................................................... 20
Figure 2. Average Item Weight vs Total Cost Difference by Holding Fraction........ 37
Figure 3. Unit Rate vs Total Cost Difference by Holding Fraction........................... 37
Figure 4. Simulation Flowchart.................................................................................. 46
Figure 5. Analysis A: 3-Group Solution – Cluster Variate = MB and SC Actions 112
Figure 6. Analysis B: 3-Group Solution – Actions Profile ..................................... 113
Figure 7. Analysis B: 3-Group Solution – Cluster Variate = 10 Action Categories114
Figure 8. Analysis A: 3-Group Solution – Actions Profile..................................... 114
Figure 9. Analysis B: 4-Group Solution – Cluster Variate = 10 Action Categories116
Figure 10. Analysis B: 4-Group Solution – Actions Profile ................................... 117
Figure 11. Analysis C: 3-Group Solution – Cluster Variate = MB, SC, and Org
Change Actions ...................................................................................... 118
Figure 12. Analysis C: 4-Group Solution – Cluster Variate = MB, SC, and Org
Change Actions ...................................................................................... 119
Figure 13. Analysis C: 5-Group Solution – Cluster Variate = MB, SC, and Org
Change Actions ...................................................................................... 120
Figure 14. Analysis C: Supply Chain Group .......................................................... 123
Figure 15. Analysis C: Market-based Group .......................................................... 123
Figure 16. Analysis C: Organizational Change Group ........................................... 124

1
Chapter 1. Introduction
The retail grocery industry is the second largest retail category in the U.S.
(U.S. Census Bureau, 2005) with annual sales of $635 billion in 2004 (McTaggart
and Heller, 2005). Yet, despite relatively stable sales growth (Agnese, 2005), intense
competition and historically narrow profit margins (Frankel et al., 2002) describe an
industry in continual flux with many firms examining the viability of their long-term
strategic objectives (The Progressive Grocer, 2005). According to Kurt Salmon
Associates, a leading industry consultant, emphasis in three fundamental areas –
continued sales growth, differentiation strategies, and control of supply chain costs –
will distinguish the leaders from the laggards over the next decade (Mathews, 2005).
This research examined the supply chain management practices in the retail
grocery industry from two different perspectives. First, this research targeted the
tactical-level inventory control decisions of the retail grocer seeking to improve the
replenishment process and reduce total inventory costs. This effort examined one
way firms can trim costs via inventory control by modeling the joint replenishment of
multiple stock-keeping units at the store-level. Second, this research examined the
strategic implications of supply chain activities that contribute to and enable sustained
firm performance. Emphasis in only one area of the supply chain, such as inventory
control, does not ensure success. Rather, firms develop multiple supply chain
solutions, tailored for different products, different customers, and different channels.
Therefore, this second research agenda examined the proposition that multiple supply
chain solutions contribute to the firm’s financial performance and that alignment of
2
supply chain strategies with the overall business strategy is a key factor in sustainable
financial performance.
This chapter continues with an overview of the retail grocery industry and the
competitive landscape. The supply chain management practices within the industry
are also discussed highlighting their importance in cost control, customer service, and
financial performance. In chapter 2, the joint replenishment process is introduced and
the joint replenishment models are developed. Chapter 3 introduces the methodology
used to test the inventory models with the results presented in chapter 4. The broader
implications of supply chain activities on firm performance are introduced in chapter
5 using a competitive dynamics framework. In this chapter, the hypotheses are
developed relating market-based and supply chain actions to firm performance.
Chapter 6 outlines the methodology using structured content analysis with the results
discussed in chapter 7.
1.1. Overview of the Retail Grocery Industry
The retail grocery industry is dominated by the supermarket store format
accounting for 72 percent, or $457 billion, of total annual sales in 2004. The
remaining market is captured by wholesale clubs ($32.6 billion), convenience stores
($127.2 billion), and small grocery stores ($17.5 billion) (McTaggart and Heller,
2005). In 2004, there were approximately 34,200 supermarkets in the United States,
operated by chain and independent retailers. The majority of these supermarkets
were categorized as traditional supermarkets. Approximately six percent were
categorized as supercenter store formats (e.g., Wal-Mart, Target, and K-Mart), selling
3
grocery items along with general merchandise (Currie, 2005; McTaggart and Heller,
2005).
The supermarket store format is the focus of most industry analysis and
academic research due to its dominance in the marketplace and the availability of
detailed data for both public and private firms, as collected by trade associations and
trade publications.
1.2. Competition in the Retail Grocery Industry
Although dominated by a few large national companies, the retail grocery
industry is fiercely competitive (Whiteoak, 1999) and remains fragmented (Agnese,
2005), where supermarkets compete at the local level for the consumer’s food budget.
The competitive pressure is felt on two fronts: price competition from the
proliferation of extreme-value store formats and strong growth by niche marketeers in
areas such as high-end specialty stores, organic, or ethnic foods (Agnese, 2005).
Pressure on the low-cost front has been growing over the past decade with the
expansion of the supercenter and warehouse club formats (Kinsey and Senauer,
1996). Between 1995 and 2002, the traditional grocery channel lost approximately 13
percent of grocery sales, most of which were transferred to supercenters. Indeed, the
traditional grocery channel, which has historically penetrated 100 percent of U.S.
households, lost 1 percent of shoppers in 2004 to other grocery channels (Currie,
2005). Despite these competitive pressures for the individual consumer dollar,
concentration at the national level has increased. Between 1998 and 2004, the market
share of the top five firms grew 18 percent (30.3% to 48.3%) (McTaggart and Heller,
2005).
4
The evolution of alternative food channels, coupled with changing consumer
preferences, has prompted many innovations in the industry aimed at differentiation
and cost reduction. From a business strategy perspective, innovations include home
meal replacements, expanded deli and bakery sections, on-line shopping, home
delivery, pharmacies, expanded private label lines, redefined store layouts, brand
repositioning, and capacity expansion (Agnese, 2005; Currie, 2005; McTaggart and
Heller, 2005; The Progressive Grocer, 2003). To complement innovative business
strategies, firms within the industry are also focused on controlling supply chain
costs, improving efficiency, and improving customer service (Butner, 2005). Indeed,
supply chain management is an area that has received significant attention within the
food industry with extensive sponsorship and analysis by industry trade
organizations.
Supply chain efficiency is important at the store-level, where replenishment
process improvements and customer service are immediately realized, and at the firm-
level, where system-wide improvements are designed to meet strategic objectives. It
is on these two levels where this research is anchored. The next section provides an
overview of supply chain management initiatives within the industry, highlighting
relevant research and trends.
1.3. Supply Chain Management in the Retail Grocery Industry
Efficient Consumer Response (ECR) was launched in 1992 by representatives
of the food manufacturing and retailing sectors as a means to eliminate waste in the
supply chain. ECR committees are sponsored by trade organizations, such as the
Grocery Manufacturers Association (www.gmabrands.com) and Food Marketing
5
Institute (www.fmi.org), to provide analysis and recommendations on supply chain
strategies to improve customer value and reduce costs. ECR addresses the “total
supply chain – suppliers, manufacturers, wholesalers and retailers, working closer
together to fulfill the changing demands of the grocery consumer better, faster, and at
less cost” (Fernie, 1999). ECR emphasizes four key areas—product assortment,
product promotion, new product development, and product replenishment—which are
supported by enabling technologies (Copacino, 1997; Fernie, 1999). Many industry
initiatives come together under ECR in order to improve material and information
flow: category management, electronic data interchange (EDI), radio frequency
identification (RFID), point-of-sale ordering, direct store delivery, cross-docking,
continuous replenishment, collaborative forecasting, and activity-based costing
(Whiteoak, 1999).
Despite the inferred benefits of ECR, evidence in the grocery industry points
to a slow adoption due, in part, to the complexity of the supply chain, inexperience
with new initiatives, and an uncertainty of the true costs. In a survey of Australian
food retailers and manufacturers, Kurnia and Johnston (2003) found that a lack of
understanding of ECR and a shortage of the requisite skills were the fundamental
reasons for firms not adopting ECR initiatives. They also found that pressure from a
dominant trading partner often drove ECR adoption. While similar barriers to ECR
adoption may exist in the US market, there appears to be wider acceptance among US
retailers. In the Progressive Grocers 70
th
Annual Report of the Grocery Industry
(2003), nearly half of the top 25 programs retail grocers planned to initiate or expand
during 2004 were supply chain related involving reductions in inventory, expanded
6
use of electronic interchange data, collaborative forecasting, continuous
replenishment programs, stronger relationships with manufacturers, and increased
investment in information technology. In the Grocery Manufacturers Association
2005 Logistics Survey, driving down logistics costs remained a high priority in
managing firm financial objectives (Butner, 2005).
The topic of supply chain management in a highly competitive environment is
relevant on several fronts. First, supply chain management centers not on one well-
developed plan within a single firm, but rather emphasizes efficiency at every level
within the firm and between firms. Even so, efficiency at the lowest level is still
essential. Therefore, this research develops an inventory model to improve the
replenishment process at the retail store level. Second, “the implementation of SCM
[supply chain management] enhances customer value and satisfaction, which in turn
leads to enhanced competitive advantage for the supply chain, as well as each
member firm” (Mentzer et al., 2001a). Therefore, adding to the body of empirical
evidence, this research seeks to examine how supply chain activities can be an
essential part of the overall business strategy in creating disequilibrium in the market
place.
7
Chapter 2. Joint Replenishment with Transportation Costs
2.1. Introduction
With the continuous advances in information systems, the exchange of
information along the supply chain has enabled more efficient solutions in inventory
management. For example, electronic data interchange (EDI) and the availability of
point-of-sale data facilitates more efficient centralized inventory solutions and
automated replenishment programs (Ricks, 1997). This is particularly true in the
retail grocery industry with an increased use of efficient consumer response (ECR)
programs (Agnese, 2005; Kurnia and Johnston, 2003). However, even with the rapid
growth of technology in the grocery industry, only 53 percent of grocery retailers use
automatic replenishment (Bearing Point, 2003). Furthermore, many sophisticated
inventory control programs require investment in information systems and
infrastructure, an investment in which many small independent grocery retailers lag
behind their large grocery chain counterparts. In a survey conducted by The
Progressive Grocer, the average independent grocer was just beginning to invest in
point-of-sale technology and often relied on their wholesaler for technology solutions
(Tarnowski, 2005).
Even with a trend toward automated replenishment, the ordering process
remains an essential element in maintaining customer service levels and controlling
inventory costs. In a study of the root causes for out-of-stock items in the retail food
industry, Corsten and Gruen (2003) concluded that for U.S. firms poor ordering
practices at the store level accounted for 51 percent of the stockouts. Poor ordering
practices can be the result of ordering too few items, ordering too late, or ordering
8
based on a faulty forecast. This study examines the first two items, order quantity
and order interval, in a single-retailer, single-supplier setting. Specifically, this study
compared three multi-item periodic review inventory policies. This type of joint
replenishment problem has been studied, but with limited attention given to
transportation costs. Cetinkaya and Lee (2000) argued that substantial savings can be
realized when transportation decisions are coupled with replenishment decisions.
With rising transportation costs, the impact of transportation on optimal inventory
modeling should not be ignored. The joint replenishment models developed in this
research focused on near-optimal solutions for the retailer with limited technology to
connect real-time consumer demand with back-end inventory systems, while
considering transportation costs explicitly in the decision calculus.
The next section reviews the extant literature on joint replenishment policies.
In section 2.3 the textbook approach is presented and a fully specified model is
developed taking into consideration the impact of transportation costs on inventory
replenishment decisions. A numerical example illustrates the differences between
these two models and a heuristic is proposed based on the performance of the fully
specified model. Chapter 3 develops the methodology used to test the impact of
model parameters on inventory policy selection. The experimental design for a
simulation study is also presented to test the normality assumption of demand. The
results and managerial implications are presented in chapter 4.
2.2. Literature Review of Joint Replenishment Inventory Policies
Joint replenishment policies (JRPs) are designed to coordinate the ordering of
multiple items in such a way as to minimize the number of orders placed, thereby
9
reducing inventory costs. Most JRPs fall into the class of the periodic (R, T) policy,
although variations for continuous review have been proposed. In the (R, T) policy,
inventory levels for a group of items are reviewed every T units of time and a
sufficient quantity is ordered to raise each item i up to the base stock level,
i
R . Rao
(2003) proved the convexity of the (R, T) cost function which permits optimal
solutions for the parameters R and T. While optimal solutions are feasible, they
require complicated searches. Therefore, near-optimal heuristics are often proposed.
The joint replenishment models reviewed in this section are listed in table 1.

Table 1. Joint Replenishment Models in the Literature
JRP Description Limitations Author (s)
Can-Order
Policy (s, c, S)

• Continuous Review
• Reorder point
• Can-order point
• Order-up-to level
• May not synchronize
ordering of heterogeneous
items
• Parameters difficult to find
Federgruen, Groenevelt,
& Tijms (1984)

Periodic Review
(R, T)
• Fixed order interval
• Synchronizes ordering
• Assumes independence
between R and T
Atkins & Iyogun (1988)

Modified
Periodic Review
(R, T)
• Order interval varies
by item

• Assumes independence
between R and T
Atkins & Iyogun (1988)

Continuous
Review
QS
• Joint reorder point,
order-up-to level
• May not trigger order when
only a few items are short
Pantumsinchai (1992)

Periodic (s, S) • Periodic Review
• Reorder point, order-
up-to level
• Does not synchronize
transportation with
replenishment
Viswanathan (1997)

Continuous
Q(s, S)
• Joint reorder point,
item reorder point,
order-up-to level
• Does not synchronize
transportation with
replenishment
Nielsen & Larsen (2005)

One of the earliest joint replenishment policies proposed was the continuous
review ( ) , ,
i i i
s c S policy, also known as the can-order policy. In this control policy,
an order is triggered when item i in a family of items falls below its reorder point,
i
s .
10
In addition, any other item j in the family at or below its can-order level,
j
c , is also
included in the order. All items k are ordered up to their base stock level,
k
S .
Federgruen, Groenevelt, and Tijms (1984) developed a heuristic for the can-order
policy under Poisson demand and constant lead times. Across a wide range of
inventory parameters, they demonstrated that a suboptimal can-order policy
outperforms individually controlled order-point, order-up-to (s, S) policies. A
limitation with the ( ) , ,
i i i
s c S can-order policy is its complexity, such that optimal
parameters may be difficult to find (Nielsen and Larsen, 2005). Furthermore, when a
group of items is relatively heterogeneous in terms of demand patterns or cost
structure, the can-order policy may trigger an order when only one item falls below
its reorder point and no other items meet the can-order rule. Thus, the policy may not
necessarily synchronize ordering across multiple items (Cachon, 2001).
Atkins and Iyogun (1988) proposed two periodic variations of the (R, T)
policy as alternatives to the can-order policy. The first policy was a periodic (P)
heuristic and set the review period to the same length for all items in the family. The
second policy was a modified periodic (MP) heuristic and took into account item-
specific fixed cost differences such that the review period for each item was set to
some integer multiple of the base period. Atkins and Iyogun (1988) demonstrated
that the periodic review policies resulted in lower total inventory costs when
compared with the can-order or individual (s, S) policies. Further, the MP policy
performed slightly better than the P policy for medium range order costs, while the
common order interval, P policy, resulted in lower total costs for both high and low
order costs. In addition to total cost considerations, the periodic review policies are
11
easier to understand and easier to implement than more complex ( ) , ,
i i i
s c S policies
(Atkins and Iyogun, 1988).
Another approach to the joint replenishment problem is the QS policy, which
sets a joint reorder point for a family of items. The QS policy is a continuous review
control policy, such that when the combined inventory position for all items drops to
a predetermined group reorder point, Q, each item, i , is raised to its respective base
stock level,
i
S . Comparing the QS, can-order, and periodic (P/MP) policies,
Pantumsinchai (1992) found that no one policy was consistently superior. For
example, the can-order policy tended to order more frequently and therefore
performed well when order costs were low. On the other hand, the QS and MP
policies tended to order less frequently and thus performed well when order costs
were high. One disadvantage of the QS policy is the potential for one item in the
group to run short, even when the group reorder point has not been reached, implying
a homogeneous family of items might be more desirable.
Building on the robustness of the periodic control policies, Viswanathan
(1997) developed a periodic (s, S) policy, denoted P(s, S), that takes into
consideration the inventory position of each item at the time of the review. Similar to
the P policy developed by Atkins and Iyogun (1988), the review period is fixed, but
flexibility is added by including in the order only those j items at or below their
order points,
j
s . The result of the P(s, S) policy is a slight reduction in the total
inventory cost over the MP and QS policies.
Finally, a continuous review Q(s, S) policy was proposed by Nielsen and
Larsen (2005). Similar to the QS policy, an order is triggered when the total
12
consumption since the last order equals Q. However, rather than a single order-up-to
rule, the Q(s, S) policy includes an item-level reorder point,
i
s . Under Poisson
demand and constant lead times, they developed a dual search algorithm to find Q
and the (s, S) parameters that minimize total costs. They demonstrated that the
variable nature of the review period in the Q(s, S) policy adds flexibility and reduces
total inventory costs in all cases when compared to the P(s, S) policy. Further, the
Q(s, S) policy performed better than or equal to the QS policy.
In general, the continuous review joint replenishment policies perform better
than the periodic review policies, as expected. Continuous review policies often
result in near-optimal solutions and lower total costs. However, they also require
constant monitoring of the inventory status, often with each transaction, and
necessitate an automated inventory system. This may not be ideal for many small
independent grocers, who may not connect point-of-sale scanner data with inventory
ordering systems. In a periodic review policy, the inventory status is determined at
fixed intervals, requiring less frequent oversight and often fewer orders. The trade-
off is the potential for larger inventories to protect against stockout during the fixed
review period and replenishment lead time. However, larger inventories do not
necessarily imply higher costs. Considerable cost savings may result when inventory
review is coordinated across multiple items (Federgruen et al., 1984) by reducing the
labor required to monitor inventory levels and economizing on order costs.
Furthermore, since periodic review policies tend to order less frequently than
continuous review policies, transportation can be coordinated to improve utilization.
13
Cachon (2001) addressed transportation utilization in a joint replenishment
problem where the retailer balanced inventory costs, transportation constraints, and
shelf space constraints. He compared three policies with stochastic demand and fixed
lead times. The first model was a variation on Pantumsinchai’s (1992) QS policy,
where the joint reorder point was determined exogenously as a fixed fraction of the
truck capacity. The second model was a full service (R, T) model, where every T
units of time, orders were shipped up to their base stock level,
i
R , which was set equal
to the shelf space constraint for the item. Finally, he considered a minimum quantity
periodic review policy. In the minimum quantity periodic review policy, every T
units of time, the inventory status was determined and orders were shipped such that
the trucks had at least a minimum shipping quantity. While the continuous review
policy, in general, resulted in lower total inventory costs, the periodic review policies
performed nearly as well, particularly when the review period, T, was less than the
average time for total demand to equal truck capacity.
This study develops a set of models for the multi-item problem similar to
those proposed by Cachon (2001). However, the models developed here focus
specifically on the differential in transportation shipping rates in determination of the
order interval. Generally, inventory models seek to minimize costs by balancing the
cost of holding inventory with the cost of ordering inventory. Transportation rates are
either neglected or treated as constant, which can significantly distort the true cost of
inventory. The next section develops the models for this study, presents a numerical
example, and then recommends a simple heuristic based on the results of the example
that is both practical and intuitive.
14
2.3. Joint Replenishment Inventory Model Development
In this study, a fully specified inventory control policy was developed for the
joint replenishment of a family of items in a single-supplier, single-retailer setting.
The fully specified model was compared with a textbook baseline (R, T) model
resulting in the recommendation of a simple near-optimal heuristic. Most notably, the
fully specified model included the cost of transportation as a key cost parameter.
2.3.1. Model Assumptions and Notation
1) The supplier has sufficient stock to satisfy all retailer orders.
2) Demand is
( )
,
i i
X X
N µ ? ? , independent and identically distributed, and
uncorrelated across items.
3) Unsatisfied demand is backordered.
1

4) The lead time, L , is a random variable ( ) ,
L L
N µ ? ?
5) Demand and lead times are independent of each other.
2

6) Sufficient capacity is assumed at the retailer location.
7) Holding and penalty costs are linear and all items incur the same order costs.
8) Except for the baseline model, the base stock level,
i
R , and order interval, T, are
dependent.
3

9) Freight terms are FOB origin and the retailer is responsible for freight costs.


1
In a retailer setting lost sales may be more realistic and can be examined in future research. The
fundamental difference between the backorder case and the lost sales case is the level of safety stock
held and hence holding costs. However, the use of backordering over lost sales is not expected to
significantly impact the analysis (Tersine, 1994).

2
Independence between demand and lead time reasonably approximates reality (Silver and Peterson,
1979).

3
Fixed order size models often assume independence between the reorder point and the order quantity.
However, in an order interval model, demand uncertainty occurs not only during the replenishment
lead time, but also during the order interval. Therefore independence between the base stock level
and order interval is not a reasonable assumption (Tersine, 1994).
15

The JRP models developed in this study are variations on the standard
economic order interval, or periodic (R, T) policy. The order interval, T, is calculated
so as to minimize the expected inventory costs (transportation, ordering, holding, and
shortage) during the lead time, L, and the review interval, T. In a periodic review
policy, if an order is placed now at
0
t , the next order cannot be placed until
0
t T +
and will not be available until
0
t T L + + . Therefore, the base stock level,
i
R , protects
against demand uncertainty during the order interval, T, and replenishment lead time,
L. The joint replenishment inventory problem includes two types of order costs
(Federgruen et al., 1984; Pantumsinchai, 1992). A major order cost is incurred
anytime a review takes place (Viswanathan, 1997) and is associated with order
placement. The major order cost also includes the cost to assess and update the
inventory status. A minor order cost, or line-item cost (Atkins and Iyogun, 1988), is
associated with each item included in the order to cover the cost of picking, packing,
or other special handling required to process the item for shipment. In addition to
being an effective control policy when continuous review of inventory is not possible,
a periodic review policy allows for control over truck utilization, a possible source of
cost reduction. Truck utilization can be improved by adjusting the order interval to
coincide with a fixed delivery schedule, as studied by Cetinkaya and Lee (2000), or to
maximize truck capacity, as studied by Cachon (2001) and in this research.
The first model presented is the baseline (R, T) model with which to compare
the other models. The second model is a fully specified (R, T) model which includes
all relevant inventory costs. Finally, the third model is a truckload (R, T) heuristic
16
which is based solely on truck capacity. The notation used throughout this paper is
listed in table 2.
Table 2. Notation
i
D
Annual demand for item i (units)
( )
,
i i
X X
N µ ? ?


i
X Average daily demand for item i (units)
i
P Purchase cost of item i ($/unit)
C Major order cost ($/order)
n Number of joint items
c Minor order cost associated with each individual item, line-item cost
i i
H PF = Annual holding cost for item i ($/unit/year)
F
Holding fraction, percent of unit cost
i
K Annual shortage cost per unit for item i ($/unit)
i
R Base-stock level for item i (units)
i
S Safety stock for item i (units)
T
Order interval (years)
t
Q Capacity of truck (units)
k
Q

Shipping quantity (units)
L
Lead time (days)
( ) ,
L L
N µ ? ?

( )
ˆ
i T L
X
+
Expected demand during order interval and replenishment lead time for item i (units)
( ) i T L
?
+

Standard deviation of demand during order interval and lead time for item i (units)
i
Z Standard normal deviate for item i
( )
i i
P X R > Probability of a stockout for item i
| |
i i
E X R > Expected stockout quantity for item i
k
G Unit shipping cost ($/unit) associated with shipping quantity,
k
Q
0
G Truckload unit shipping cost ($/unit)
1
G Less-than-truckload unit shipping cost ($/unit)
2.3.2. Base (R, T) Policy
The baseline (R, T) inventory policy (referred to as the Base model in
remainder of the paper) is the textbook multi-item economic order interval inventory
model. In this model, the order interval,
Base
T , is selected to minimize inventory costs
with respect to order and holding costs alone and does not consider the cost
17
differential in truckload (TL) and less-than-truckload (LTL) transportation rates. In
the Base model it is assumed that the base stock level,
i
R , and the order interval,
Base
T ,
are independent, which simplifies the calculation of
Base
T . The total relevant cost
function (TRC) is given in equation (1) and includes the annual order cost and
holding cost for cycle stock. For simplicity, the summation limits were dropped.
Summation occurs over all i items unless otherwise noted.
TRC Annual Order Costs Annual Holding Costs = +

( )
2
i i
C nc TF
TRC T PD
T
+
= +
?
(1)

Taking the partial derivative of equation (1) with respect to T and setting this equal to
zero, the order interval,
Base
T , is given in equation (2).
( ) 2
Base
i i
C nc
T
F PD
+
=
?
(2)

The expected cost of safety stock equals the cost of holding safety stock plus
the cost of shortages, given by ( )
| | i i i
K E X R
i i i T
TC S FPS
>
= + , where
( ) i i i T L
S Z ?
+
= . This
leads to the total cost function for the baseline model in equation (3), where the
transportation rate per unit,
k
G , is the rate in the transportation freight schedule
associated with the average shipping quantity
k Base i
Q T D =
?
.
( )
| |
2
i i i
Base
Base i i k i i i i i
Base Base
K E X R
C nc T F
TC T PD G D PD F PS
T T
>
+
= + + + + +
?
? ? ? ?
(3)

The advantage of the Base model is that it is easy to understand and
implement. The order interval can be found using only a calculator or simple
18
spreadsheet and, therefore, can be easily adjusted as model parameters change. A
limitation with this model is that it does not attempt to optimize the order interval
with respect to the cost of transportation. In general, less-than-truckload shipping
rates are higher than full truckload rates, sometimes with a substantial difference in
price. In the 2005 Grocery Manufacturers Association Logistics Survey,
transportation accounted for 62 percent of total logistics costs for those food
manufacturers surveyed. Further, transportation costs per mile increased 23 percent
between 2001 and 2004 due to high fuel prices and driver/capacity shortages. The
rise in costs have resulted in a shift in modal choice toward higher volume/truckload
shipments (Butner, 2005). To consider the impact of transportation costs on the order
interval, a fully specified joint replenishment model was developed in the next
section.
2.3.3. Full (R, T) Policy
The fully specified model (also referred to as the Full model) considers the
trade off among all costs (transportation, holding, penalty, and order) in determining
the order interval. The Full model was developed by making three fundamental
changes to the Base (R, T) policy: 1) transportation costs were included as a major
cost component, 2) holding costs were adjusted to include the unit cost of
transportation, and 3) the assumption of independence between the order interval and
base stock levels was relaxed.
A fundamental characteristic of the Full (R, T) model is the inclusion of a
non-linear transportation function. The transportation function used in the Full model
is similar to that used in the all-units freight discount problem; such that a single rate
19
is applied to the entire shipment provided the appropriate rate breakpoint is attained.
However, the transportation function,
k
G , is defined to account for the indifference
points in the rate schedule which leads to the practice of over-declared shipments.
This is similar to the transportation function used by Russell and Krajewski (1991) in
a lot sizing model for a single inventory item. They noted that phantom freight, or an
over-declared shipment, occurs when the “actual shipping weight falls within a range
that lies between the rate breakpoint and an indifference point which is a function of
the particular freight rate schedule.” This leads to a non-linear relationship between
the shipping quantity and transportation costs and can be represented by two
transportation functions; one that is applied for shipments between a rate break and
the indifference point and a second function applied for shipments between the
indifference point and the next higher rate break. Given the base truckload (TL) rate
per unit,
0
G , and the less-than-truckload (LTL) rate per unit,
1
G , the transportation
function,
k
G , can be defined by equation (4), where
t
Q equals the truck capacity in
units and
i
Q T D =
?
is the shipping quantity associated with order interval T.
( )
( )( )
0 2
1
0 1 2
2, 4, 6,...
3, 5, 7,...
t
t
Q
k
Q
k
Q
k
Q
G k
G
G G k
?
¦
=
¦
=
´
? =
¦
¹
(4)

Using the transportation function in equation (4) a transportation rate schedule
can be constructed as shown in table 3. In this example, and truck capacity equals
50,000 pounds and all items weigh 50 pounds. Therefore, the unit capacity of the
truck,
t
Q , equals 1,000 units. The truckload (TL) rate is $6.00 per hundred weight
(cwt.), such that
0
G equals $3.00 per unit, while the less-than-truckload (LTL) rate is
20
$10.00 per cwt, where
1
G equals $5.00 per unit. This results in an indifference point
of 600 units below which the LTL rate applies.
Table 3. Transportation Rate Schedule
Order Quantity
(units)
Transportation Rate
($/unit)
1 – 600
1 1
G G =
601 – 1000
( )
2 0
t
Q
Q
G G =
1001 – 1600
( )
3 0 1 1
t
Q
Q
G G G G = ? +
1601 – 2000
( )
4 0
2
t
Q
Q
G G =
2001 – 2600
( )
5 0 1 1
2
t
Q
Q
G G G G = ? +
2601 – 3000
( )
6 0
3
t
Q
Q
G G =

The transportation rates and shipment costs are shown in figure 1 for
shipments between 1 and 3,000 units. It can be seen that the total cost of
transportation for a single shipment is the same whether 601 units or 1000 units are
shipped, in this example. Thus, for a shipping quantity of 800 units, the shipper
would over-declare the shipment as a full truckload and ship 200 units of phantom
freight, rather than pay the higher LTL shipping rate.
0.00
1.00
2.00
3.00
4.00
5.00
6.00
0
2
0
0
4
0
0
6
0
0
8
0
0
1
0
0
0
1
2
0
0
1
4
0
0
1
6
0
0
1
8
0
0
2
0
0
0
2
2
0
0
2
4
0
0
2
6
0
0
2
8
0
0
3
0
0
0
3
2
0
0
3
4
0
0
3
6
0
0
3
8
0
0
4
0
0
0
4
2
0
0
4
4
0
0
4
6
0
0
Order Quantity
U
n
i
t

S
h
i
p
m
e
n
t

R
a
t
e

(
$
/
u
n
i
t
)
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
$16,000
S
h
i
p
m
e
n
t

C
o
s
t

(
$
)
Unit Shipment Rate Total Transportation Cost

Figure 1. Shipment Rates with Phantom Freight

21
The total cost function for the full (R, T) policy is shown in equation (5) and
includes the incremental unit cost of transportation in the holding costs as
recommended by Buffa and Reynolds (1977) and Tersine (1994).
( )
( )



TC Annual Purchase Costs Annual Order Costs
Annual Holding Costs Cycle Stock
Annual Holding Cost SafetyStock Annual Shortage Cost
= +
+
+ +


( ) ( )
( )
| |
2

i k i i k i
i
i i i
i k i
C nc TF
TC T PD G D P G D
T
K E X R
F P G S
T
+
= + + + +
>
+ + +
? ? ?
?
?
(5)


The order interval,
Full
T , is found by taking the first derivative of the total cost
function in equation (5) with respect to T and setting this equal to zero. This leads to
the solution in equation (6) and the first approximation for
Full
T . The derivation of
order interval is provided in appendix 1.
| | ( )
( ) ( )
2
2
i i i
Full
i k i i k i
C nc K E X R
T
F P G D F P G X
+ + >
=
+ ? +
?
? ?
(6)
The solution to equation (6) is found using an iterative approach. However,
before this iterative approach is presented, it is important to understand how the
expected value and variance of demand during the lead time and order interval in a
periodic review model differs from that in a typical lot sizing model.
First, consider
( )
ˆ
i T L
X
+
, the expected value of demand during the order interval
and replenishment lead time in a periodic (R, T) policy. Recall that under a periodic
review policy, the base stock level,
i
R , must protect against demand uncertainty
22
during the order interval and the replenishment lead time. Because both demand and
lead time are stochastic, daily demand varies as does the length of the lead time.
Conditioning is used to find the expected value of demand during the replenishment
period and a variable lead time. For example, if one conditions on the lead time, L,
when the lead time is known (e.g., L l = ), then E X L l = (
¸ ¸
can be solved. By
definition,
| |
L
E X E E X L ( = (
¸ ¸ ¸ ¸
where the outer expectation is taken with respect to
the distribution of Y (Ross, 2002). It is further assumed that demand and lead time
are independent, such that the expected demand during the T + L can be derived as
shown in equation (7).
( ) ( )
| | | |
| | ( ) | |
| | | | | |
1 1
ˆ
T L T L
i T L i i T L i T L
i i
i
i
i i
X E X E X E X T L
E T L E X
E L T E X
E L E X TE X
+ +
+ + +
= =
( (
(
= = = +
( (
¸ ¸
¸ ¸ ¸ ¸
= +
= +
= +
? ?


( )
ˆ
i i i T L
X LX TX
+
= + (7)
Where
i
X is defined as the daily demand for item i , T (measured in days) is the
order interval and treated as a constant, and L is the variable lead time.
Similarly, the variance of demand during the order interval and lead time is
found by conditioning on the lead time, where the variance of the constant T is zero,
( ) 0 Var T = , as shown in equation (8).
23
( )
( )
( ) ( ) ( ) | | ( )
| | ( ) | | ( )
| | ( ) ( ) ( ) ( )
1
1 1
2
2 2
i
T L
i i T L
i
T L T L
T L i i
i i
T L i i
i i
X i
Var X Var X
E Var X T L Var E X T L
E T L Var X Var T L E X
E T L Var X E X Var T L
E L T X Var L Var T ?
+
+
=
+ +
+
= =
+
| |
=
|
\ ¹
( | | | | (
= + + +
| |
(
(
\ ¹ ¸ ¸ ¸ ¸ \ ¹
( = + + +
¸ ¸
= + + +
= + + +
?
? ?


( )
2 2 2 2 2
i i
X X i L i T L
L T X ? ? ? ?
+
= + + (8)
Once the variance of demand during T+L is determined, the safety stock for itemi
,
i
S
,
can be calculated if it assumed that
( )
ˆ
i T L
X
+
is normally distributed. Therefore,
( )
2 2 2 2
i i
i i i i L X X i T L
S Z Z L T X ? ? ? ?
+
= = + + , where
i
Z is the standard normal deviate.
The base stock level is then given by,
( )
ˆ
i i i T L
R X S
+
= + . Similarly, the expected
stockout quantity, | |
i i
E X R > , equals | |
( )
i i T L
E Z ?
+
, where | |
i
E Z is the expected
quantity in the tail of the cumulative distribution function of
i
Z .
It is now possible to find a first approximation of the order interval for the
Full model using an iterative approach for convergence in
i
R and T.
Iterative solution for
Full
T , equation (6):
1) Compute T when the expected stockout quantity, | |
i i
E X R > , equals zero.

2) Use T to compute the shipping quantity,
k i
Q T D =
?
and the appropriate
shipping unit rate,
k
G , given in equation (4).

3) Calculate the probability of a stockout, ( ) ( )
i i i k i
P X R TF P G K > = + , which
is the first derivative of the total cost function with respect to
i
R (see appendix
1 for the derivation of the probability of a stockout).

24
4) Compute the base stock level,
i
R , given by
( )
ˆ
i i i T L
R X S
+
= + .

5) Use ( )
i i
P X R > to find
i
Z , | |
i
E Z , and | |
i i
E X R > .

6) Recompute T using the new value for the expected stockout quantity,
| |
i i
E X R > , found in step 5.

7) Repeat steps 2 through 6 until convergence in
i
R and T occurs.

It should be noted that the expected stockout quantity, | |
i i
E X R > , is also a
function of T, since | | | |
( )
| |
2 2 2 2
i i
i i i i i L X X i T L
E X R E Z E Z L T X ? ? ? ?
+
> = = + + .
However, | |
i i
E X R > was treated as a constant in the derivation of the order interval
in equation (6). This was done because the inclusion of the order interval, T , under
the radical makes the total cost equation intractable. Therefore, the solution for
Full
T
given by equation (6) yields only a first approximation for the order interval. The
optimal order interval can be found using an incremental search in T for the lowest
total cost. This is a common approach in inventory modeling when the simplifying
assumptions are relaxed.
2.3.4. Comparing Models: A Numerical Example
The Base (R, T) policy is compared with the Full (R, T) policy using a
numerical example with the parameters listed in table 4. Consider a retailer managing
two items. The annual demand for item 1 is 24,000 units and costs $45 per unit. The
annual demand for item 2 is 22,000 units and costs $36 per unit. The remaining costs
and problem parameters are the same for each item. Using these parameters, the
order interval was calculated for the Base model.
25
Table 4. Numerical Example Parameters
Item 1 Item 2
i
D

Annual demand (units) 24000 22000
i
X
? SD daily demand (units) 20 15
i
P

Item cost 45 36
C Major order cost 100
n Number items 2
c Minor order cost 15
F Holding fraction 0.4
i
K

Shortage cost 5
L Lead Time (days) 5
L
? SD lead time (days) 1.5
TL Truck capacity (wt) 50000
t
Q

Truck capacity (units) 1000
0
G

TL rate ($/unit) 3
1
G

LTL Rate ($/cwt) 5
w Item weight 50

The first approximation for the order interval in the Full model was found
using equation (6) and a search for the lowest total cost was used to find the optimal
order interval as discussed in section 2.3.3. Table 5 compares the order intervals,
demand during T+L for both items, and the total cost of inventory for each model.
In this example, the Full (R, T) policy led to fewer orders per year, a larger
average shipping quantity,
k
Q , and a lower total annual cost of inventory when
compared to the Base (R, T) policy. Further, a 16 percent increase in the average
shipment size (857 units in Base model and 1000 units in the Full model) had a
relatively small impact on the traditional order, holding, and shortage costs (0.7%
cost reduction), yet produced a large decrease in annual transportation shipping costs
($161,026 for Base model and $138,000 for Full model, or 14 percent).

26
Table 5. Inventory Model Comparison for Numerical Example
Base Model Full Model
Avg demand during L+T,
( ) 1
ˆ
T L
X
+

779 854
Avg demand during L+T,
( ) 2
ˆ
T L
X
+

708 776
Safety Stock,
1
S
159 150
Safety Stock,
2
S
150 143
Base Stock Level,
1
R
937 1004
Base Stock Level,
2
R
858 919
Expected stockout quantity,
| |
1 1
E X R >
3.49 4.14
Expected stockout quantity, | |
2 2
E X R >
2.43 2.86
Shipment (Order) Quantity,
k
Q
857 1000

Order Interval, T (in years) 0.01863 0.02174
Order Interval, T (in days) 6.80 7.93
Number order cycles per year (1/T) 54 46

Annual Purchase cost $1,872,000.00 $1,872,000.00
Annual Shipping Cost 161,026.84 138,000.00
Annual Order Cost 6,976.53 5,980.00
Annual Holding Cost (Cycle Stock) 7,576.64 8,739.13
Annual Holding Cost (Safety Stock) 5,449.86 5,120.03
Annual Shortage Cost 1,589.47 1,612.56
Total Annual Inventory Costs $2,054,619.34 $2,031,451.73


This is because with each shipment in the Base model, the shipper over-
declared the shipment and sent phantom freight. This resulted in more frequent
shipments and a higher “effective” transportation per unit rate. Thus, there was a cost
disadvantage to sending phantom freight. On the other hand, the fully specified
model optimized the order interval such that each shipment filled a truck (1000 units),
taking advantage of the lowest transportation rate. This numerical example
demonstrates that transportation costs are a significant part of total inventory costs
and can result in much higher costs when excluded. While it appears that
27
transportation is the major determinant of the optimal order interval, several different
cost parameters were tested to determine if varying order, holding, and shortage costs
might yield an LTL shipment size in the Full (R, T) model. Interestingly, the fully
specified model optimized to a full truck, or integer multiple of a truck, for each
scenario tested.
This led to a simple heuristic based on anecdotal evidence used in practice—
that of higher volume shipments aimed at filling a truck with each order. Indeed, a
retailer might be attracted to the lower shipping rate and want to improve truck
utilization. A naïve approach sets the order interval as a function of truck capacity,
taking advantage of transportation economies of scale. This heuristic is developed in
the next section.
2.3.5. Truck (R, T) Heuristic
In this model the order interval,
Truck
T , is determined exogenously as a
function of truck capacity,
t
Q , as shown in equation (9). In doing so, it is expected
that, on average, the shipping quantity,
k
Q , will equal the truck capacity,
t
Q , and
therefore take advantage of the lowest truckload shipping rate,
0
G .
t
Truck
i
Q
T
D
=
?

(9)
The total annual cost of inventory is given in equation (10) and includes the
fully specified holding costs for cycle and safety stock. The Truck heuristic is a
special case of the Full (R, T) policy where no phantom freight is shipped (see
appendix 2 for a full discussion).
28
( ) ( )
( )
| |
0 0
0
2

i i i i
i
i i i
i i
C nc TF
TC T PD G D P G D
T
K E X R
F P G S
T
+
= + + + +
>
+ + +
? ? ?
?
?

(10)

The Truck heuristic is intuitively simple and economizes on the lowest
truckload shipping rates. Due to demand and lead time variability, a limiting factor
with the truckload model is that the order quantity at each review will not be exactly a
full truck load. Thus, when the order quantity,
k
Q , is less than a full truck load, the
retailer may simply ship the required amount at the corresponding shipping rate. Or,
he may chose to increase the order size of some items to fill a truck. The
disadvantage of the former option is a slightly higher shipping rate, while the risk in
the later is higher holding costs. When the order quantity is greater than a full truck
load, the retailer may, again, simply ship the required amount, paying the LTL rate
for all items over truck capacity. Rather than paying a higher shipping rate, he might
alternatively forgo ordering any quantity over
t
Q and replenish each item to an equal
fraction of the total requirement. With this allocation solution there is an increased
risk of stockout. The choice of these options depends on transportation costs versus
holding costs when
t
Q Q < and transportation costs versus shortage costs
when
t
Q Q > . As demonstrated, however, transportation costs dominate the inventory
model. Therefore, this heuristic aims to fill a truck with each order with the
expectation that actual demand does not vary significantly from the average.
The three periodic-review, multi-item inventory models were compared using
the varying cost parameters listed in table 6. The resulting order interval, average
order quantity, and total annual cost for each problem is listed in table 7.
29
Table 6. Numerical Example Problem Set

Purchase
Cost,
1
P

Purchase
Cost,
2
P

Major Order
Cost, C
Minor Order
Cost, c
Holding
Fraction, F
Shortage
Cost,
i
K

1
45 36 100 15 0.4 5
2
45 36 20 2 0.4 5
3
45 36 100 15 0.1 5
4
45 36 100 15 0.4 1
5
45 36 100 15 0.6 5
6
45 36 250 15 0.4 5
7
45 36 100 15 0.4 8
8
45 36 250 20 0.1 8
9
200 150 250 20 0.6 8
10
200 150 20 5 0.6 5

Table 7. Model Comparison with Varying Cost Parameters
Base (R, T) Full (R, T) Truck (R, T)
T(days)
k
Q

Total Cost T(days)
k
Q

Total Cost T(days)
k
Q

Total Cost
1 6.80 857 $2,054,619 7.93 1000 $2,031,452 7.93 1000 $2,031,452
2 2.92 368 $2,116,890 7.93 1000 $2,026,576 7.93 1000 $2,026,576
3 13.60 1714 $2,042,324 15.87 2000 $2,019,307 7.93 1000 $2,020,349
4 6.80 857 $2,051,542 7.93 1000 $2,028,288 7.93 1000 $2,028,288
5 5.55 700 $2,097,333 7.93 1000 $2,038,167 7.93 1000 $2,038,167
6 9.98 1258 $2,056,602 7.93 1000 $2,038,352 7.93 1000 $2,038,352
7 6.80 857 $2,055,338 7.93 1000 $2,032,179 7.93 1000 $2,032,179
8 20.32 2560 $2,043,028 23.80 3000 $2,022,972 7.93 1000 $2,027,859
9 3.99 503 $8,418,467 7.93 1000 $8,330,788 7.93 1000 $8,330,788
10 1.28 162 $8,389,082 7.93 1000 $8,312,564 7.93 1000 $8,312,564

The results in table 7 show that the textbook approach in the Base (R, T)
policy resulted in higher inventory costs, while the Full (R, T) policy produced the
lowest annual cost. It is also evident that the Truck heuristic performed well for this
numerical example in eight of the ten scenarios. Indeed, when the Full (R, T) policy
optimized to a single truck, the Full model and Truck heuristic were equal. The
performance of the Truck heuristic and Base model compared with the Full (R, T)
model is the focus of this research. The methodology and experimental design for the
proposed simulation study is detailed in the next chapter.
30
Chapter 3. Joint Replenishment Methodology and Experimental Design
This research had two main objectives. The first objective was to test the
sensitivity of the two competing models (Base model and Truck heuristic) to changes
in the model parameters when compared with the fully specified model. In particular,
the aim was to more fully understand when the competing models would perform as
well, or nearly as well, as the fully specified model, given a set of cost and demand
parameters. To investigate this first objective, a test problem was developed in which
the model parameters were varied. The three models (Base, Truck, and Full) were
then compared based on the total annual cost of inventory.
The second objective of this research was to test the sensitivity of the fully
specified model to non-normal demand. A fundamental assumption in the fully
specified model is that demand is normally distributed. However, actual demand
characteristics may, in fact, deviate from this normality assumption. To test this
second objective, actual demand data was collected from a local grocer for use in a
simulation study. This chapter describes the test problem and the data collection for
the simulation study.
3.1. Model Sensitivity and Model Selection
Theoretically, the fully specified model will determine an order interval for
the replenishment of multiple items resulting in the lowest total cost of inventory.
However, this model is cumbersome to use as demonstrated by the iterative solution
and final search in T described in section 2.3.3. For practical implementation,
inventory optimization software would be required, particularly when the number of
31
items in an order becomes large. Even when only a handful of items were
considered, determination of the optimal order interval required some programming
expertise within a spreadsheet tool. Therefore, it would be helpful to know when the
fully specified model is most appropriate, given a set of model parameters. Equally,
it would be helpful to know when the Truck heuristic or textbook approach yield
acceptable results.
3.2. Model Calculations
Microsoft Excel 2003 (Excel) was used with the support of Visual Basic to
quickly calculate the relevant variables in each model while enabling easy
manipulation of the model parameters. An Excel worksheet was used to provide the
input to the model. Input parameters included the model costs (e.g., major order cost,
minor order cost, holding fraction, and shortage cost), the item characteristics (e.g.,
annual demand, average daily demand, the standard deviation of daily demand, item
unit cost, and the average item weight), and the transportation parameters (e.g., TL
and LTL freight rates, and truck capacity). A Visual Basic program was written to
take the input parameters and calculate the order interval with resulting costs for each
model. The Visual Basic code is detailed in appendix 3.
It should be noted that the accuracy of the calculations is limited by the
precision imposed by the researcher and those inherent to Excel. First, the researcher
rounded the order quantity to integer values once the order interval was calculated
using equations (2), (6), or (9) for the Base, Full, or Truck models, respectively. This
was done because, as this problem has been defined, the items held in inventory are
discrete units. As such, the transportation weight breaks and subsequent unit breaks
32
were determined based on whole units. Rounding ensured the order quantity fell
within the defined transportation break points. The calculated order interval,
however, was not rounded to the nearest integer value. If the calculated order interval
was 3.74 days, for example, this value was carried through for all further calculations
of the order, holding, and shortage costs. While it might be expected that actual
orders would be placed every 4 days, in practice, for the purpose of model
comparison, the calculated order interval was not adjusted to reflect whole days. The
precision, with which the order interval was calculated, however, was set by the
researcher to five decimal places. This was done to speed the computations and to
ensure convergence during the iterative solution in the fully specified model. The
level of precision was originally set to a higher level, but convergence was
problematic in a few of the problems tested.
The level of precision for the calculation of the standard normal deviate,
i
Z ,
and the expected stockout quantity, | |
i i
E X R > , in the fully specified model was also
affected by the level of precision used by Excel to calculate the normal inverse
function. In Excel 2003, the version used for this study, refinements were made to
the computations of the standard normal distribution in the tail ends of the
distribution to ensure accuracy to 14 or 15 decimal places (Microsoft, 2006), more
than sufficient for this analysis. The normal inverse function was used to calculate
i
Z , given the probability of a stockout ( )
i i
P X R > , by returning the inverse of the
normal cumulative distribution function with a mean of 0 and standard deviation of 1
( ) ( ) ( )
: 1 , 0,1
i i i
Syntax Z NORMINV P X R = ? > . The expected stockout quantity
was found by multiplying the standard deviation of demand during the lead time and
33
order interval with the expected value of
i
Z , where | |
( )
| |
i i i i T L
E X R E Z ?
+
> = . Using
the standard normal loss integral, the expectation of
i
Z can be found by integrating
the probability density function of the standard normal function (Keaton, 1994),
resulting in | | ( ) ( ) ( )
1 E Z pdf Z Z cdf Z = ? ? . While there is no closed form solution
for the normal cumulative distribution function, the table look up function in Excel
2003 provides sufficient accuracy. The syntax used to calculate the expected
stockout quantity in Excel is given by
| |
( )
| |
( )
( ) ( ) ( ) { }
, 0,1, 0 1 , 0,1,1
i i i i i i i T L i T L
E X R E Z NORMDIST Z Z NORMDIST Z ? ?
+ +
> = = ? ?
.
3.3. Test Problem Description
The test problem was arbitrarily devised to consist of ten items with varying
model parameters: major order costs (3 levels), minor order costs (3 levels), holding
fraction (3 levels), shortage costs (3 levels), annual demand (3 levels), standard
deviation of daily demand (3 levels), less-than-truckload freight rate (3 levels), and
the average item weight (5 levels). Implementing a full factorial design, the total
annual cost of inventory for the Base, Truck, and Full model was calculated in 10,935
(3x3x3x3x3x3x3x5) different problems. The model parameters are defined in table 8.
The lead time parameters (mean and standard deviation), truck capacity, and
truckload freight rate were held constant in all problems examined.
34
Table 8. Problem Factor Levels
Factor Level 1 Level 2 Level 3 Level 4 Level 5
Major Order Cost ($/order) 20 300 600
Minor Order Cost ($/item) 1 5 8
Holding Fraction ($/unit/year) 0.2 0.4 0.6
Shortage Cost ($/unit) 10 25 50
Average Item Weight (lbs) 1.5 5 7 10 20
Annual Demand (units) x1 x2 x3
Standard Deviation of daily demand x1 x2 x3
Number of Items 10
Average Lead Time (days) 4
Standard Deviation of Lead Time (days) 0.5
Truck Capacity (lbs) 40,000
TL Freight Rate ($/cwt) 6.00
LTL Freight rate ($/cwt) 8.00 10.00 14.00

The demand characteristics for the ten items are given in table 9. In this problem, the
average daily demand was determined by dividing annual demand by 365 days.
Table 9. Item Demand Characteristics

Annual Demand

Average Daily Demand
Standard Deviation
of Daily Demand
Item

Purchase
Price
Level 1 Level 2 Level 3 Level 1 Level 2 Level 3 Level 1 Level 2 Level 3
1 $15.00 4500 9000 13500 12 25 37 2.0 4.0 6.0
2 $12.00 2685 5370 8055 7 15 22 1.0 2.0 3.0
3 $25.00 1000 2000 3000 3 5 8 1.0 2.0 3.0
4 $18.00 5630 11260 16890 15 31 46 2.5 5.0 7.5
5 $10.00 5200 10400 15600 14 28 43 3.0 6.0 9.0
6 $16.50 8900 17800 26700 24 49 73 5.0 10.0 15.0
7 $23.00 2500 5000 7500 7 14 21 1.0 2.0 3.0
8 $27.00 4265 8530 12795 12 23 35 3.0 6.0 9.0
9 $19.00 3100 6200 9300 8 17 25 1.0 2.0 3.0
10 $12.00 1835 3670 5505 5 10 15 0.5 1.0 1.5

The total annual cost of inventory was used as the basis for comparison
among the three models. For the purpose of meaningful comparison, the Base model
was adjusted to reflect true inventory costs. Specifically, the holding costs in the
Base model were adjusted to include the unit transportation rate,
k
G , as shown in
equation (11), in the same manner holding costs were calculated for the Truck
heuristic and Full model.
( ) ( ) ( )
| |
2
i i i Base
Base i i k i i k i i k i
Base Base
K E X R T F C nc
TC T PD G D P G D F P G S
T T
>
+
= + + + + + + +
?
? ? ? ?
(11)
35
In all 10,935 problems, the fully specified model resulted in the lowest total
cost. Therefore, a firm wishing to ensure the lowest total cost would benefit from
implementing the fully specified model. However, the Base model and Truck
heuristic performed as well, or nearly as well, in many of the problems tested. To
examine what levels of the model parameters resulted in adequate performance for
these two competing models (Base and Truck), the difference in total cost with the
Full model was calculated. A sub-sample of this cost comparison is presented in
table 10.
Table 10. Test Problem Results – Sub-Sample
S
a
m
p
l
e

P
r
o
b
l
e
m

M
a
j
o
r

O
r
d
e
r

M
i
n
o
r

O
r
d
e
r

H
o
l
d
i
n
g

F
r
a
c
t
i
o
n

S
h
o
r
t
a
g
e

u
n
i
t

c
o
s
t

A
v
e
r
a
g
e

I
t
e
m

W
t

T
L

u
n
i
t

R
a
t
e

L
T
L

u
n
i
t

R
a
t
e

F
u
l
l

O
r
d
e
r

Q
t
y

T
r
u
c
k

O
r
d
e
r

Q
t
y

B
a
s
e

O
r
d
e
r

Q
t
y

T
o
t
a
l

A
n
n
u
a
l

D
e
m
a
n
d

T
r
u
c
k

T
C

-

F
u
l
l

T
C

B
a
s
e

T
C

-

F
u
l
l

T
C

1 600 1 0.2 50 5 0.30 0.40 8000 8000 3756 39615 $0.00 $78.10
2 20 1 0.6 25 7 0.42 0.70 704 5714 680 79230 $231.43 $4.11
3 300 1 0.6 50 10 0.60 0.80 4000 4000 1546 39615 $0.00 $97.33
4 300 5 0.4 10 20 1.20 1.60 2000 2000 2012 39615 $0.00 $97.01
5 20 1 0.2 25 5 0.30 0.70 8000 8000 833 39615 $0.00 $4,861.45
6 20 1 0.2 50 7 0.42 0.70 5714 5714 833 39615 $0.00 $3,985.58
7 300 8 0.6 25 10 0.60 1.00 4000 4000 2421 79230 $0.00 $28,203.25
8 300 8 0.2 10 20 1.20 2.00 4000 2000 2965 39615 $163.53 $9,844.39
9 300 8 0.6 10 1.5 0.09 0.15 2476 26667 2421 79230 $107,113.43 $6.41
10 600 5 0.4 10 5 0.30 0.40 2739 8000 2742 39615 $7,899.57 $0.01
11 300 5 0.4 50 7 0.42 0.56 2002 5714 2012 39615 $2,745.35 $0.17
12 20 5 0.6 25 10 0.60 0.80 741 4000 735 39615 $5,849.30 $0.29
13 600 8 0.2 10 20 1.20 2.00 4000 2000 3966 39615 $3,134.66 $408.13
14 600 1 0.2 10 10 0.60 1.00 8000 4000 6506 118845 $2,120.41 $15,952.13
15 600 8 0.2 10 10 0.60 1.00 8000 4000 6869 118845 $3,160.30 $11,507.87
16 600 5 0.2 50 20 1.20 2.00 6000 2000 5484 79230 $10,001.88 $8,891.76
17 600 5 0.4 10 20 1.20 2.00 4000 2000 3877 79230 $5,770.48 $3,017.43

In sample problems 1-4 from table 10, the Truck heuristic and Base model
performed well and resulted in only marginal cost increases (ranging from 0.011 to 0
36
0.016 percent), over the total annual cost of the Full model. In sample problems 5-8,
the Truck heuristic was the preferred model. In this sub-sample, the average item
weight was larger making it easier to fill a truck, while lower holding costs allowed
for larger orders without a significant cost increase. In sample problems 9-13, the
Base model was the preferred choice, highlighting the impact of item weight on costs.
In fact, for all problems tested, the Base model dominated when the average item
weight was 1.5 pounds. Clearly, the more items required to fill a truck with each
order, the higher the cost to hold this inventory, particularly when demand was low.
Another indication in problems 9-13 that points to use of the Base model was the
higher order cost, particularly the minor (per-unit) order cost, and higher holding
costs compared to the first two sets of problems. Here, the classic approach to
balance order and holding costs alone resulted in near-optimal solutions. Finally, in
sample problems 14-17, the Full model resulted in the lowest total annual inventory
costs and was preferred over both the Truck heuristic and textbook Base model. An
interesting result for this sub-sample was that the optimal order intervals resulted in
order quantities of multiple truckloads, 2 or 3 trucks, in this example. Generally,
holding costs were low and annual demand was high to allow for such large orders.
A general recommendation of one model over another is difficult to make
simply by examining the results of the test problems individually. The interaction of
the model parameters is complex. Figure 2 and figure 3 show how the difference in
total costs varied in a non-linear manner. As the item weight increased, the difference
in costs between the Truck heuristic and Full model (Truck TC – Full TC) became
small, the magnitude of which varied depending on the holding fraction (see figure
37
2a). At the same time, however, the cost differential between TL and LTL shipping
rates significantly affected the total cost in an irregular way. On the other hand,
comparing the Base and Full models in figure 2b and figure 3b, the holding fraction
had very little impact except for very heavy items.
20.0 10.0 7.0 5.0 1.5
Average Item Weight
140000
120000
100000
80000
60000
40000
20000
0
T
r
u
c
k

T
C

-

F
u
l
l

T
C
.60 .40 .20
Holding Fraction

20.0 10.0 7.0 5.0 1.5
Average Item Weight
200000
150000
100000
50000
0
B
a
s
e
T
C

-

F
u
l
l
T
C
.60 .40 .20
Holding Fraction

(a) Truck Total Cost – Full Total Cost (b) Base Total Cost – Full Total Cost

Figure 2. Average Item Weight vs. Total Cost Difference by Holding Fraction

1.60 .80 .56 .40 .28 .20 .14 .12 .10 .06 .03
Unit Rate Difference
140000
120000
100000
80000
60000
40000
20000
0
T
r
u
c
k

T
C

-

F
u
l
l

T
C
.60 .40 .20
Holding Fraction

1.60 .80 .56 .40 .28 .20 .14 .12 .10 .06 .03
Unit Rate Difference
200000
150000
100000
50000
0
B
a
s
e

T
C

-

F
u
l
l

T
C
.60 .40 .20
Holding Fraction

(a) Truck Total Cost – Full Total Cost (b) Base Total Cost – Full Total Cost

Figure 3. Unit Rate vs. Total Cost Difference by Holding Fraction
38
While some general statements could be made regarding the relationship
between these model parameters and the total inventory cost, all model parameters
interact, non-linearly, complicating model recommendations. Further, the impact of
some parameters on total cost may be amplified depending on the level of another
parameter. Upon closer examination of the problem set, however, four distinct
categories emerged. The first category is depicted in sub-sample problems 9 through
13, where the Base model is recommended. In these problems Base TC – Full TC is
significantly less than Truck TC – Full TC. Alternatively, the second category is
shown by the sub-sample problems 5 through 8 in table 10. For these problems,
Truck TC – Full TC is significantly less than Base TC – Full TC, leading to a
recommendation in favor of the Truck heuristic. The third category favors the fully
specified model, when both the Base model and Truck heuristic result in a significant
increase in the total inventory cost over the Full model (see sub-sample problems 14
through 17). Sub-sample problems 1 through 4 demonstrate the forth category where
the use of any of the three models would result in optimal or near optimal solutions.
3.4. Discriminant Function Analysis
With these four categories appearing to distinguish the problem set,
discriminant function analysis was chosen as the appropriate statistical technique.
Discriminant function analysis (DFA) allows one to examine a set of independent
variables (in this study, the model parameters) and determine which variables help to
distinguish or predict membership in a priori defined groups. Thus, the intent of the
analysis was to identify which inventory policy was most appropriate given different
levels of the model parameters. Specifically, DFA builds a linear combination of the
39
model parameters and then determines the appropriate weight for these variables such
that the variance is maximized between the groups relative to the within-group
variance. The resulting orthogonal discriminant functions are then used to predict
group membership. Discriminant function analysis can be interpreted in much the
same manner as multivariate regression analysis. Indeed, a special case of
discriminant function analysis is logistic regression where the categorical dependent
variable is defined by only two groups (Hair et al., 1998). In this study, the predicted
group is associated with an inventory model recommendation.
Variable Selection. The difference in the total cost of inventory between the
Base and Full models, or the Truck heuristic and Full model, was useful in identifying
the groups. When the cost difference is zero, the choice to implement an inventory
model is simple – select the least complex model. However, when the cost difference
is greater than zero, a decision must be made regarding the degree to which one is
willing to accept the cost increase associated with the less complex model (Base or
Truck). Equally, when the cost difference exceeds some acceptable tolerance level,
the Full model would be the preferred choice. To clearly define these cut-points, the
percent increase in total cost was selected as the metric to define group membership.
This study examined three tolerance levels equal to 0.1, 0.5, and 1.0 percent increase
in total cost over the Full model. First, the percent increase in total cost was
calculated for the Base model and Truck heuristic as shown in equation (12), where
m denotes Base or Truck, depending on which model was being compared to the
fully specified model.
40

100

m Full
m
Full
Total Cost Total Cost
Percent Cost Increase
Total Cost
| | ?
= ×
|
\ ¹
(12)
Comparing the Base and Full models, the percent cost increase ranged from 0
to 8.5 percent in the problem set. Comparing the Truck heuristic and Full model, the
percent cost increase ranged from 0 to 19 percent. The percent cost increase, along
with the tolerance levels, defined four mutually exclusive and exhaustive groups.
These groups identified the inventory model most appropriate as measured by the
total annual cost of inventory. Thus, when the 0.1 percent tolerance level was used,
the model choice would be determined as shown in table 11. The groups were
similarly defined for the 0.5 and 1.0 percent tolerance levels. The categorical
dependent variable was defined as group number, 1 through 4, based on the grouping
metric.
Table 11. Group Membership – Percent Cost Increase Over Full Model
Grouping Metric Recommended Model Group Number
IF % 0.1
Base
Cost Increase ? AND
% 0.1
Truck
Cost Increase > , THEN
Base 1

IF % 0.1
Truck
Cost Increase ? AND
% 0.1
Base
Cost Increase > , THEN
Truck 2

IF % 0.1
Truck
Cost Increase > AND
% 0.1
Base
Cost Increase > , THEN
Full 3

IF % 0.1
Truck
Cost Increase ? AND
% 0.1
Base
Cost Increase ? , THEN
Any Model: Base,
Truck, or Full
4

It should be noted that the percent cost increase for either the Truck heuristic
or the Base model was never greater than 1.0 percent in any of the 10,935 problems
examined in this study. Therefore, when a 1.0 percent tolerance level was used to
41
define group membership, group 3, which recommended use of the fully specified
model, was not present. If the potential for a 1.0 percent deviation from the true cost
of inventory is an acceptable margin of error, then at least one of the less complex
models (Base or Truck) would be appropriate. This error margin, however, cannot be
generalized beyond this test problem. Although the problem was designed to vary the
model cost parameters and item-level demand characteristics, it is not known if more
extreme variations in the parameters would yield the same 1.0 percent cut-point
where group 3, which recommends use of the Full model, disappears.
The independent variables were selected from the model parameters in the
total cost function. They included: major order cost, minor order cost, holding
fraction, unit shortage cost, total annual demand, average item weight, and the unit
rate difference. The average item weight and unit rate difference were chosen
because they directly impact the transportation rate in the total cost function. The
unit rate difference, LTL unit rate - TL unit rate, was chosen because, even when the
TL and LTL freight rates were the same between two problems, the actual unit
transportation rate varied depending on the average item weight. The results of the
discriminant function analysis are discussed in chapter 4.
3.5. Simulation Study
A simulation study was designed to examine the sensitivity of the fully
specified model to non-normal demand. Through a series of interviews and a site
visit, actual item demand was collected from a local independent retail grocer,
Miller's Food Market, Inc. This independent grocer operates a single store,
supporting a local population of approximately 17,000 people. Miller's Food Market
42
maintains approximately 15,000 items valued at $151,200 in 8,400 square feet of
retail space. Inventory is replenished three times each week by a cooperative
wholesaler and inventory orders are determined manually by assessing the inventory
position for each item.
3.5.1. Data Collection
Weekly sales reports were collected from Miller's Food Market between
January 1, 2005 and December 31, 2005. Sales data was used in this study as a proxy
for demand. Demand, a function of the consumer's available budget and preferences,
is often approximated based on historical sales data (Tersine, 1994). Based on
interviews with the general grocery manager at Miller's Food Market, historical sales
played a major role in the ordering process.
The weekly sales reports included sales data for 4,865 items sold in the
general grocery, frozen, and dairy departments. The 52 weekly reports were
combined and checked for consistency, removing duplicate entries, missing data, and
outliers attributed to data entry errors. The average purchase price and profit margin
were calculated, along with total annual demand. Using the random function in
Excel, 100 items were selected.
Input Analysis: For each randomly selected item, a theoretical probability
distribution was fit to the demand data using the Input Analyzer in Arena 9.0. The
appropriateness of the theoretical distribution for the data was assessed using the Chi-
squared and Kolmogorov-Smirnov (K-S) goodness-of-fit tests. Both tests have
limitations. The Chi-squared test is highly sensitive to the number of intervals used
to represent the data, greatly affecting the significance of the test statistic. However,
43
the K-S test, while more powerful, is not valid for all distributions. The item-level
demand characteristics, probability distributions, and cost parameters are listed in
appendix 4. In many cases the goodness-of-fit tests were not statistically significant
indicating the demand data was not well represented by the theoretical distribution
function. Rather, the chosen distributions were the best choice, using the minimum
mean square error as a metric, compared with all other possible distributions. The
limitation of ill-fitted probability distributions was largely ignored in this study since
the purpose was not to accurately model the original system, but rather to provide a
representative sample of non-normal demands.
Cost Parameters: The purchase price for each item was taken as the average
purchase price over the 52 weeks of data. The stockout cost was assumed to equal
the profit margin lost for each stockout occurrence. The profit margin (in dollars)
was averaged over all items to arrive at a common shortage cost. While shortage
costs generally include the loss of goodwill, backordering costs, or costs associated
with substitution, such costs are difficult to determine and were not available from
Miller's Food Market. Consumers of retail goods, particularly groceries, are
generally store-loyal and much more likely to substitute an item or delay the purchase
than to switch to another retailer (Zinn and Liu, 2001). In this study, it was assumed
that consumers forgo or delay the purchase of out-of-stock items. The major order
cost was approximated using the labor cost of assessing inventory levels, determining
order quantities, placing the order, and receiving/stocking inventory.
The major order cost was equal to $300.00 based on the labor requirements to
prepare each order. The minor order cost associated with each line item was assumed
44
to equal zero, since no such data were available from Miller's Food Market. The
actual cost of holding inventory was unknown; therefore the holding fraction, F, was
set to 0.4 percent per year. The average weight for all items was approximated to
equal two pounds. The cost of transportation was taken from the literature (Russell
and Krajewski, 1991) and was the same cost structure used for the test problem. The
truckload transportation rate was $6/cwt, while the less-than-truckload rate was set to
$10/cwt. It was not feasible to determine the actual cost of transportation from
Miller's Food Market since transportation costs were included in the overall surcharge
assessed for each order placed. This surcharge, however, was determined based on
volume and similar to a transportation rate schedule.
3.5.2. Simulation Model
Two multi-item, periodic review inventory models were designed with Arena
9.0 simulation software using the logic depicted in figure 4. The only distinction
between the two models was the demand characteristics. In the first model demand
was assumed to be normally distributed using the mean, µ , and standard deviation,
? , for each item listed in appendix 4. The second simulation model used the fitted
demand distributions derived from the historical data. Demand occurred daily with
appropriate adjustments to the on-hand inventory levels for each item. Inventory
holding costs and shortage costs were accumulated at the end of each day. As with
the analytic model, daily demand was rounded to the closest integer following each
draw from the probability distribution. Some distributions, such as the normal
distribution, allow for negative values. Negative values were discarded and a new
value was drawn.
45
The inventory review process occurred at equal intervals. The order interval,
Full
T , and base stock levels,
i
R , were calculated for the fully specified model using
the Visual Basic program in appendix 3. The order interval was found to equal 18.58
days for the 100 grocery items. The lengthy order interval was due mainly to the
small number of items and low item weight. At each review, an order was placed for
all items with inventory positions below their respective base stock levels. The order
quantities were aggregated and the unit shipping rate was determined using the rate
function in equation (4). The purchase, transportation, and order costs were
accumulated in every review cycle. The delivery lead time was set as a random
variable with a mean of 2 days and standard deviation of 0.25 days. Upon receipt of
each order, the on-hand inventory level and inventory position for each item was
adjusted.
46
Is inventory
position for
item i < R
i
?
Place order for all k
items
Yes
No
Incur purchase, t ransport at ion,
and order cost s
Inventory Evaluation
(Periodic Review)
Accumulate Statistics
Order arrival
event
Det ermine order quant it y for
it em i
(R
i
- Invent ory Posit ion)
Schedule order arrival
event,with lead time L
Schedule next evaluation
event
Increment inventory position
and on-hand level for all k items
Return
Demand event
Generate demand size
for item i
Decrement inventory position
and on-hand level for item i
Schedule next demand event
for item i
Incur holding and shortage
costs for item i
Return
Determine shipping rate,
G
k

Figure 4. Simulation Flowchart
3.5.3. Model Measurement
The performance of the system was measured in terms of in-stock fill rates
and total costs. The fill rate for each item was used to determine the steady state of
the system, while the total cost of inventory was used to compare the models (normal
demand and non-normal demand) with the calculated values. The fill rate for item i
was defined as one minus the ratio of the average number of units short to total units
demanded, shown in equation (13).
47
| |
1 1

i i
i
i
E X R
Expected Number of Stockouts
Fill Rate
Total Number of Units Demanded Q
>
= ? = ? (13)
Ensuring steady state of the system is important to remove sample bias due to
the starting conditions of the various model parameters. If the simulation output is
dependent upon the initial values of the model parameters the true performance of the
system cannot be accurately measured. Output analysis was used to eliminate or
minimize sample bias arising from the initial conditions (Law and Kelton, 2000).
This was done by identifying and eliminating the transient behavior in the item-level
fill rates brought about by the starting inventory levels. The fill rate for 10 items was
plotted against the simulation time to identify the transient period. The system was
found to be in steady state after 200 days. This value was used as the warm-up period
after which all statistical accumulators were reset to zero. The simulation run length
was 365 days and the annual costs were calculated.
To ensure independence between each simulation run and eliminate
autocorrelation, the random number stream was separated by 100,000 for each
replication. Observations were collected by replicating the model 40 times. The
results of the discriminant function analysis and simulation are discussed in chapter 4,
to include recommendations and managerial implications.
48
Chapter 4. Joint Replenishment Results and Discussion
4.1. Discriminant Function Analysis (DFA)
The 10,935 test problems described in section 3.3 were randomly divided into
two groups. Fifty percent of the problem set was randomly chosen to estimate the
discriminant functions, while the remaining sample was used to validate the results.
Because the four grouping categories (Base, Truck, Full, Any) were of unequal size,
the estimation sample was randomly selected proportionate to group size.
For each tolerance level, the discriminant functions (DF) were estimated,
group membership was predicted, and the overall fit of the DFs was assessed. For
clarity in the discussion, DFA using 0.1 percent as the cut-point is labeled Analysis
A, the 0.5 percent tolerance level is labeled Analysis B, and 1.0 percent is labeled
Analysis C. Recall from section 3.4 that group membership represents the most
appropriate inventory model given the model parameters. For example, if a test
problem was predicted in the Truck category, then the combination of model
parameters resulted in a cost increase smaller than or equal to the tolerance level
when the Truck heuristic was used in place of the fully specified model. Similarly, a
case in the Base group would indicate that the textbook approach would result in a
cost increase over the fully specified model no greater than the tolerance level for the
given model parameters.
Goodness-of-fit was evaluated first by testing whether the discriminant
functions resulted in significantly different groups and second by assessing the
accuracy of the predictions in the holdout sample. For Analyses A and B, three
discriminant functions were estimated. Two discriminant functions were estimated
49
for Analysis C, since only three groups emerged. In all analyses, the estimated
discriminant functions were statistically significant, shown in table 12, indicating that
the discriminant functions resulted significantly different groups. For Analyses A and
B, the first two functions, X and Y, accounted for most of the between-group
variability, 99.6 and 97.7 percent, respectively. Wilk's lambda tests the significance
of the discriminant functions (DF). All DFs were statistically significant with p-
values < 0.000.
Table 12. Discriminant Analysis Significance Tests
Discriminant
Function

Eigenvalue
Cumulative
% Variance
Canonical
Correlation
Wilk's
Lambda
2
?

p-value
Analysis A – 0.1%
X 1.175 95.8 0.735 0.437 4531.98 0.000
Y 0.047 99.6 0.211 0.950 278.54 0.000
Z 0.005 100.0 0.072 0.995 28.53 0.000
Analysis B – 0.5%
X 0.613 82.2 0.617 0.546 3270.37 0.000
Y 0.116 97.7 0.322 0.881 685.22 0.000
Z 0.017 100.0 0.130 0.983 92.24 0.000
Analysis C – 1.0%
X 0.614 69.6 0.617 0.489 3865.96 0.000
Y 0.268 100.0 0.460 0.789 1281.47 0.000

Although the discriminant functions were statistically significant, prediction
accuracy is not necessarily guaranteed. Prediction accuracy was assessed using the
classification matrix and hit ratio. The classification matrix provides information on
the actual groups to which observations belong, along with predicted group
membership as calculated by the discriminant functions. The hit ratio measures the
percent of observations correctly classified. Analysis A, with a tolerance level equal
to a 0.1 percent cost increase over the fully specified model, had the highest hit ratio,
shown in table 13. Accurate predictions were made for nearly 85 percent of the cases
for both the original sample and holdout sample. With a very low tolerance for cost
50
increases, Analysis A accurately predicted 86.6 percent of the Base models, 91
percent of the Truck models, and 84.1 percent of the Full models in the holdout
sample. Of the misclassified cases, only those misclassified in the Truck group were
problematic. In the holdout sample, 64 Full cases and 182 Base cases were predicted
in the Truck group. For these misclassified cases, the Truck heuristic would actual
result in a cost increase greater than 0.1 percent.
Table 13. Analysis A Classification Matrix – Cut-off = 0.1%
Predicted Group Membership Actual Group
Membership
BASE TRUCK FULL ANY
Total
BASE 1,423 192 63 0 1,678
TRUCK 234 2,917 19 0 3,170
FULL 0 49 313 0 362
C
o
u
n
t

ANY 72 200 0 0 272
BASE 84.8 11.4 3.8 0 100.0
TRUCK 7.4 92.0 0.6 0 100.0
FULL 0.0 13.5 86.5 0 100.0
O
r
i
g
i
n
a
l

S
a
m
p
l
e

%
ANY 26.5 73.5 0.0 0 100.0
BASE 1,486 182 48 0 1,716
TRUCK 238 2,799 38 0 3,075
FULL 0 64 338 0 402
C
o
u
n
t

ANY 74 186 0 0 260
BASE 86.6 10.6 2.8 0 100.0
TRUCK 7.7 91.0 1.2 0 100.0
FULL 0.0 15.9 84.1 0 100.0
H
o
l
d
o
u
t

S
a
m
p
l
e

%
ANY 28.5 71.5 0.0 0 100.0
Original 84.9% Correctly
Classified
Holdout 84.8%

Analysis B, representing a 0.5 percent cost increase over the fully specified
model was the next best predictive model (see table 14). The classification accuracy
for the Truck heuristic and Base model was still high, although the accuracy dropped
to 62.7 percent when classifying the fully specified model in the holdout sample. The
percent of fully specified models misclassified in the Truck heuristic group also
increased to 28.4 percent.
51
Table 14. Analysis B Classification Matrix – Cut-off = 0.5%
Predicted Group Membership Actual Group
Membership
BASE TRUCK FULL ANY
Total
BASE 1,358 9 17 77 1,461
TRUCK 114 1,926 13 393 2,446
FULL 0 25 38 12 75
C
o
u
n
t

ANY 297 552 0 580 1,429
BASE 93.0 0.6 1.2 5.3 100.0
TRUCK 4.7 78.7 0.5 16.1 100.0
FULL 0.0 33.3 50.7 16.0 100.0
O
r
i
g
i
n
a
l

S
a
m
p
l
e

%
ANY 20.8 38.6 0.0 40.6 100.0
BASE 1,449 18 10 83 1,560
TRUCK 126 1,924 15 435 2,500
FULL 0.0 19 42 6 67
C
o
u
n
t

ANY 307 551 0.0 539 1,397
BASE 92.9 1.2 0.6 5.3 100.0
TRUCK 5.0 77.0 0.6 17.4 100.0
FULL 0.0 28.4 62.7 9.0 100.0
H
o
l
d
o
u
t

S
a
m
p
l
e

%
ANY 22.0 39.4 0.0 38.6 100.0
Original 72.1% Correctly
Classified
Holdout 71.6%

As the tolerance level increased, the number of cases in the ANY category
increased. When the tolerance level was set to 1.0 percent, in table 15, the FULL
group disappeared. Specifically, if the potential for a 1 percent cost increase is
acceptable, at least one of the less complex models (Base or Truck) could be
implemented. In Analysis C, the predictive accuracy of the DFs dropped to 71.9
percent for the original sample and 70.3 percent for the hold-out sample. Analysis C
also did a poor job in classifying the Truck heuristic model, with accurate predictions
for only 47 percent of the cases.
52
Table 15. Analysis C Classification Matrix – Cut-off = 1.0%
Predicted Grp Membership Actual Group
Membership
BASE TRUCK ANY
Total
BASE 1,010 0 235 1,245
TRUCK 17 760 777 1,554
FULL - - - 0
C
o
u
n
t

ANY 247 244 2,118 2,609
BASE 81.1 0.0 18.9 100.0
TRUCK 1.1 48.9 50.0 100.0
FULL - - - 0
O
r
i
g
i
n
a
l

S
a
m
p
l
e

%
ANY 9.5 9.4 81.2 100.0
BASE 1,022 0 272 1,294
TRUCK 22 759 831 1,612
FULL - - - 0
C
o
u
n
t

ANY 253 264 2,104 2,621
BASE 79.0 0.0 21.0 100.0
TRUCK 1.4 47.0 51.6 100.0
FULL - - - 0
H
o
l
d
o
u
t

S
a
m
p
l
e

%
ANY 9.7 10.1 80.3 100.0
Original 71.9% Correctly
Classified
Holdout 70.3%

The discriminant loadings in table 16 allow for interpretation of the
discriminant functions by identifying which model parameters contribute the most in
defining group membership. In analysis A, transportation-related factors best
describe the first discriminant function (DF X). As the average weight of the items
increased and the difference between the truckload and less-than-truckload rates
increased, the score on DF X increased. Recall that a score of 1 is associated with the
Base model, 2 equals the Truck heuristic and 3 equals the Full model. When the
discriminant function score equals 4, any model can be used. Therefore, as the
transportation-related model parameters increase the score on DF X tends to predict
the Truck heuristic or fully specified model. This makes sense since it is easier to fill
a truck with heavier items without adversely impacting holding costs. Coupled with
lower TL rates, inventory costs would be significantly reduced by filling a Truck with
53
each order. Discriminant function X also had the greatest explanatory power of all
other DFs, accounting for over 95 percent of the variability in the dependent variable
(see table 12). This provides further support for the inclusion of transportation in the
inventory model.
Table 16. Analysis A Discriminant Loadings
Discriminant Function
Model Parameter X Y Z
Average Item Weight 0.780 * -0.227 0.433
Unit Rate Difference 0.547 * -0.484 0.152
Holding Fraction -0.148 * -0.129 -0.044
Major Order Cost 0.184 0.842 * -0.297
Total Annual Demand 0.224 -0.163 -0.637 *
Minor Order Cost -0.016 0.228 0.550 *
Unit Shortage Cost -0.004 -0.032 0.279 *
* Represents largest absolute correlation between model parameter and discriminant function

The second discriminant function, DF Y, was most highly associated with the
major order cost. As order costs increased, order frequency dropped resulting in
larger orders. Thus, the Truck heuristic or Full model were predicted with higher
scores on DF Y. Finally, annual demand and minor orders costs best described DF Z.
As annual demand increased, the score on DF Z decreased in favor of the Base model
(DF score = 1). This makes sense since high demand will tend to result in larger
order quantities, thereby improving transportation utilization even when using the
textbook approach.
In table 17 the descriptive statistics for each group (Base, Truck, Full, Any)
further support model selection given the level of transportation-related factors, order
costs, and annual demand. Except for the transportation-related factors, the average
value of the model parameters was fairly consistent when comparing the Base model
and Truck heuristic. The average item weight and difference in transportation rates
(TL/LTL) were much larger for the Truck heuristic than for the Base model.
54
Therefore, the Truck heuristic is the appropriate model when the truckload
transportation rate is sufficiently smaller than the less-than-truckload rate and the
items are of medium weight. In practice, if a slight increase in the current shipment
size would fill a truck, transportation rates should be the deciding factor when
choosing between the Base and Truck (R, T) policies.
Table 17. Analysis A Descriptive Statistics
Model Variable Mean SD
BASE Major Order Cost 271.12 237.78
Minor Order Cost 4.72 2.87
Holding Fraction 0.43 0.16
Unit Shortage Cost 28.04 16.43
Average Item Weight 3.70 3.93
Unit Rate Difference 0.14 0.20
Total Annual Demand 70,424 31,674
TRUCK Major Order Cost 287.18 229.16
Minor Order Cost 4.60 2.89
Holding Fraction 0.39 0.16
Unit Shortage Cost 28.42 16.59
Average Item Weight 10.48 5.48
Unit Rate Difference 0.49 0.37
Total Annual Demand 82,042 32,133
FULL Major Order Cost 513.81 135.94
Minor Order Cost 4.62 2.70
Holding Fraction 0.32 0.15
Unit Shortage Cost 27.24 16.39
Average Item Weight 19.14 2.80
Unit Rate Difference 0.86 0.49
Total Annual Demand 100,132 24,865
ANY Major Order Cost 395.44 245.65
Minor Order Cost 5.47 2.58
Holding Fraction 0.38 0.16
Unit Shortage Cost 29.06 16.74
Average Item Weight 8.04 3.46
Unit Rate Difference 0.28 0.26
Total Annual Demand 69,908 27,954

When high levels in the transportation-related factors were also accompanied
by high order costs and large annual demand, the Full model minimizes inventory
costs. This does not necessarily imply implementation of the Full (R, T) model
whenever high levels of ordering and transportation costs are present. Recall from
the sub-sample of test problems presented in section 3.3, table 10, the Full model
55
resulted in the lowest total cost when the order quantity resulted in multiple
truckloads. The Truck heuristic could be modified to calculate the total cost for
multiple truckload shipments. For example, the order interval for two truckload
shipments would equal
2
2
Truck t i
T Q D =
?
. Comparing the single-shipment Truck
heuristic with a modified multi-shipment Truck heuristic, the lowest total cost could
be found.
Interestingly, the holding and shortage costs had very little impact on model
selection. The average value for these costs was similar across all groups. Thus, the
traditional approach of balancing ordering and holding costs may not be effective
when faced with high or increasing transportation charges. Transportation can be a
very large component of the total cost of inventory. Therefore, the Truck heuristic, or
a modified Truck heuristic for multiple loads, is a reasonable and simple approach to
cost minimization. The heuristic is easy to calculate and can be quickly adjusted to
meet changing demand conditions. One disadvantage of the Truck heuristic,
however, is the potential for larger inventories which may increase the risk of
obsolescence. However, shipment frequency and volume in the grocery industry
lends itself to truckload shipments.
The large impact of transportation-related factors on inventory costs shown in
this study raises the question on whether the (R, T) policies discussed in section 2.2,
are truly near-optimal solutions. The models in the extant literature may suboptimize
the system by not considering transportation costs and limit their use in practice.
Indeed, Silver (1981) questioned the practicality of inventory research and
recommended the development of good rather than optimal solutions. Since optimal
56
solutions are rarely easy to implement, the Truck heuristic was developed as
alternative when considering all relevant inventory costs, particularly transportation.
The results of the simulation study are discussed in the next section highlighting the
impact of non-normal demand on inventory costs.
4.2. Simulation Results
The simulation study addressed a key assumption often made when
developing analytic solutions to inventory models. Specifically, demand is assumed
to be normally distributed. This assumption allows various model characteristics to
be calculated, such as the demand during the leadtime and replenishment period,
safety stock, the probability of a stockout, and stockout quantities. To examine
violations of the normality assumption, two models were developed: one with
normally distributed demand and one using non-normal demand distributions derived
from industry data. Point estimates for the total cost of inventory were calculated for
each model taking the average over 40 replications. A 95 percent confidence interval
was constructed with which to compare the simulated costs with calculated costs,
shown in table 18.
When demand was normally distributed, in model 1, the simulation produced
results consistent with the calculated costs. The calculated total cost of inventory was
$540,667 which fell within the 95 percent confidence interval for model 1. However,
the total cost using actual demand (model 2) with varying demand distribution
characteristics resulted in approximately a 2 percent increase over the calculated
costs. The results suggest that the order interval and item base stock levels calculated
when demand is assumed to be normally distributed were suboptimal for model 2.
57
This is shown by examining the various cost components in model 2. The
transportation costs were higher than expected implying the shipment of phantom
freight for some or all of the orders. Additionally, less inventory was held in model 2
than anticipated by the analytic model, since holding costs were lower. At the same
time shortage costs increased indicating a higher stockout rate. The purchase costs
were also higher in model 2 indicating the higher demand for and subsequent
ordering of more expensive items. These results suggest that item heterogeneity may
significantly affect the implementation of the simplified Truck heuristic (in lieu of the
fully specified model) which is based entirely on truck capacity and annual demand.
The true cost, however, for this problem is unknown since the optimal
parameters were not found. Indeed, the optimal parameters for the order interval and
base stock levels would be impossible to determine analytically, given the variety of
demand distribution patterns shown in appendix 4. The optimal parameters might be
found using optimization and search techniques, but the computation effort would be
significant and would only be applicable to this problem of 100 inventory items.
For an inventory manager, understanding how non-normal demand impacts
the expected costs when calculated in the Full model or Truck heuristic is more useful
from a practical perspective. The results of this simulation study indicate that the
calculated costs in the Full model may represent a lower bound for total costs. True
costs could actually be higher assuming actual demand deviates from normality.
58
Table 18. Simulation Output – Inventory Costs

Annual
Purchase
Cost
Annual
Trans
Cost
Annual
Order
Cost
Annual
Holding
Cost
Annual
Shortage
Cost
Total Annual
Inventory
Cost
Calculated Costs $481,454 $47,136 $5,892 $5,991 $193 $540,667
Avg $480,807 $48,210 $5,700 $5,598 $289 $540,605
SD $1,478 $225 $0 $58 $24 $1,650
95% CI Min $480,335 $48,138 $5,700 $5,580 $282 $540,077
M
o
d
e
l

1

N
o
r
m
a
l

D
e
m
a
n
d

95% CI Max $481,280 $48,282 $5,700 $5,617 $297 $541,132
Avg $490,101 $49,772 $5,775 $5,492 $529 $551,668
SD $3,942 $497 $132 $67 $53 $4,437
95% CI Min $488,840 $49,613 $5,733 $5,470 $513 $550,249
M
o
d
e
l

2

A
c
t
u
a
l

D
e
m
a
n
d

95% CI Max $491,361 $49,931 $5,817 $5,513 $546 $553,088

4.3. Discussion and Managerial Implications
The three multi-item inventory models developed for this research targeted the
small retailer with limited order processing technologies. The objective of the fully
specified model was to include the cost of transportation in determining the order
interval and, therefore, more accurately evaluate the impact of ordering decisions on
total costs. Building on the previous literature on joint replenishment programs, the
Base (R, T) model was modified to include all relevant transportation costs and the
possibility of shipping phantom freight. Specifically, the fully specified model
included the cost disadvantage of less-than-truckload shipments, a factor not
addressed in the extant literature on joint replenishment. Furthermore, the fully
specified model was evaluated against the Base model and Truck heuristic over a
range of varying model parameters. The results of the discriminant function analysis
showed that transportation-related factors had the greatest impact on total annual
costs in favor of the Truck heuristic. Further, modifications to the truck heuristic to
calculate multiple truckload shipments could be easily implemented when ordering
59
costs and annual demand are high. Indeed, an inventory manager would not need to
implement the complex and difficult-to-calculate fully specified model. A
comparison of the total cost for the Truck heuristic and modified Truck heuristic
would reveal the cost minimizing solution.
When demand was not normally distributed, the fully specified model
suboptimized the order interval. Specifically, deviations from a truckload shipping
quantity increased costs. One approach might be to adjust the order quantities, either
positively or negatively, in order to exactly fill a truck(s). In practice, such a policy
would be easy to implement, adding or deleting pallets when needed.
4.4. Future Research
There are several extensions to the research that warrant further investigation.
First, when demand was non-normally distributed the fully specified model resulted
in a lower bound. Actual costs in the simulated model were 2 percent higher than
calculated costs. A natural extension would be to find the upper bound of this cost
increase. While an absolute upper bound may be difficult to calculate, it would be
interesting to understand how varying model parameters affect total costs under
actual demand conditions, particularly with respect to item heterogeneity. A study
could be designed to vary both the probability distributions of demand and the
variation of demand to better understand how demand patterns affect total costs
compared with the calculated costs in the Full model. Such a study could examine
whether items with similar demand patterns should be grouped together under a
common order interval. Furthermore, variations in other cost parameters (e.g.,
transportation, order, holding, and shortage) might impact the total cost of inventory
60
differently when demand patterns vary. For example, the calculated order interval
was shown in this study to be suboptimal for non-normal demand. If, for example,
the calculated order interval is smaller than the optimal order interval, more frequent
orders would occur. Given high order costs, would the model with non-normal
demand still result in a 2 percent cost increase? A simulation study with varying
model parameters, similar to the test problem in this research, might provide useful
information on an upper bound of the total inventory cost.
Second, it would be useful to test the affect of the allocation approach when
order quantities deviate from a truckload shipping quantity. Given that non-normal
demand actually increased costs, a simulation study could be devised to test whether
strict implementation of the Truck or modified Truck heuristic helps to lower costs.
For example, when the order quantity is less than truck capacity,
k t
Q Q < , the number
of items ordered would be increased to exactly fill a truck(s). Similarly, when
k t
Q Q > , fewer items would be ordered. The objective of such a study would be to
determine whether increases in holding and shortage costs using an equal allocation
policy would outweigh the cost benefit of truckload shipments.
The third extension to this research would be to examine the impact on total
costs when using an integer value for the order interval. For example, when the
calculated order interval is 3.7 days, does underestimating the order interval at 3 days
or overestimating at 4 days result in the smallest cost deviation? Furthermore, would
an allocation policy to add or delete items, as needed, to fill a truck mitigate any cost
increase associated with integer values of the order interval?
61
Finally, the characterization of the transportation function should be
considered in future research. This study considered a weight-break transportation
function and demonstrated that deviations from a full truck shipment raised inventory
costs. Alternatively, Cachon (2001) treated transportation as a fixed cost per truck
dispatch, such that the per unit transportation rate decreased hyperbolically up to
truck capacity. This is not unlike the over-declared portion of the transportation
function considered in this study. However, given a fixed cost per truck dispatch,
shipping quantities slightly larger than truckload capacity substantially increase the
per unit transportation cost and should have a similar impact on the order interval as
shown in this study.
4.5. Limitations
The limitations of this study should be noted. The simulation study found that
the true inventory costs were approximately 2 percent higher when demand was not
normally distributed. This cost increase was measured with respect to the calculated
expected costs in the fully specified model which assumed demand normality.
However, for non-normal demand the optimal inventory policy may be very different
from the one used in this study. Specifically, the order interval and base stock levels
for each item in an optimal policy under non-normal demand will not necessarily be
the same as when demand is normally distributed. The optimal inventory policy for
non-normal demand was not found and was beyond the scope of this study. While an
optimal policy would be limited to this problem, a comparison between the Full
model and the optimal policy would be useful in understanding the extent to which
the assumption of demand normality impacts the total cost of inventory.
62
Another limitation of this study which could impact inventory policy
decisions was the assumption of unlimited storage space. Storage or shelf-space
constraints can limit the ability to implement truckload shipments, particularly for
small grocery retailers. For example, Miller's Food Market, the retail grocer
interviewed for this study, placed three weekly orders. Each shipment was, on
average, one pallet short of a full truckload. While cognizant that full truckload
shipments could reduce costs, order frequency was driven primarily by storage space
constraints at the store. While storage constraints would be a concern for any size
retailer, this study provided evidence that transportation costs can outweigh holding
costs, suggesting that expansion of backroom storage space might be a wise
investment.
The applicability of the Truck heuristic to industries characterized by high
shortage costs is another limitation to the study. Shortage costs in this study were
shown to have very little impact on the total costs, even when these costs were varied.
However, some industries might have very little tolerance for shortages. In such
cases stockout costs could outweigh any cost savings derived by improved
transportation utilization. Nevertheless, the fully specified model, would still be an
appropriate inventory policy, assuming all costs are managerially relevant.

63
Chapter 5. Supply Chain Actions in the Grocery Industry
5.1. Introduction
Strategic management focuses on “the coordination and resource allocation
both within and across firm boundaries” (Madhok, 2002). These internal and
external management actions are of particular interest when examining firm
performance in the context of supply chains. Supply chains are “links of partially
discrete, yet interdependent, entities that collectively transform raw materials into
finished products” (Hult et al., 2002). The strategic management literature informs us
of the importance of the supply chain with an understanding of the determinants and
consequences of vertical integration (Majumdar and Ramaswamy, 1994; Walker and
Weber, 1984; Williamson, 1975), the market-based alternatives to vertical integration
along the supply chain (Afuah, 2001; Gulati, 1998), and the benefits of cooperative
buyer-supplier relationships (Bensaou and Anderson, 1999; Kotabe et al., 2003;
Mudambi and Helper, 1998). Furthermore, there is growing attention regarding the
impact of supply chain structure (in terms of upstream and downstream influences) on
firm performance (Cool and Henderson, 1998; Randall and Ulrich, 2001). Yet, there
remains a limited understanding of how the interdependence of firms along the supply
chain impacts a firm’s competitive strategy (Frohlich and Westbrook, 2001; Tan et
al., 2002).
There are two dominant views of competitive strategy. From the vantage
point of Porter’s (1980) five forces model, competitive strategy is “aimed at altering
the firm’s position in the industry vis-à-vis competitors and suppliers” (Teece et al.,
1997), where the firm's position is largely determined by barriers to entry/exit,
64
industry concentration, and upstream/downstream dominance. On the other hand, the
Schumpeterian perspective attends to a dynamic market process (Jacobson, 1992) and
views competitive strategy as a “series of actions and reactions among firms” (Smith
et al., 2001). The competitive dynamics research has studied this interdependence
among rivals, demonstrating a strong link between firm actions, competitor actions,
and firm performance. The actions among rivals emphasized in this stream of
research centers on market-based actions, such as the pricing, marketing, and
signaling activities of the firms. However, firms are also involved with coordinating
their activities along the supply chain in order to enhance the performance objectives
of the firm. These coordinating actions along the supply chain have not been
considered in the competitive dynamics framework as a determinant of firm
performance.
This research attempted to fill that gap by exploring a broader set of actions
that may enhance a firm’s competitive position; specifically, this research examined
the supply chain actions of the firm and the impact these types of actions had on firm
performance. This research addressed the following questions:
1) Is there a diverse portfolio of competitive moves in which firms engage to affect
their competitive position? More specifically, does the quantity and diversity of
supply chain actions positively impact firm performance?

2) Do supply chain actions moderate the relationship between market-based actions
and firm performance?

3) Do certain types of supply chain actions align more closely with the firm’s
competitive strategy to enhance firm performance?

Drawing on the competitive dynamics and supply chain management areas of
research, this research attempted to incorporate supply chain actions into the
65
competitive action fold as a determinant of firm performance. This chapter begins
with a review of the competitive dynamics literature, focusing on the relationship
between firm actions and firm performance. Next, the supply chain empirical
research is presented to uncover the types of supply chain actions that may impact
firm performance. With this foundation, hypotheses are developed to relate actions
with firm performance. Chapter 6 describes the data collection process and methods
used to test the hypotheses. The analysis and results are presented in Chapter 7, to
include a discussion of the key findings and managerial implications.
5.2. Theoretical Foundations: Competitive Dynamics
Competitive dynamics addresses a key area in the study of firm performance,
that of firm behavior and conduct within an industry. While industrial organizational
economics emphasizes the structure-conduct-performance (SCP) paradigm, industry
structure remains the key determinant of performance. In contrast, the competitive
dynamics research argues that beyond industry structure, actions and responses define
the competitive strategies of the firm and directly influence performance (Smith et al.,
2001). Competitive dynamics rests on entrepreneurial discovery and the dynamic
market process of Schumpeterian economics (Jacobson, 1992) where firms search out
opportunities to disrupt market equilibria (Grimm and Smith, 1997) and affect change
within the industry. Many characteristics of firm actions have been studied, to
include the impact of strategic versus tactical actions on imitation and the likelihood
of response (Smith et al., 1991), the sequence or pattern of actions and reactions
(Ferrier and Lee, 2002), action complexity and intensity (Smith et al., 2001), action
timing (Ferrier et al., 1999), the timeliness of rival response (Chen and Hambrick,
66
1995; Smith et al., 1991), the number and diversity of actions (Ferrier et al., 1999),
and the relationship between firm size and the speed and likelihood of actions and
responses (Chen and Hambrick, 1995). The results of this research are largely
consistent: aggressive competitive action (in terms of the number and intensity of
actions) is positively related to firm performance and the persistence of market share
leadership (Ferrier et al., 1999). Aggressive competitive action has also been linked
with a first- and fast-second mover advantage (Lee et al., 2000), showing that lagging
firms and late adopters of innovations accrue little, if any, competitive advantage
(Ferrier et al., 1999; Smith et al., 1991; Smith et al., 2001).
The relationships between firm action, rival response, and firm performance
are drawn mainly from the study of market-based actions. Specifically, market-based
actions are those actions firms employ to capture customers. The types of market-
based actions studied include pricing actions, marketing actions, new product actions,
capacity- and scale-related actions, service actions, and signaling actions (Smith et
al., 2001). In contrast, Shaffer et al. (2000) investigated the impact of non-market-
based actions on firm performance, where non-market-based actions were defined as
public policy- and governmental-related actions. This paper focuses on a different
type of non-market-based action, specifically, supply chain actions.
5.3. Supply Chain Activities
Supply chains exist whether or not they are actively managed (Mentzer et al.,
2001a). However, it is in the management of supply chains and supply chain
activities that firms make decisions about the internal integration of processes and
external integration with other organizations in order to facilitate the flow of material
67
and information in support of the firm’s strategic objectives (Houlihan, 1985;
Mentzer et al., 2001a; Scott and Westbrook, 1991). This section briefly examines the
supply chain literature to better understand the types of supply chain activities in
which firms engage and how these activities relate to firm performance.
Supply Chain Material Flow. One of the fundamental reasons to manage
the supply chain is to improve the flow of material to the end customer. Many areas
of research focus on this issue, to include inventory management, just-in-time
purchasing (Fazel, 1997), strategic supplier sourcing (Anderson and Katz, 1998),
distribution and centralization, service quality, production, and new product
development (Swink, 1999). Indeed, efficiency in material flow and improvements in
cycle times are often driving forces in supply chain management. For example, in
the furniture industry time compression strategies have been shown to positively
impact firm performance (Vickery et al., 1995). Similarly, Stock et al (2000), found
that operational improvements arise from improved material flow via integrated
logistics activities within and between firms.
Supply Chain Information Flow. Coupled with material flow, information
flow is essential to coordinate supply chain activities. A dominant theme in supply
chain research is the reduction in information asymmetry along the supply chain. The
exchange of information, particularly information concerning consumer demand, has
been shown to reduce excess inventory (Lee et al., 1997), improve service quality
(Mentzer et al., 2001b), and facilitate coordinated manufacturing processes via
enterprise information systems (Rabinovich and Evers, 2002). Empirical evidence
has shown that the efficient flow of information along the supply chain positively
68
impacts firm performance. Droge and Germain (2000) found that electronic data
interchange (EDI) capabilities reduced inventory investment and had a positive
impact on financial performance. Similarly, effective knowledge transfer has been
shown to improve supply chain performance, as measured by cycle time (Hult et al.,
2004). One way firms affect the flow of material and information is through
coordination with other firms. Coordination with supply chain member firms and the
integration of processes with external organizations has empirically been shown to
improve performance.
Supply Chain Relationships. The motives to collaborate within the supply
chain are often driven by efficiency goals, scale economies, and quality improvement
objectives (Tan et al., 1998). Supply chain collaboration can also provide greater
access to resources (Gulati, 1998) and a competitive advantage (Ireland et al., 2002).
The empirical research on supply chain relationships focuses on two fundamental
issues—the determinants of supply chain relationships and the resulting benefits.
Research examining the determinants of supply chain relationships is primarily
grounded in transaction cost economic theory, particularly in the strategic
management literature. For example, Bensaou and Anderson (1999) found that
buying firms are more willing to initiate buyer-supplier relationships by committing
relationship-specific investments when such relationships involve higher task
complexity and technological uncertainty. Transaction cost economics views
relationship-specific investments as idiosyncratic investments which cannot be re-
deployable to another relationship, thereby creating bilateral dependency
(Williamson, 1998). Williamson (1999) points to a large body of empirical research
69
that supports a strong relationship between idiosyncratic investment and tighter
governance of firm-to-firm relationships.
Benefits to forging tighter supply chain relationships are reduced costs and
improved performance. For example, long-term buyer-supplier relationships have
been shown to benefit supplier operational performance (e.g., product design, quality,
and lead time) (Kotabe et al., 2003). Similarly, Shin et al. (2000) found that higher
levels of supply management orientation (measured in terms of relationships, supplier
selection, and supplier involvement) improved supplier and buyer quality and
delivery performance.
5.4. Supply Chain Actions
The aforementioned supply chain literature and activities served as the basis
for defining and operationalizing supply chain actions, the focus in this study. Supply
chain actions were defined as documented supply chain activities relating to the flow
of material, the flow of information, or supply chain relationships. As has been done
in the competitive dynamics research (Ferrier et al., 1999), a supply chain action was
defined as an instance in a published article that describes a supply chain activity in
an associated pre-defined supply chain category. For example, an article describing
the warehouse expansion for a firm would be classified as a supply chain action in the
category identified as Warehousing. Similarly, an article describing changes in a
vehicle fleet would be classified as a supply chain action in the category identified as
Transportation. The supply chain categories related directly to material flow,
information flow, and supply chain relationships were derived from the publication
70
data source used in this research and described more fully in the methods section,
chapter 6.
It is noted that some supply chain activities may not be readily observed or
documented in a published source. While internal process improvements may
support firm strategic goals, internal actions are less likely to affect the competitive
landscape. The Schumpeterian perspective argues that actions must be observable to
disrupt the status quo thereby signaling an intended course of action by the firm
(Jacobson, 1992). Thus, while unobserved actions may indeed facilitate material and
information flow along the supply chain, this study captured only observable actions
that may be seen by rivals. The relationships between supply chain actions, market-
based actions and firm performance are hypothesized in the next section.
5.5. Hypotheses Development
In The Competitive Advantage of Nations, Porter (1990) argues that
competitive advantage is derived through acts of innovation. Further, once a
competitive advantage is achieved, the firm must continually upgrade in order to
sustain this advantage. Supply chain management is one way firms can reengineer
processes within and across organizations and provide the basis for continuous
improvement as raw materials are transformed into finished goods. That a
competitive advantage must be continually upgraded and enhanced underlies the
concept of first-mover and fast-second mover advantage (Lee et al., 2000).
Because supply chain management drives internal and external efficiencies
(Mentzer et al., 2001a), some supply chain actions might be considered value-added
actions (Hines et al., 1998) that are directed at improving the firm’s resource position
71
(Grimm and Smith, 1997). For example, centralization of inventory at a distribution
center may, in the short-run, reduce inventory investment and improve delivery
efficiencies. However, in the long-run, such supply chain actions are geared toward
more strategic goals of improved customer service, greater market share and higher
firm profits (Wisner and Tan, 2000). Therefore, the following hypotheses were
tested,

H1a: The total number of supply chain actions is positively related to sales growth.

H1b: The total number of supply chain actions is positively related to performance.


In addition to the relationship between the total number of supply chain
actions and firm performance, it is expected that the positive relationship between
market-based actions and firm performance will still be present, as strongly supported
in the competitive dynamics literature. Therefore, the following hypotheses were
tested,

H1c: The total number of market-based actions is positively related to sales growth.

H1d: The total number of market-based actions is positively related to performance.

Supply Chain Action Diversity: The competitive dynamics research has
found a positive relationship between the complexity of the competitive action
portfolio and sustained performance. Firms that relied on a narrow set of market-
based actions were more likely to be out maneuvered by competitors (Ferrier et al.,
1999), whereas firms that relied on a diverse set of competitive actions realized
higher levels of performance than that of competitors. Consistent with the notion of
72
action diversity, the supply chain management literature often considers the degree to
which firms integrate their supply chains as a measure of their supply chain focus or
external orientation. In a survey of 322 manufacturing firms, Frohlich and Westbrook
(2001) investigated supply chain integration activities (e.g., joint EDI, customization,
joint planning, information sharing) and found that firms characterized as outward-
facing (integration with both upstream and downstream supply chain members)
performed better than firms that were inward-facing or only focused effort in one
direction (e.g., upstream or downstream, but not both). Further, inward-facing firms,
those that engaged in limited supply chain integration activities, showed consistently
lower performance than all other firms. In a similar study, firms that were more
supply management oriented (with high coordination between buyers and suppliers)
yielded higher operational benefits for both suppliers and buyers (Shin et al., 2000).
Trends in the retail grocery industry suggest that the greatest benefits from Efficient
Consumer Response arise when a wide variety of initiatives are implemented
(Frankel et al., 2002). Therefore, it is suggested that firms that employ a more
diverse set of supply chain actions will realize higher performance benefits than firms
that engage in a narrow set of supply chain actions. Specifically, the following
hypotheses were tested,

H2a: The greater the diversity of supply chain actions, the greater the growth in
sales.

H2b: The greater the diversity of supply chain actions, the higher the performance.

Action Interaction: Logistics as a value-adding activity within the firm
received momentum with Porter’s concept of the value chain in the 1980’s (Stock,
73
1997). It is widely held that the short-term objective of supply chain management is
to increase productivity, reduce inventory, and improve cycle times, while the long-
term, strategic goal of supply chain management supports the overall firm objectives
of improved customer service, increased market share and higher firm profits (Wisner
and Tan, 2000). Considering this view that supply chain actions support the strategic
goals of the firm, the interaction of market-based actions and supply chain actions
was test as it relates to firm performance. It was hypothesized that market-based
actions when coupled with supply chain actions improved firm performance.
Specifically,

H3a: The interaction of the total number of supply chain actions and the total number
of market-based actions positively impacts sales growth.

H3b: The interaction of the total number of supply chain actions and the total number
of market-based actions positively impacts performance.

5.6. Supply Chain Strategies
The competitive dynamics literature views strategy as action. Firms act in the
marketplace, competitors react, and consequences are assessed in a cyclic manner.
Thus, learning takes place through a feedback mechanism that enables future action
(Grimm and Smith, 1997). Firm strategy is then revealed by discovering the types
and patterns of competitive actions that firms enact. For example, price-cutting
actions have been associated with low-cost strategies in the U.S. Airline industry,
whereas airlines focused on differentiation strategies engaged in more marketing
actions (Smith et al., 1997). The competitive dynamics literature characterizes the
pattern of market-based actions as the competitive strategy of the firm.
74
Supply chain strategies have been investigated in the supply chain literature.
In a survey of the grocery industry, Lynch et al. (2000) found that when a firm's
logistics capabilities were appropriately matched with business strategies (cost leader
or differentiation) performance was enhanced compared with firms that did not match
capabilities with strategy. Similarly, manufacturing and business strategy alignment
have been shown to enhance performance (Ward and Duray, 2000).
It might be expected that many combinations of supply chain actions and
market-based actions are equally effective in achieving higher performance (Ward
and Duray, 2000). For example, Morash (2001) found that demand-orientation (a
customer focus) was highly correlated with the firm excellence. On the other hand,
Tan (2002) and Tan et al. (2002) found that of 25 different supply chain activities,
some were more highly correlated with firm performance than other activities.
However, these studies failed to address other activities, such as the market-based
actions of the firm, that impact performance. As a result, there is little consistency in
the existing supply chain management research with respect to the types of supply
chain activities that might have a greater impact on performance. Without a strong
theoretical foundation to hypothesize which patterns of supply chain actions might be
more likely to affect performance, an exploratory study was conducted to investigate
the supply chain and competitive strategies of the firms in this study.
Using cluster analysis, this exploratory study attempted to uncover the
patterns of actions that might characterize the firm's strategy in terms of supply chain
and market-based actions at a more disaggregated level. Specifically, the exploratory
75
analysis investigated the types of actions that were most prevalent in the sample data
and whether the patterns varied based on organizational characteristics.
5.7. Research Setting
The retail grocery industry was selected for this longitudinal study during the
period 2000 to 2004. A single industry was chosen because inter-industry effects can
be directly controlled without the introduction of variables to account for varying
degrees of capitalization, technological change, product introduction clock speed,
scale economies, or other distinctive industry characteristics. The retail grocery
industry, in particular, was selected because it met three basic criteria: 1) there was a
high level of supply chain activity within the industry, 2) a large number of supply
chain actions and market-based actions were visible and easily documented through
trade publications, and 3) there was a sufficiently large sample size. Because of the
first two points and the ability to collected data on over 1,100 firms in the industry, it
was possible to capture many competitive actions in each year for a robust
longitudinal study.
The grocery industry was also ideal because most U.S. firms were not
diversified, although some firms were involved in the manufacturing of private label
food products. The notable exceptions were Wal-Mart, K-Mart, and Target who
operated predominantly in the discount general merchandise industry. Furthermore,
the majority of U.S. retail grocery firms did not operate in foreign countries, with
only a few minor exceptions (Gale, 2005). Therefore, the U.S. grocery industry
might be considered a relatively closed system, in which investment in resources,
76
supply chain advancements, and the competitive actions of firms were aimed
primarily at markets within the U.S.
Defining the boundaries for this study, the data was collected using the North
American Industry Classification System (NAICS) Code 44511, Supermarkets and
other Grocery Stores. The industry defines a supermarket as a store with at least $2
million in annual sales carrying a full line of food and non-food items (Gale, 2005),
and therefore this study did not include convenient stores or small grocery retailers.
Warehouse clubs that sell directly to the public (e.g., Sam’s Club or Cosco) were also
excluded from the study since these types of firms fall under a different classification
(NAICS Code 45291) and outside the scope of this study. Finally, supercenter-type
firms (e.g., Wal-Mart, Target, and K-Mart), with a significant impact in the industry
were included in this study. While NAICS 44511 is not the primary industry for
supercenter-type firms, the grocery operations of these firms do fall under this
industry classification. Therefore, a search in NAICS 44511 includes supercenter-
type firms.
77
Chapter 6. Supply Chain Actions Data Collection and Methodology
The purpose of this research was to test the relationship between the various
types of firm actions and performance in the retail grocery industry. Following the
competitive dynamics literature, a content analysis method was chosen to document
firm actions from the existing trade publications. This chapter discusses the data
collection process, develops the regression model for hypothesis testing, and details
the exploratory study using a cluster analysis methodology.
6.1. Structured Content Analysis
Structured content analysis is a useful method that can describe trends,
identify intentions or characteristics of the communicator or subject and reveal
patterns from the underlying data (Weber, 1985). This methodology was chosen to
identify trends in supply chain actions by assessing the number and type of supply
chain and market-based actions documented in the trade literature for the firms in the
grocery industry. Based on these trends, inferences were drawn regarding the impact
of competitive activity on sales growth and performance. Structured content analysis
has been used in many fields of study (Jauch et al., 1980) and is a dominant method
to measure competitive actions in the competitive dynamics literature. Content
analysis rests on a classification procedure to analyze and code each article as
recommended by Jauch et al.(1980). The content analysis classification schedule is
much like a survey questionnaire where the objective is to measure specific variables
of interest. The classification schedule used in this analysis was based on pre-
defined categories into which supply chain and market-based actions were placed.
78
The next sections discuss the sources of data, the data collection process and the
classification schedule used to categorize firm actions.
6.2. Data Sources
Action Articles: The supply chain and market-based actions were identified
based on published news articles. The relevant publications for this study were
identified by reviewing the retail grocery industry trade press, professional
organization web sites, and industry newsletters. A list was compiled of the weekly
and monthly publications that report both local and national news within the industry.
This list was then compared to the publications contained in the Thomson Gale
Business and Company Resource Center (BCRC). BCRC is a web-based archive of
articles available by subscription through the University of Maryland Library. The
BCRC database contained all of the publications on the original list and included a
broad range of business, company and industry related content from a large list of
academic and trade journals, trade newsletters, general national and local news
sources, and company press releases. A full list of sources included in the BCRC
database can be found at the Thomson Gale website, www.gale.com, while a short list
of the relevant grocery industry trade publications are listed in appendix 5. A search
procedure, described in section 6.3, was used to collect the articles from the BCRC
database during the period 2000 to 2004. An overview of the number of articles
collected is given in table 19.
Table 19. BCRC Articles by Year

2000 2001 2002 2003 2004
Total
Articles
Supply Chain Categories 667 883 1,234 1,742 1,173 5,699
Market Based Categories 3,813 4,325 6,185 7,006 6,068 27,397
Totals 6,480 7,209 9,421 10,751 9,245 33,096
79
Firm Data: The firm-level data and market characteristics were collected
from two industry sources: The Marketing Guidebook: The Blue Book of Grocery
Distribution and Market Scope: The Desktop Guide to Supermarket Share. These
guides are published annually by Trade Dimensions International and The
Progressive Grocer and contain detailed information on both public and private
grocery firms. Trade Dimensions maintains store-level data compiled on every
supermarket in the United States from which they produce company profiles and
estimate firm sales and market share data. The data is compiled year-round via direct
company contact (questionnaires and telephone calls) and maintained in the Trade
Dimensions Retail Site Database (Currie, 2005). Fifty mutually exclusive market
areas area consistently defined in both publications. The Marketing Guidebook, was
used to collect market area demographics and aggregate sales. The firm-level market
share data was extracted from Market Scope, a companion publication. Market Scope
includes every firm operating within each market area, listing the number of
supermarkets operated by the firm and the share of the market area supermarket sales.
The market share for supercenter-type firms was collected by Trade
Dimensions in the same manner as traditional supermarkets through scanner data and
direct company contact. The key difference was that only supermarket-type
merchandise was used to estimate market share for supercenter firms. For example,
58% of the total sales were attributed to supermarket-type merchandise for Wal-Mart
(Tarnowski and Heller, 2004).
80
6.3. Data Collection: Action Articles
The Thomson Gale Business and Company Resource Center (BCRC) was the
sole source of news articles used to document the supply chain and market-based
actions for the firms in this study. This on-line repository of business content is
searchable by industry using the either the North American Industry Classification
System (NAICS) or the Standard Industrial Classification System (SIC). The North
American Industry Classification System (NAICS) was used for this study,
specifically, 44511 – Supermarkets and Other Grocery (except Convenience) Stores.
An initial search of BCRC under NAICS 44511 returned over 79,000 articles, as well
as a list of subdivisions with which to narrow this broad search. These subdivisions
served as the basis for the categories used for the content analysis classification.
6.3.1. Supply Chain Action Categories
The first content coding scheme was developed for supply chain actions. A
first step in developing a comprehensive coding schema would be to examine the
extant literature. However, taxonomies and inclusive functions of supply chain
management vary from author to author (Mentzer et al., 2001a). Therefore, the
starting point for this study was the pre-existing subdivisions in the Thomson Gale
BCRC database. These pre-existing subdivisions, or categories, were selected
consistent with the general definition of the supply chain management, specifically
focusing on the flow of material and information (Houlihan, 1985; Mentzer et al.,
2001a; Scott and Westbrook, 1991) and the interdependence, or relationships among
firms along the supply chain (Hult et al., 2002). The BCRC categories relevant to
material flow, information flow, and supply chain relationships are listed in table 20.
81
Table 20. BCRC Categories
Supply Chain Actions Market-Based Actions
Alliance Acquisition Marketing
Buildings and Facilities Advertising Marketing Agreements
Capacity Competition Mediation
Contracting Design and Construction Mergers
Customer Relations Divestment Negotiation
Distribution Downsize Organization Dissolution
E-Commerce Endorsements Organization Formation
Equipment and Supplies Environmental Policy Prices and Rates
Information Management Facility Closure Product Defects & Recalls
Inventory Franchise Product Discontinuation
Labeling Green Market Product Enhancement
Logistics Growth Product Introduction
Outsourcing Innovation Property
Packaging Investment Public Relations
Partnerships Investor Relations Remodeling
Product Development Joint Venture Renovation
Purchasing Labor Relations Reorganization
Quality Management Licensing Agreements Restructuring
Service Development Location Service Discontinuation
Storage Market Research Service Enhancement
Suppliers Market Share Service Introduction
Technology Market Size Target Marketing
Transportation
Warehousing

The use of pre-existing categories is advantageous because the classification
of articles is consistent throughout the BCRC database and facilitates replication.
One could argue that some supply chain management practices are absent from table
20. For example, common practices such as electronic data interchange (EDI),
vendor management, continuous replenishment, radio frequency identification
(RFID), category management, and efficient consumer response are not categories in
the BCRC. However, upon review of the articles in the pre-existing categories, the
supply chain management practices noted above were captured. The BCRC
categories Technology and Information Management include articles on EDI and
RFID programs. Similarly, the categories Suppliers and Partnerships include articles
documenting continuous replenishment and vendor programs. It was therefore
82
determined that the pre-existing categories in the BCRC were sufficient to capture the
supply chain activities of grocery retailers.

6.3.2. Market-Based Action Categories
A second coding scheme was developed for market-based actions. The
previous competitive dynamics research has used categories such as pricing,
promotion, marketing, and signaling to define market-based actions as shown in table
21.

Table 21. Market-Based Actions in the Literature
Market-Based Action Category Examples Study
Pricing Price Cuts
Fares
Ferrier, Smith & Grimm (1999)
Shaffer, Quasney, & Grimm (2000)
Chen & Hambrick (1995)
Mergers & Acquisitions Shaffer, Quasney, & Grimm (2000)
Chen & Hambrick (1995)
Services New Service
Service Improvement
Change in Service
Customer Loyalty Programs
Shaffer, Quasney, & Grimm (2000)
Chen & Hambrick (1995)
Products Airports
Airline Routes
New Products
Ferrier, Smith & Grimm (1999)
Shaffer, Quasney, & Grimm (2000)
Chen & Hambrick (1995)
Lee et al (2000)
Marketing Ferrier, Smith & Grimm (1999)
Promotion Advertising Chen & Hambrick (1995)
Market Expansion Capacity Addition
Vertical Integration
Entry/Exits
Ferrier, Smith & Grimm (1999)
Chen & Hambrick (1995)
Legal New Legal Actions Ferrier, Smith & Grimm (1999)
Signaling Intentions to Act Ferrier, Smith & Grimm (1999)

Signaling, as used in previous competitive dynamics research, focused on
announcements made by a firm which may or may not actually transpire. The
argument is that such overtures trigger a competitive response by rivals. A Signaling
category did not emerge in this research. In its place, however, is the category
83
Competition. The BCRC categories used to capture market-based actions in this
study are listed in table 20.
6.3.3. Extracting data from BCRC
Although the BCRC is a searchable on-line archive, the news articles cannot
be directly downloaded to a usable format. Therefore, a web-crawler program, Visual
Web Task 5.0, was used to extract the appropriate news articles from BCRC and
convert the information to a format that could be easily manipulated in a Microsoft
Access database. Visual Web Task (VWT) 5.0 takes user-defined criteria to search
an internet website, maps the hyperlinks of the search, and then extracts the
information to a user-defined format. With the BCRC as the target website, a
program was built in VWT 5.0 using NAICS 44511 and the United States as top-level
search criteria for the industry code and country. The inclusion of the United States
narrowed the population of potential articles from over 79,000 to approximately
33,000 during the time period in this study. Next, the BCRC category and year of
interest were included as variables to be changed each time the program was run.
The articles were downloaded in groups of 300 articles or less due to design
limitations of the VWT 5.0 software which distinguishes active and inactive
hyperlinks. While this size limitation slowed the process, there were several
advantages to extracting the articles in small groups. First, it was possible to assign
each BCRC category the articles as they were downloaded. The categories could not
be captured if all 33,000 articles were downloaded together. Second, accurate article
counts could be maintained. On occasion, the Visual Web Task program did not
execute properly, omitting several articles. This problem was addressed immediately.
84
Finally, and perhaps, most importantly, by extracting the articles in small groups it
was possible to review the headlines (titles) and ensure the articles accurately
reflected the category to which they were assigned.
The VTW 5.0 program extracted the article title, full text (when available),
publication, publication date, and article number (a unique article identifier). Upon
execution of each download, the applicable BCRC category and inclusive dates were
entered. The inclusive dates were tailored to ensure at most 300 articles were
returned. Once the VWT 5.0 program extracted the information, the file was saved in
an ASCII text format. The program was run 374 times to download 33,069 articles
reporting on supply chain and market based actions in the retail grocery industry.
Each of the 374 text files was prepared for direct import to a Microsoft Access
database, removing stray formatting characters and adding tab delimiting brackets
where needed to separate the information fields. Upon import to Microsoft Access,
each file was reviewed for accuracy using a rigorous quality control process. The
article count was verified and corrected when necessary. In some instances a whole
article or groups of articles were omitted for unknown reasons. These were manually
entered into the database using the cut/paste method. In other instances, only part of
an article was extracted. This was evidenced when the Article Number, a unique
number assigned by the BCRC, was dropped in the download process. Again, these
problems were addressed by manually entering the information into the database
using the cut/paste method.
85
6.3.4. Reliability
The content coding process detailed above relied heavily on electronic search,
using key word parameters rather than an in-depth review of each article. While,
content analysis often takes advantage of electronic search, a more active method of
coding has dominated the competitive dynamics literature. However, due to the large
volume of articles an in-depth review of each article was not possible. It was
therefore necessary to assess the reliability of the coding process and ensure the
categories assigned to each article in the keyword search accurately reflected the
content of the article. There were essentially two steps in assessing the reliability of
the article coding. The first step was ensuring consistency with which the articles
were categorized in the Business and Company Resource Center. The Thomson Gale
Business Development Group has a large editorial and technical staff that creates
taxonomies and automated indexing tools in order to ensure accurate and relevant
content. Therefore, there was a high level of assurance that the BCRC categories
were consistently applied to the journal articles (Gale, 2006). The second step to
ensure the BCRC categories accurately reflected the supply chain or market-based
activities this study was designed to measure. As noted, the articles were collected
incrementally which allowed for close scrutiny of the article content.
The article headlines were scanned during both the download and quality-
control processes. For the vast majority of the articles an accurate category
assignment was made based on the researcher's professional expertise in the field of
logistics and academic studies. However, four potential problems were identified for
resolution. First several articles were missing the full text. One hundred and forty-
86
one articles contained no information beyond the title and 801 articles contained an
abstract only. For these partial articles, the abstract or title were used to assign the
article to a firm, when specific firm information was provided therein. The manual
retrieval of the complete article is left for future research.
The second area of concern was the reliability of the supply chain category
Purchasing. The intent of the Purchasing category was to capture the supply-side
activities of the firm, such as vendor programs and other purchasing agreements
between buyers and the suppliers of goods and services. However, upon review of
this category of articles, it was determined that a majority of the articles did not
document buyer-supplier activities, but rather acquisition-related activities, such as in
the headline, “Kroger purchases 13 Food Town stores.” Each of the 288 articles
originally assigned to the Purchasing category was reviewed, resulting in the
recategorization of 155 articles.
The next area of concern was the duplication of articles in redundant
categories. While an article might be coded in multiple categories, it was necessary
that the categories be unique and, in fact, document distinct activities of the firm.
Through a series of queries to the database on the article number identifier, duplicate
articles were identified and the categories to which they were assigned were
reviewed. Two categories were deleted: Distribution Agreements and Shipment
Data. The articles in these categories were completely documented in the category
Distribution and determined not to be unique supply chain categories. All other
supply chain and market-based action categories were evaluated and found to be
unique, even when articles were classified in more than one category.
87
The final area of concern with the downloaded articles was the documentation
of foreign activities of U.S. firms. A search of the database identified three U.S.
grocery retailers, A & P, Safeway, and Wal-Mart, operating in foreign markets,
specifically Canada, the United Kingdom, Mexico, and Japan. One thousand, two
hundred and ninety-seven (1297) articles were marked as documenting overseas
activities. Each article was reviewed and 1053 articles were deleted from the
database.
6.4. Data Collection: Firm-Level Data
Firm-specific market share information, market area statistics, and regional
statistics were collected from The Marketing Guidebook and Market Scope. Total
population and total food sales were manually collected from The Marketing
Guidebook for each market area and entered into a Microsoft Access database for
each year in the study. The total food sales documented in The Marketing
Guidebook, however, also includes food sales at small grocery and convenience
stores. Therefore, supermarket sales as a percent of total food sales were collected
from Market Scope. Supermarket sales were then calculated in each market area.
Detailed market share information for all supermarkets operating in each
market area was collected from Market Scope based on check-out scanner data. The
same market definitions are used in both The Marketing Guidebook and Market
Scope, although Market Scope only publishes for the 48 contiguous markets.
Therefore, this study excluded Alaska and Hawaii in the analysis. In each of the 48
contiguous market areas, the following firm-level data was collected from Market
Scope for each year in the study:
88
1) Market share for each grocery retailer operating in each market area
2) The number of supermarkets each retailer operated in their respective area
3) The Supplier for each retailer
4) Advertising group market share
4

6.4.1. Extracting data from Market Scope
The market share and number of supermarkets for each firm in Market Scope
was published in tabular format, but not available electronically. Therefore the data
collection process required significant effort to convert the data to a usable electronic
format. To minimize errors in data entry, the process was automated to the greatest
extent possible with rigorous screening for quality control. Each market area in
Market Scope was electronically scanned using Readiris Pro 7.5 text recognition
software. Readiris Pro 7.5 converted each scanned page for export directly to
Microsoft Excel. While the accuracy of the converted text was very high,
typographical errors were still present. Therefore, each Excel worksheet was
carefully compared with the original, correcting typographical errors when needed.
Additionally, the number of supermarkets and market share values were double
checked for accuracy. With each Excel worksheet, the data was prepared for export
into a Microsoft Access database, using Visual Basic to move data to a single row for
each record. Further, the market share data was verified to ensure 100 percent in
each market area. This process resulted in 240 Excel worksheets, one for each market


4
Independent retailers may belong to a member-owned cooperative and operate under a common name
for the purpose of advertising (e.g., IGA and Piggly Wiggly) (Trade Dimensions, 2005).
89
area (48) and each year (5) in the study. These Excel worksheets were imported
directly to the Microsoft Access database.
6.4.2. Firm Names and Parent Corporations
With the firm-level information in the database, queries were used to
aggregate the data for each firm and check for consistency across years. For example,
“SaveRite” was changed to “Save Rite” in a particular year when all other entries
included the space. These changes were only made when there was a very high
probability that the entries referred to the same firm, such as when the firm location
and market area of operation was the same across all years. Prudent judgment was
also used to adjust firm names. For example, in 2000, “Lances New Market”
operated 9 supermarkets in the Indianapolis market area. In 2001 through 2004,
“Lances SuperValu Inc” operated 9 supermarkets in the Indianapolis market area. It
was assumed that these entries reflect the same firm, particularly since the
headquarters location was the same for both companies. Thus, the 2000 entry
“Lances New Market” was change to “Lances SuperValu Inc." If there was any
ambiguity in the firm name or doubt in ownership, further research was conducted
before making adjustments to firm names. This was because many distinct firms
have similar names in the retail grocery industry. For example, “Food Giant,” “Food
Giant Inc,” and “Food Giant Supermarkets Inc” are all separate firms. Hoover’s was
used to verify whether or not firms with similar names were distinct. By comparing
the firm location and the operating markets with those published in the Hoover’s
company profile, adjustments were made when appropriate. Company web sites were
also referenced, when available. A majority of the similarly named firms were
90
confirmed to be distinct. For the remaining few firms that could not be resolved the
ambiguous entries were kept unaltered and treated as separate firms.
Another problem arose due to changes in ownership and brand name
licensing. Through mergers and acquisitions, ownership of a firm may change
without necessarily a change in the brand name. For example, Shaw's Supermarkets,
Inc. was acquired by Albertsons, Inc in 2004, yet the Shaw's brand name was
retained. It was therefore necessary to clarify changes in ownership in order to
attribute sales to different parent corporations before and after the acquisition.
Furthermore, some brand names are licensed or franchised, such as “Save-A-Lot,”
“Cub Foods,” and “Piggly Wiggly.” Because these store names are licensed to many
different owners, it would be incorrect to aggregate all sales under the “Piggly
Wiggly” banner to one firm. To clarify ownership, the parent corporation was added
to the database using a list of parent corporations and subsidiaries published in the
Marketing Guidebook. This parent and subsidiary list was used to populate the
database. In some instances Hoovers was used to validate the information. The firm-
level data was aggregated to the corporate level when a clear parent corporation-
subsidiary relationship existed. Data for firms with no parent headquarters (e.g.,
wholly-owned firms) was left disaggregated. This resulted in 1,164 individual
organizations, though not all operated in each year of the study, as shown in table 22.
Table 22. Number of Grocery Retailers and Average Market Share by Year

Year
Number of
Firms*
Average
Market Share
2000 763 5.39
2001 783 5.23
2002 907 4.58
2003 836 5.00
*Note: Refers to Parent Corporations and Wholly-Owned Firms
91
6.4.3. Associating Articles with Parent Corporations
To determine the number of competitive and non-competitive actions enacted
by each parent corporation or wholly-owned firm, each article downloaded from the
BCRC was associated with each organization. A database query was used to search
the text (or title when the full text was not available) of each article for reference to
the parent corporation, its subsidiary, or each individual wholly-owned firm. Firm
ownership was carefully tracked due to franchise licensing and acquisition without
rebranding. For example, Fleming Co. and Kroger Co. both operated discount
grocery stores under the "Food 4 Less" banner. Furthermore, rebranding did not
always occur following an acquisition. For example, Hannaford Brothers was not
rebranded following their acquisition by Delhaize America, Inc. Similarly,
Albertson's, Inc. retained the Shaw's Supermarket brand name following the
acquisition of Shaw's Supermarket Inc. Therefore it was necessary to distinguish
between Parent A - Subsidiary A and Parent B – Subsidiary A by carefully
constructing the search parameters using logic operators (e.g., AND, OR, NOT) in the
SQL search statements. Article counts, by action category, were then assigned to
each parent corporation or wholly-owned firm and used to calculate the action
variables discussed in the next section. For simplicity in the discussion, parent
corporations and wholly-owned firms are generically labeled firm in the remainder of
the paper.
6.5. Model Specification and Variables
The hypotheses were characterized with direct relationships between the
supply chain and market-based actions and performance. These relationships were
92
tested using linear regression on the panel dataset shown in equation (14). The
dependent, independent, and control variables are operationalized in this section.
( )
0 1 2 3 4 1
5 6 7
8 9

_
it it it it it i t
it it it
it it
Y SCActions MBActions SDIV SC MB
Supermarkets MktServed Population
Wt HHI Year
? ? ? ? ?
? ? ?
? ? ?
+
= + + + +
+ + +
+ + +
(14)
The descriptive statistics and Pearson correlation coefficients for the key variables are
in table 23 and table 24, respectively.
Table 23. Descriptive Statistics
Mean Std. Deviation N
GROWTH $2,641,564,755 $58,687,498,893 2964
ROE -7.81 71.32 110
MB Actions 30.05 237.70 4128
SC Actions 11.20 70.47 4128
MBxSC 15,954.66 205,483.27 4128
SDIV 0.48 1.49 4128
Supermarkets 29.38 149.93 4128
MktServed 1.92 3.50 4128
Population 13,726,452 23,294,864 4128
Wt_HHI 1,402.13 563.72 4128

Table 24. Pearson Correlation Coefficients
1 2 3 4 5 6 7 8
1 GROWTH
2 ROE 0.04
3 MB Actions 0.27 ** 0.09
4 SC Actions 0.24 ** 0.13 0.93 **
5 SDIV 0.16 ** 0.11 0.55 ** 0.65 **
6 Supermarkets 0.31 ** 0.18 0.80 ** 0.80 ** 0.54 **
7 MktServed 0.42 ** 0.20 * 0.64 ** 0.71 ** 0.55 ** 0.76 **
8 Population 0.38 ** 0.19 * 0.61 ** 0.69 ** 0.55 ** 0.73 ** 0.96 **
9 Wt_HHI 0.02 0.21 * 0.03 ** 0.04 * 0.04 * 0.05 ** 0.05 ** -0.01
** Correlation is significant at the 0.01 level (2-tailed)
* Correlation is significant at the 0.05 level (2-tailed)

93
6.5.1. Dependent Variables
Firm performance is the primary outcome in this study. However, a
significant number of firms in the sample were privately owned and profitability
measures were not available. On the other hand, higher competitive activity has been
shown to result in market share gains (Ferrier et al., 1999). In addition, grocery
industry studies emphasize sales growth as a measure of success (Mathews, 2005).
Therefore, the primary measure of performance in this study was growth, measured as
the absolute change in sales. For a sub-sample of firms (N = 110), return on equity,
ROE, was used as a financial performance measure. Return on equity, often used in
the strategy research to measure profitability, was collected from COMPUSTAT.
Growth: Sales growth was measured as the absolute change in total annual
firm sales across all markets the firm operated between time t and t - 1. Total firm
sales was calculated for each year, t, by multiplying the firm’s share in each market,
m, with the total market area supermarket sales, aggregated over all markets in which
the firm operated, ( )
1
M
it imt mt
m
Total Sales MS SuperSales
=
= ×
?
. For parent corporations, total
sales were calculated as the sum of all subsidiaries. Growth, or the absolute change
in sales, was calculated as shown in equation (15).
( ) 1

it it i t
GROWTH Total Sales Total Sales
?
= ? (15)
6.5.2. Total Supply Chain and Market-Based Actions
The number of supply chain actions was defined as a count of articles
published in each supply chain category by a firm during each year of the study.
Therefore,
ijt
S was defined as the number of supply chain actions for firm i in BCRC
94
category j in year t. The total number of supply chain actions for firm i in year t is
given by equation (16). A summary of the supply chain action categories by year is
in appendix 6.
1
J
it ijt
j
SCActions S
=
=
?
(16)
Similar to the total supply chain actions, the total number of market-based
actions was measured by the aggregate of all BCRC market-based K categories
carried out by firm i in year t, and given by equation (17). A summary of the market-
based action categories is in appendix 7.
1
K
it ikt
k
MBActions M
=
=
?
(17)
The interaction of market-based and supply chain actions was measured by
multiplying the total number of supply chain actions with the total number of market-
based actions for each firm.
6.5.3. Supply Chain Action Diversity
Supply chain action diversity was measured as the inverse of the action
repertoire simplicity ratio used by Ferrier et al. (1999). Just as market-based action
categories served as the dimensions of action diversity in their work, supply chain
action categories were used in this study to capture the degree to which firms engage
in a broad range of supply chain activities. The inverse of the Ferrier et al. (1999)
measure was used because the intent was to capture diversity rather than simplicity.
The variable was calculated by taking the squared ratio of the number of actions in
95
each
j
supply chain category for firm i in year t and the total supply chain actions for
firm i in year t, summed over all J supply chain categories, as shown in equation (18).
By taking the inverse, larger values indicated that the firm engaged in activities in a
larger number of supply chain categories during year t.
( )
1
2
1
ijt
it
J
S
S it
j
SDIV
?
=
(
=
(
¸ ¸
?
(18)
The hypotheses predicted a positive relationship between the action variables
and sales growth or performance. The actions taken by a firm in the year 2000 would
then be associated with a growth in sales over the next year, between the years 2000
and 2001. Similarly, actions taken by the firm in year t were associated with return
on equity of the firm in year t + 1.
6.5.4. Control Variables
Firm size: Firm size has been shown to affect competitive action. Larger
firms, with greater resource endowments, often have a stronger resource position with
which to leverage competitive action (Grimm and Smith, 1997). However, inertial
forces may also induce a large firm to be complacent (Hannan and Freeman, 1984)
and hinder aggressive competitive actions. Chen and Hambrick (1995) found that, in
the U.S. airline industry, small firms were faster to initiate market-based actions than
larger firms. Whether this same relationship between firm size and propensity for
action holds for supply chain actions is unknown. However, many supply chain
actions involve large capital investment in infrastructure, equipment, and systems
96
which might tend to favor larger firms. Therefore, it is expected that firm size is
positively related to competitive actions and thus, firm performance.
Several different variables were considered to measure firm size. Total sales
volume is often used in the management literature as a measure of firm size, but sales
was already the main component of the dependent variable, GROWTH. Furthermore,
total sales provide information regarding the volume and scale of operations, but not
necessarily scope. The extent of operations between two firms, for example, may be
very different even when the annual sales for both firms are equal. One firm may
operate a few stores in several markets, while the other firm has greater penetration
with many stores in a single market. A similar argument might be made for the use
of total number of supermarkets, alone, as a measure of firm size, since this measure
was highly correlated with total sales. Instead, the total number of supermarkets
across all m markets and the total number of markets was used to better assess the
footprint of the firm. The total number of markets was calculated, as shown in (19),
where
imt
MktServed equaled 1 when firm i operated in market m in year t and 0
otherwise.
1
M
it imt
m
MktServed MktServed
=
=
?
(19)
Market Area Characteristics: Market conditions have a significant impact
on the structure of markets, the conduct of firms operating in that market, and
performance. Market area population was used to measure market size, one market
condition that affects the number of sellers. The total population potentially served
by each firm was calculated by aggregating the population for each market the firm
operated, as shown in (20).
97
( )
1
M
it imt mt
m
Population MktServed Population
=
= ×
?
(20)
Market Concentration: Market concentration was calculated for each of the
48 market areas in this study. Competition among grocery retailers occurs locally and
the 48 market areas used in this study were the most concise areas for which data was
available. These 48 market areas were mutually exclusive and consistently defined
across all 5 years in this study. The Herfindahl-Hirschman index (HHI) was
calculated based on market share, MS, for each firm, i, in each Market Area, m, and
each year, t. Concentration was calculated using a series of queries on the data
extracted from Market Scope. First, the market share for each firm was aggregated
within each market area for each year in the study. This was necessary because the
data in Market Scope was listed by supplier. When a firm had multiple suppliers in a
single market, the firm market share data was entered separately as it applied to each
supplier. The HHI was then calculated for each market as in equation (21).
2
1
I
mt imt
i
HHI MS
=
=
?
(21)

A total HHI could be calculated over all markets in which the firm operated, similar
to total population, however, such a measure would not capture the relative
importance of each market to the firm. Therefore, a weighted average of HHI was
calculated as shown in equation (22) based on the firm's share in each market.
( )
1
_
M
it imt imt mt
m
Wt HHI MktServed MS HHI
=
= × ×
?
(22)
98
6.6. Exploratory Analysis of Market-Based and Supply Chain Actions
The exploratory stage of the supply chain actions analysis investigated the
structure of the data with particular emphasis on the types of actions firm employed.
The objective of this investigation was to identify whether firms varied in the types of
actions they enacted and if so, how the different market-based and supply chain
action repertoires were related to firm characteristics such as firm size, growth, or
performance.
A multivariate technique that can help uncover an underlying structure in the
data is cluster analysis. The objective of cluster analysis is to classify objects, firms
in this case, within the population based on pre-determined identifying characteristics.
The result of the analysis is clusters of firms that exhibit greater homogeneity within
each group than between the groups. Cluster analysis is exploratory in nature and
therefore more descriptive than inferential. There is no statistical basis to compare
one clustering solution with another. In fact, clustering solutions are not unique and
highly dependent upon the clustering variables and cluster methods (Hair et al., 1998)
even within the same dataset (Aldenderfer and Blashfield, 1984). Despite a lack of
theoretical underpinnings, cluster analysis is a useful technique to uncover patterns
that may later be used for more rigorous statistical analysis.
There are four essential components of the cluster analysis: 1) determining
the clustering method, 2) defining the clustering variables which represent the
characteristics on which firms are to be compared, 3) determining the appropriate
similarity measure for which observations are compared, and 4) determining the
number of groups to form that result in relatively homogeneous clusters.
99
Agglomerative Clustering Method: The clustering algorithm used to assign
cluster membership was the hierarchical agglomerative Ward's method, where all
observations begin in individual groups. In each step of the analysis, observations are
permanently linked, based on the similarity measure, such that the within-group error
variance is minimized. The step-wise approach continues until all observations are
assigned to a pre-determined number of clusters (Hair et al., 1998). The hierarchical
agglomerative method is the most frequently used clustering method and results in
non-overlapping groups. Another clustering method is the non-hierarchical approach,
but requires the number of groups a priori, and therefore, deemed not appropriate.
One limitation of the hierarchical method is that once an observation is linked in a
cluster the observation cannot be reassigned latter in the partitioning process
(Aldenderfer and Blashfield, 1984). Thus, an observation that appeared very similar
to other members in a group when it was originally assigned could, in fact, be very
dissimilar to other cluster-members upon completion of the clustering procedure.
Clustering Variables: Central to cluster analysis is the cluster variate, the set
of variables used to compare objects and determine group membership. In this
exploratory analysis, the action variables form the cluster variate. The disaggregated
categories used to identify supply chain or market-based actions were too numerous
to effectively group firms. Therefore, these action categories were aggregated on two
different levels. At the highest level of aggregation, the total number of market-based
actions and supply chain actions served as the first cluster variate. The second level
of aggregation formed a set of ten action categories, three supply chain categories and
seven market-based categories. These ten action categories were essentially the same
100
categories used to identify the relevant subdivisions in the BCRC database. The
supply chain actions were categorized as those firm activities relating to the material
flow, information flow, and supply chain relations as discussed in section 5.2.1 (see
table 26) (Mentzer et al., 2001a; Scott and Westbrook, 1991). The market-based
actions were categorized based on prior research in the competitive dynamics
literature. The market-based action categories used in prior research include
promotion, marketing, market expansion, pricing, products, services, and signaling
(Ferrier et al., 1999; Smith et al., 2001). These same categories were used in this
study, for the mid-level aggregation, with some minor adjustments. First, the number
of actions in the Product and Services categories was relatively small compared to
other categories. Furthermore, the actions identified as Innovations were also small
in number (777 firm actions) and captured mainly product and service innovations
made by the firms. Therefore, Products, Services, and Innovations were combined to
form a single category. The second adjustment was to replace the Signaling category
used in prior research with a category labeled Competition. The articles in this
category documented various methods firms use to compete or leverage a competitive
advantage. The last category added as a cluster variable was Organizational Change.
This category included the internal actions of the firm associated with acquisitions,
joint ventures, and restructuring. This category was delineated for two main reasons.
First, the total number of market-based actions (124,045), which included those
identified as organizational change actions (40,322), significantly out-numbered the
total number of supply chain actions (46,250) carried out by the firms in the dataset
(see table 25). Distinguishing Organizational Change as a separate category
101
provided more balance among the clustering variables. More importantly, however,
organizational theorists contend that organizational factors, such as decision-making
and internal structure, are important determinants of firm performance and differ
significantly among firms. It is such firm heterogeneity that provides the foundation
for unique internal capabilities and helps explain differences in performance beyond
industry and other economic factors (Hansen and Wernerfelt, 1989). The BCRC
categories associated with each clustering variable are listed in table 26 along with
descriptive statistics.
Table 25. Aggregate Action Categories
Clustering Variable
N Min Max Total Mean SD
MB Actions* 655 0 3,195 83,723 127.82 389.62
SC Actions 655 0 1,360 46,250 70.61 164.73
Org Change Actions 655 0 2,160 40,322 61.56 204.59
* Market-based actions exclude organizational change activities

102
Table 26. Clustering Variables and Descriptive Statistics
Clustering
Variable BCRC Categories N Min Max Total Mean SD
Advertising
Endorsements
Licensing Agreements
Promotion
Public Relations
655 0 125 2,956 4.51 15.51
Green Market
Market Research
Marketing
Marketing Agreements
Marketing
Target Marketing
655 0 1,300 43,548 66.49 191.40
Market Share
Market Size
Market
Expansion
Growth
655 0 270 7,292 11.13 36.20
Pricing
Prices and Rates
655 0 360 7,526 11.49 37.09
Competition
Competition
655 0 360 6,469 9.88 33.74
Innovation
Service Development,
Enhancement, Introduction
Service Discontinuation
Product Defects & Recalls
Product Discontinuation,
Development, Introduction
Product &
Service
Innovations
Product Enhancement
655 0 230 4,888 7.46 24.92
Acquisition, Mergers
Divestment, Downsize
Joint Venture
Organization Formation
M
a
r
k
e
t
-
B
a
s
e
d

A
c
t
i
o
n

C
a
t
e
g
o
r
i
e
s

Organizational
Change
Reorganization, Restructuring
655 0 2,160 40,322 61.56 204.60
Buildings and Facilities
Capacity
Distribution
Equipment and Supplies
Inv, Labeling, Packaging
Logistics, Transportation
Materiel Flow
Warehousing, Storage
655 0 770 27,146 41.44 91.40
E-Commerce
Information Management
Information
Flow
Technology
655 0 175 5,721 8.73 22.13
Alliances, Partnerships
Contracting, Outsourcing
Purchasing
Quality Management
Suppliers
S
u
p
p
l
y

C
h
a
i
n

A
c
t
i
o
n

C
a
t
e
g
o
r
i
e
s

Relationships
Customer Relations
655 0 565 12,591 19.22 56.73

103
The clustering variables were measured as a percent of the total, rather than
quantity, as shown in equation (23). This was done to shift the emphasis from the
sheer magnitude of firm actions toward the relative combination of actions.

%_

it
it
it
Number of Articles in Action Category
Action Category
Total Number of Articles
= (23)
Simply a function of size, larger firms with larger resource endowments tended to
enact more competitive actions than smaller firms. The clustering variables measured
as simple action counts only magnified this size effect. The objective of this
exploratory study, however, was to examine the manner in which firms divide their
effort among competitive and non-competitive activities. For example, two firms
with a significant difference in the sheer number of actions, but yet, equally divide
their activities between market-base and supply chain actions, would most likely be
assigned different clusters. On the other hand, if the clustering variables were defined
as the percent of market-based and supply chain actions, these firms have a higher
probability of being grouped together identifying a balanced approach to competitive
actions as the key clustering characteristic.
Table 27. Action Categories as a Percent of Total Firm Actions
Clustering Variable
(Percent of Total Actions) N Min Max Mean SD
MB Actions* 655 0 1.00 0.26 0.32
SC Actions 655 0 1.00 0.64 0.39
Org Change Actions 655 0 1.00 0.10 0.19
* Market-based actions exclude organizational change activities

Cluster Similarity Measure: In assessing the underlying structure of the
data, cluster analysis techniques identify similar observations and place them into
groups. Similarity between observations can be measured in terms of distance,
104
correlation, or association. Distance measures assess the proximity of the
observations in n-dimensional space and, therefore, are most often used when the
magnitude of the clustering value is emphasized. Correlation measures of similarity
examine the patterns, rather than the magnitude of the clustering variables. Using this
type of similarity measure, the observations within each cluster would be more highly
correlated than the observations in different clusters. Finally, association measures of
similarity are used for non-metric variables.
In this analysis the Pearson correlation coefficient was used to assess
similarity among the firms. A correlation measure was chosen over a physical
distance measure for the same reason the clustering variables were measure as the
percent of the total number of actions. A distance measure of similarity would
emphasize the firm size effect rather than emphasize how the firms divide their
efforts between the different types of activities.
Dataset: A sub-sample of the database was used in the cluster analysis which
included only those firms with at least one action during the period of the study (N =
655). Cluster analysis was attempted on the entire dataset before deciding to limit the
sample to only those firms with at least one action. However, the large number of
observations with no action data tended to obscure the comparatively small number of
observations with only a few actions.
105
Chapter 7. Discussion – Supply Chain Actions
7.1. Panel Data Regression Results
The results of the regression analysis and exploratory study are discussed in
this chapter. With a cross-sectional time-series dataset, the assumptions necessary for
ordinary least squares (OLS) are often violated. Nevertheless, OLS regression was
performed with the inclusion of firm dummy variables and the key assumptions were
tested. The model was statistically significant with an F test statistic of 4.121 (p <
0.000). The interaction term was tested by examining the incremental increase in R
2
.
While the change in R
2
was small, R
2
= 0.001, it was statistically significant at the 10
percent level (p < 0.058), providing support for inclusion of the interaction between
market-based actions and supply chain actions (MBxSC) in the model. The results
are reported table 28. Heteroskedasticity was detected in a scatter plot of the
standardized residuals and standardized predictor variables. Attempts to transform
the data failed to correct this heteroskedasticity. Additionally, negative
autocorrelation was present in the dataset with a Durbin-Watson statistic of 2.58.
Classic OLS regression also assumes that the observed values of the regressor
variables are determined independent of the dependent variable and thus uncorrelated
with the error term. The potential for correlation between the regressor variables and
error term is higher in a panel dataset due to multiple observations of the same firm.
Further, variations within a firm over multiple time periods cannot be accurately
captured in an OLS regression which only models between-group variations. The
addition of firm dummy variables attempts to capture the unobserved firm
106
heterogeneity, but may be inefficient. Therefore, fixed-effects and random-effects
models were estimated.
The application of a fixed-effects or random-effects model depends on the
assumptions made regarding the error term. With a fixed-effects model, the
unobserved firm effect captured in the error term is assumed to be correlated with the
predictor variables and time invariant. When the unobserved firm component in the
error term is uncorrelated with the independent variables, the model can be specified
with random-effects (Greene, 2003). Table 28 reports the results of the fixed- and
random-effects models.
Table 28. Regression Models for Growth as Dependent Variable
OLS
1
Fixed-Effects Random-Effects
Growth ß t ß t ß z
SC Actions 1.13E+08 2.33 * 1.13E+08 2.33 * -2.80E+08 -6.11 ***
MB Actions 4.54E+07 2.19 * 4.54E+07 2.19 * 4.87E+07 3.22 ***
MBxSC 3.36E+04 1.90 † 3.36E+04 1.90 † 46056.76 3.14 **
SDIV -1.70E+09 -1.09 -1.70E+09 -1.09 -2.07E+09 -1.92 †
Supermarkets 2.97E+08 3.68 *** 2.97E+08 3.68 *** -1.97E+07 -1.53
MktServed 9.10E+08 0.18 9.10E+08 0.18 1.18E+10 10.94 ***
Population -9.54E+02 -1.23 -9.54E+02 -1.23 -5.30E+02 -3.48 ***
Wt_HHI 5.34E+05 0.10 5.34E+05 0.10 -1.72E+06 -0.90
yr2000 3.07E+08 0.12 3.07E+08 0.12 -5.08E+09 -2.01 *
yr2001 2.35E+09 0.91 2.35E+09 0.91 -2.06E+09 -1.03
yr2002 1.78E+09 0.74 1.78E+09 0.74 -1.19E+09 -0.48
Constant -2.58E+08 -0.01 5.97E+08 0.06 -6.09E+10 -1.76 †



N 2964 2964 2964
R
2
0.67 0.06 0.21
? R
2
0.001 †
F 4.12 *** 16.27 ***
?
2
629.79 ***
Durbin_Watson 2.58
† < 0.1
*< 0.05
**< 0.01
***< 0.001
1. OLS regression included firm dummy variables (not reported)
107
The Hausman specification test was performed to asses which model, fixed or
random, was most appropriate for the data. The Hausman specification test specifies
the null hypothesis as the difference in the coefficients from the fixed- and random-
effects models with the assumption that the regressor variables and error term are
uncorrelated. The test statistic,
2
?
, was 1666.25 (p-value < 0.000), therefore the null
hypothesis was rejected that the fixed- and random-effects models were equal, in
favor of the random-effects model. The Beusch-Pagan Lagrange Multiplier test,
however, still detected heteroskedasticity in the data. The null hypothesis of equal
error variance (homoskedasticity) in the random-effects model was rejected with a
2
?
of 674.91 (p-value < 0.000).
To correct the problems with autocorrelation and heteroskedasticity, the
model was transformed using generalized least squares. It was assumed that the
structure of the error term across the panels was heteroskedastic (based on the
Beusch-Pagan Lagrange Multiplier test) and uncorrelated (based on the Hausman
specification test). Estimating the autocorrelation coefficient, ? , based on the
Durbin-Watson statistic, the transformed model was calculated taking the difference
between each observed value and the once-lagged value multiplied by ? , shown in
(24), as recommended by Pindyck and Rubinfeld (1998). The resulting error term
satisfies the assumptions of homoskedasticity with no autocorrelation.
( ) ( )
( )
( )
( )
1 1 1 it it it i t i t i t
y y x x ? ? ? ? ??
? ? ?
? = ? + ? (24)
The results of the generalized least squares regression are in table 29. Observations
(N = 156) with data in only 1 year were dropped from the estimation, since a lagged
108
value could not be calculated. The model was statistically significant with a
2
?
test
statistic of 884.49 (p-value < 0.000).
Table 29. Generalized Least Squares
GLS – Growth
1
GLS – ROE
1

Variable ß z ß z
SC Actions 7.08E+07 2.94 ** 0.009 0.44
MB Actions 2.68E+07 2.62 ** 0.003 0.43
MBxSC -12.29E+03 -0.40 -6.02E-06 -1.00
SDIV -2.05E+09 -16.11 *** 0.410 0.34
Supermarkets -5.46E+07 -4.70 *** 0.005 0.62
MktServed 9.68E+08 4.10 *** -0.711 -0.44
Population -42.5 -2.45 * 1.10E-07 0.47
Wt_HHI -3.73E+05 -3.52 *** 0.008 0.77
yr2000 -4.15E+08 -4.36 *** 5.731 0.79
yr2001 3.58E+08 4.46 *** 5.231 0.81
yr2002 3.58E+08 6.46 *** 5.466 0.94
yr2003 2.153 0.50
Constant 1.33E+08 0.54 -14.689 -0.84

N 2808 109
?
2
885 *** 5.21
LL - 64315 -464.6
* < 0.05
** < 0.01
*** < 0.001
1. 156 observations dropped with only 1 observation in the group

The first set of hypotheses predicted a positive relationship between the total
number of supply chain and market-based actions and performance, as measured in
terms of sales growth and return on equity (ROE). Hypothesis 1 was partially
supported. The results in table 29 indicate that higher numbers of supply chain
actions do result in higher sales growth (H1a) (p-value < 0.01), but not ROE (H1b).
This supports an objective to reduce costs through supply chain management
practices. In particular, the implementation of efficient consumer response programs
by the grocery retailers in this sample was shown to positively impact sales growth.
While there was no support for the positive impact of supply chain activities on
profitability, this may be due to the small sub-sample of firms (N = 110) for which
109
financial performance data was available. In fact, none of the hypotheses regarding
the relationship between competitive or non-competitive actions and ROE were
supported.
It was expected that aggressive market-based actions would be positively
related to performance. Hypothesis 1c was supported; the higher the competitive
activity of the firm, as measured in terms of the number of market-based actions, the
greater the sales growth (p-value < 0.01). Thus aggressive competitive activity, such
as marketing, pricing, and product/service innovations, can result in performance
benefits even in a highly competitive industry like the retail grocery industry.
Hypotheses 2a and 2b predicted that firms engaged in a broader variety of
supply chain activities would realize higher performance gains. Supply chain
diversity (SDIV) was statistically significant (p-value < 0.001) for sales growth, but
was in the opposite direction hypothesized. Higher levels of supply chain diversity
resulted in a decline in sales or negative sales growth, for the firms in this study. This
is inconsistent with a systems-view of the supply chain, where emphasis in only a few
functional areas can result in suboptimization. This may suggest that investment in a
wide range of supply chain activities is less effective in the retail grocery industry.
Given the high level of competition and narrow profit margins that characterize the
industry, grocery retailers may benefit more by focusing their efforts on a few cost
saving supply chain activities rather than diversifying. This result, coupled with the
strong relationship between the total number of supply chain actions and sales
growth, suggests that heavy emphasis in a few key areas yields the greatest benefits.
No support was found for performance benefits in terms of ROE (H2b).
110
Finally, hypotheses 3a and 3b predicted that the interaction of supply chain
and market-based activities was positively related to sales growth (H3a) and ROE
(H3b). Neither hypothesis was supported. While the OLS regression supported
inclusion of the interaction term with a significant change in R
2
, the percent of
variance in the dependent variable attributed to the interaction term was very small
(R
2
= 0.001). Thus, the impact of market-based actions on sales growth is not
necessarily enhanced by higher levels of supply chain activity. The inclusion of the
interaction term in the model does, however, alter the interpretation of the coefficients
for the supply chain and market-based actions. That is, with the interaction term
included, the coefficient for supply chain actions estimates the conditional
relationship with sales growth when market-based actions equal zero, and visa versa.
Omission of the interaction term did not change the overall results, but did strengthen
the main effects for supply chain (p-value < 0.001) and market-based actions (p-value
< 0.001).
7.2. Cluster Analysis Results
The exploratory study examined whether different sets of actions can be
attributed to higher performance. A sub-sample of the database was used which
included only those firms with at least one action during the period of the study (N =
655). Cluster analysis was attempted on the entire dataset before deciding to limit the
sample to only those firms with at least one action. However, the large number of
observations with no action data tended to obscure the comparatively small number of
observations with only a few actions.
111
To move away from the size effect in which no distinguishing strategies
emerged, the percent of the total number of actions in each action category was used
to cluster the observations. Three sets of clustering variables were used, each on the
sample subset of firms with at least one action during the study period (N=655).

Analysis A) Percent market-based actions and percent supply chain actions.
Analysis B) Percent of the total in each action category:
- Percent promotion actions
- Percent market expansion actions
- Percent product and service innovation actions
- Percent marketing actions
- Percent pricing actions
- Percent competition actions
- Percent relationship actions
- Percent materiel flow actions
- Percent information flow actions
- Percent organizational change actions

Analysis C) Percent market-based actions (re-specified to exclude organizational
change actions), percent supply chain actions, and percent organizational
change actions.

7.2.1. Cluster Analysis A and B
The first two approaches are shown in figure 5 and figure 6. In analysis A, the
clustering variables were the two main actions categories, market-based and supply
chain, measured as a percent of the total number of actions for each firm, in each
year. In analysis B, the clustering variables were the ten action categories defined in
Table 26, also measured as a percent of the total number of actions for each firm, in
each year.
112
Analysis A and B demonstrate that group profiles are dependent upon the
cluster variate. In Analysis A, group A1 is the largest group with 374 observations
(see figure 5). These firms focused nearly all of their effort on supply chain
activities. On the other hand, for the next largest group (A2) approximately 80
percent of the actions were market-based with some emphasis on supply chain
activities. The last group, A3, was balanced between market-based and supply chain
actions. When the cluster variate was changed for Analysis B (10 action categories),
the cluster profile in the three-group solution was distinctly different, as shown in
figure 6. Groups B1 and B2 were similar with a dominant focus: Group B1
emphasized mainly supply chain actions, while group B2 emphasized market-based
actions. The third group, however, in analysis B was no longer a balanced group.
Rather, group B3 was also heavily invested in supply chain activities.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
MB Actions SC Actions
Group Average
P
e
r
c
e
n
t
Group A1 (N = 374) Group A2 (N = 256) Group A3 (N = 25)

Figure 5. Analysis A: 3-Group Solution – Cluster Variate = MB and SC Actions

113
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
MB Actions SC Actions
Group Average
P
e
r
c
e
n
t
Group B1 (N = 363) Group B2 (N = 235) Group B3 (N = 57)

Figure 6. Analysis B: 3-Group Solution – Actions Profile


A closer examination of the 10 action categories in figure 7 shows that the two
supply chain groups (B1 and B3) differ in terms of their supply chain focus. Group
B1 emphasized materiel flow actions (e.g., distribution, transportation, and
warehousing) while group B3 emphasized supply chain integration activities related
to information flow and supply chain relationships. In analysis A, the supply chain
integration group was replace with Group A3 which balanced marketing and
organizational change actions with materiel flow actions (see figure 8).
114
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
C
o
m
p
e
t
i
t
i
o
n
I
n
f
o
F
l
o
w
M
a
r
k
e
t
E
x
p
a
n
s
i
o
n
M
a
r
k
e
t
i
n
g
M
a
t
F
l
o
w
O
r
g
C
h
g
P
r
i
c
i
n
g
P
r
o
d
S
e
r
v
I
n
n
o
v
P
r
o
m
o
t
i
o
n
R
e
l
a
t
i
o
n
s
h
i
p
s
Group Average
P
e
r
c
e
n
t
Group B1 (N = 363) Group B2 (N = 235) Group B3 (N = 57)

Figure 7. Analysis B: 3-Group Solution – Cluster Variate = 10 Action Categories

0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
C
o
m
p
e
t
i
t
i
o
n
I
n
f
o
F
l
o
w
M
a
r
k
e
t
E
x
p
a
n
s
i
o
n
M
a
r
k
e
t
i
n
g
M
a
t
F
l
o
w
O
r
g
C
h
g
P
r
i
c
i
n
g
P
r
o
d
S
e
r
v
I
n
n
o
v
P
r
o
m
o
t
i
o
n
R
e
l
a
t
i
o
n
s
h
i
p
s
Group Average
P
e
r
c
e
n
t
Group A1 (N = 374) Group A2 (N = 256) Group A3 (N = 25)

Figure 8. Analysis A: 3-Group Solution – Actions Profile

Firms that engaged in mainly market-based activities (groups A2 and B2)
tended to be larger firms, in terms the number of supermarkets and market areas
served and realized higher than average sales growth (see table 30). There was no
evidence of higher performance for firms engaged in supply chain activities (groups
A1, B1, and B3) or those with a balanced approach (group A3).
115
Table 30. Analysis A&B 3-Group Solution – Characteristics and Performance
Percent Standardized Values
Analysis
(Group Size) Description
MB
Actions
SC
Actions
Total
Sales
Number
Supers
Markets
Served Growth
A1 (N = 374) SC 1 0.05 0.95 0.10 0.20 0.29 0.00
A2 (N = 256) MB 0.81 0.19 1.57 1.63 1.69 0.59
A3 (N = 25) Balanced 0.50 0.50 -0.03 0.04 0.04 -0.03

B1 (N = 363) SC 1 0.12 0.88 0.11 0.24 0.34 0.00
B2 (N = 235) MB 0.81 0.19 1.70 1.72 1.77 0.63
B3 (N = 57) SC 2 0.06 0.94 -0.02 0.04 0.05 0.03

Number of Clusters: Because cluster analysis is exploratory, there are no
objective guidelines or statistical criterion to determine the number of clusters to
form. There are ad hoc procedures, but these are generally applied when distance
measures are used to define cluster membership. Even with these ad hoc procedures,
the number of clusters to form is highly subjective. In this study, a range of three to
six cluster solutions was calculated for each analysis (A through C). From a practical
point, fewer clusters are easier to communication the distinguishing characteristics.
As a minimum, three clusters seemed reasonable, with one group emphasizing
market-based actions, one group emphasizing supply chain actions, and at least a
third group with some other action repertoire. Each n-cluster solution was examined
to see if the cluster variables resulted in distinguishable groups. Firm attributes, such
as the total sales, total number of supermarkets, and the number of markets served,
along with firm performance measures were also examined to understand how the
clusters varied on these measures. The best alternative was selected when the
addition of a cluster resulted in a new group of firms with a distinctly different action
profile.
116
N-group solutions: A 4-group, 5-group, and 6-group solution did not emerge
in analysis A, with only one observation was assigned to the fourth, fifth, or sixth
group, respectively. Therefore, when the percent of market-based actions and percent
to supply chain actions were used as the clustering variables, three primary groups
emerge, a supply chain group, a market-based group, and a balanced group (figure 5).
This was not the case in Analysis B, where the cluster variate was comprised
of the ten action categories in table 26. In the 4-group solution, two supply chain
groups and two market-based groups emerged, each emphasizing different types of
actions, as shown in figure 10. The two supply chain groups were unchanged in the
4-group solution compared with the 3-group solution, as shown in figure 9. The firms
emphasizing market-based activities, however, now formed two distinct groups.
Group B2 activities were dominated by organizational change actions (40%),
followed by marketing actions (20%). Group B4, on the other hand, emphasized
mostly marketing actions (55%).
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
C
o
m
p
e
t
i
t
i
o
n
I
n
f
o
F
l
o
w
M
a
r
k
e
t
E
x
p
a
n
s
i
o
n
M
a
r
k
e
t
i
n
g
M
a
t
F
l
o
w
O
r
g
C
h
g
P
r
i
c
i
n
g
P
r
o
d
S
e
r
v
I
n
n
o
v
P
r
o
m
o
t
i
o
n
R
e
l
a
t
i
o
n
s
h
i
p
s
Group Average
P
e
r
c
e
n
t
Group B1 (N = 363) Group B2 (N = 121) Group B3 (N = 57) Group B4 (N = 114)

Figure 9. Analysis B: 4-Group Solution – Cluster Variate = 10 Action Categories

117
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
MB Actions SC Actions Group Average
P
e
r
c
e
n
t
Group 1 (N = 363) Group 2 (N = 121) Group 3 (N = 57) Group 4 (N = 114)

Figure 10. Analysis B: 4-Group Solution – Actions Profile
With this result greater consideration was given to the treatment of
organization change as an action category. Previous research has included activities
such as acquisition, mergers, and reorganization as market-based actions (Chen and
Hambrick, 1995). This is consistent with the organizational theory of adaptation
where firms make organizational structure changes to adapt to changing or uncertain
environmental factors (Hannan and Freeman, 1984). While mergers or divestment
may signal to competitors a firm’s intent to expand to new markets or close less
profitable ones, organizational change actions also capture internal managerial
actions, such as organizational learning and decision-making (Hansen and Wernerfelt,
1989). It is reasonable, then to redefine the top-level action categories in this
exploratory phase, with organizational change as a distinct category from all other
market-based actions. In cluster analysis C, organizational change actions were
considered as a separate category. The cluster variate was defined as the percent of
the total firm actions in three main categories: supply chain actions, market-based
118
actions, and organizational change actions. The market-based actions were re-
specified to exclude all organizational change activities.
7.2.2. Cluster Analysis C
The 3-, 4-, and 5-group solution for cluster analysis C are depicted in figure
11 through figure 13. Three distinct groups, each emphasizing a different action
category emerged in the 3-group solution shown in figure 11. The three groups were
characterized as a supply chain group, a market-based group, and an organizational
change (or internal action) group. These groups, however, were characteristically
different from the three groups formed in analysis A which did not include
organizational change as a clustering variable. Specifically, the balanced market-
based and supply chain group in analysis A (group A3) did not emerge in the 3-group
solution for analysis C.
0
0.2
0.4
0.6
0.8
1
1.2
MB Actions (Respec) SC Actions Org Change
Group Average
P
e
r
c
e
n
t
Group C1 (N = 369) Group C2 (N = 236) Group C3 (N = 50)

Figure 11. Analysis C: 3-Group Solution – Cluster Variate = MB, SC, and Org
Change Actions

119
This balanced group, however, did emerge in the 4-group solution for
Analysis C, shown in figure 12. In the 4-group solution, the supply chain (C1) and
organizational change (C3) groups were unchanged. The market-based action group,
which accounted for 236 firms in the 3-group solution, however, was reduced in size
to 197 firms in the 4-group solution. The remaining 39 firms formed a fourth group
(C4) with a balanced 50/50 approach to market-based and supply chain actions.
Viable 5- and 6-group solutions also formed, each eroding the market-based action
group (C2), and forming relatively small new groups. In the 5-group solution, a
group (N = 25) formed emphasizing 40% of their effort in market-based actions and
40% in organizational change actions. To complement this, a sixth group emerged in
the 6-group solution (N = 15) emphasizing 40% of their effort in supply chain actions
and 40% in organizational change actions (not depicted).
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
MB Action (Respec) SC Actions Org Change
Group Average
P
e
r
c
e
n
t
Group C1 (N = 369) Group C2 (N = 197) Group C3 (N = 50) Group C4 (N = 39)

Figure 12. Analysis C: 4-Group Solution – Cluster Variate = MB, SC, and Org
Change Actions

120
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
MB Action (Respec) SC Actions Org Change
Group Average
P
e
r
c
e
n
t
Group C1 (N = 369) Group C2 (N = 172) Group C3 (N = 50)
Group C4 (N = 39) Group C5 (N = 25)

Figure 13. Analysis C: 5-Group Solution – Cluster Variate = MB, SC, and Org
Change Actions

7.2.3. Performance and Descriptive Attributes
The group characteristics and performance averages are summarized in table
31 and table 32. A consistent result in all cluster analyses performed (A, B and C),
was the higher than average performance for market-focused firms, as shown in
previous research (Ferrier et al., 1999). These performance benefits vanished,
however, when firms split their action profile between market and supply chain
actions, as with group C4. There also appeared to be no performance advantage to
firms with a supply chain-only focus (C1) or firms with a high degree of
organizational change (C3). The exception was a slight performance advantage for
group C5, which emphasized market-based (40%) and organizational change (40%)
actions. While firms with a supply chain strategy (C1), organizational change
strategy (C3), or balanced strategy (C4) did not realize larger than average
performance benefits, these firms were not at a competitive disadvantage either.
121
These firms tended to converge to the middle with average sales growth during the
period of the study.
An interesting result of the exploratory study was with respect to firm size.
Organizational change often involves considerable cost in terms of the redistribution
of assets and personnel. Larger firms would be better equipped to absorb such costs.
While the organizational change-only firms (C3) were larger than average, the largest
firms in the study were those that coupled organizational change with market-based
actions (C5). These firms were significantly larger in terms of the number of
supermarkets and the markets served. The next largest group of firms was the group
focusing mainly on market-based actions. This is consistent with prior competitive
dynamics research finding larger firms with greater access to resources are able to
enact more competitive actions. On the other hand, small firms have been shown to
employ different strategies in order to compete effectively (Chen and Hambrick,
1995). In this study the strategy of mid-sized firms was distinctly different. Firms
with a strictly supply chain focus tended to be smaller and operate in fewer markets.
Table 31. Analysis C – Group Action Profile
Percent of Total Actions
Cluster Solution
(Group Size)
Description MB
1
SC Org Change
C1 (N = 369) SC 0.02 0.96 0.02
C2 (N = 236) MB
1
0.65 0.24 0.11
C3 (N = 50) Org Change 0.17 0.19 0.64
C1 (N = 369) SC 0.02 0.96 0.02
C2 (N = 197) MB
1
0.69 0.19 0.13
C3 (N = 50) Org Change 0.17 0.19 0.64
C4 (N = 39) Balanced MB
1
& SC 0.48 0.50 0.02
C1 (N = 369) SC 0.02 0.96 0.02
C2 (N = 172) MB
1
0.72 0.19 0.09
C3 (N = 50) Org Change 0.17 0.19 0.64
C4 (N = 39) Balanced MB
1
& SC 0.48 0.50 0.02
C5 (N = 25) MB
1
& Org 0.46 0.18 0.36
1. Market-based action respecified to exclude organizational change actions.
122
Table 32. Analysis C – Group Attributes and Performance Summary
Standardized Values
Cluster Solution
(Group Size) Description
Rank
Size
Total
Sales
Number
Supers
Markets
Served Growth
C1 (N = 369) SC 3 0.105 0.213 0.337 0.00
C2 (N = 236) MB
1
1 1.557 1.598 1.592 0.66
C3 (N = 50) Org 2 0.630 0.735 0.859 -0.05
C1 (N = 369) SC 3 0.105 0.213 0.337 0.00
C2 (N = 197) MB
1
1 1.848 1.873 1.813 0.79
C3 (N = 50) Org 2 0.630 0.735 0.859 -0.05
C4 (N = 39) Balanced MB
1
& SC 4 0.087 0.211 0.479 0.00
C1 (N = 369) SC 4 0.105 0.213 0.337 0.00
C2 (N = 172) MB
1
2 1.782 1.747 1.604 0.87
C3 (N = 50) Org 3 0.630 0.735 0.859 -0.05
C4 (N = 39) Balanced MB
1
& SC 5 0.087 0.211 0.479 0.00
C5 (N = 25) MB
1
& Org 1 2.297 2.735 3.250 0.24
1. Market-based action respecified to exclude organizational change actions.


7.2.4. Changes in Firm Strategies
Focusing on the 3-group solution in Analysis C, there was little change in the
group profiles when examined over each year of the study. Figure 14 through figure
16 show the three primary clusters: supply chain, market-based, and organizational
change. In the aggregate these groups remained relatively stable in terms of their
focus on a particular type of action. Examining the individual firms, the majority of
firms made no change in their strategy during the five year period. However, some
firms did change group membership. Thirty firms made one change in their action
repertoire. Most often these firms changed their strategic focus for one year and then
returned to their previous strategy. For other firms, the change was permanent
through the remainder of the study period. A very small number of firms switched
focus several times – nine firms changed their strategy twice and four firms changed
group membership three or more times.
123
Supply Chain Group (C1)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
MB1 SCActions OrgChg
P
e
r
c
e
n
t
C1 Yr 2000 (N = 64) C1 Yr 2001 (N = 48) C1 Yr 2002 (N = 76)
C1 Yr 2003 (N = 104) C1 Yr 2004 (N = 77)

Figure 14. Analysis C: Supply Chain Group

Market-Based Group (C2)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
MB1 SCActions OrgChg
P
e
r
c
e
n
t
C2 Yr 2000 (N = 45) C2 Yr 2001 (N = 38) C2 Yr 2002 (N = 47)
C2 Yr 2003 (N = 50) C2 Yr 2004 (N = 56)

Figure 15. Analysis C: Market-based Group

124
Organizational Change Group (C3)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
MB1 SCActions OrgChg
P
e
r
c
e
n
t
C3 Yr 2000 (N = 9) C3 Yr 2001 (N = 11) C3 Yr 2002 (N = 9)
C3 Yr 2003 (N = 10) C3 Yr 2004 (N = 11)

Figure 16. Analysis C: Organizational Change Group

7.3. Discussion
This study examined the relationship between firm performance and the
competitive and non-competitive activities of the firm using the Schumpeterian
perspective that firm action creates a rivalrous environment. The study examined
170,295 market-based and supply chain actions for 1,163 firms (parent corporations
or wholly-owned firms) documented in 33,000 articles over a five year period. The
results of the hypotheses testing are summarized in table 33.
Table 33. Summary of Results
GROWTH ROE
Total SC Actions H1a: Supported H1b: Not Supported
Total MB Actions H1c: Supported H1d: Not Supported
SC Diversity H2a: Opposite of Hypothesized Direction H2b: Not Supported
MB x SC H3a: Not Supported H3b: Not Supported

With respect to competitive actions, the results were largely consistent with
the previous research; grocery firms realized a higher growth in sales when engaged
125
in a larger number of market-based actions such as pricing, promotional, and
marketing activities. These benefits accrued even when factors such as firm size and
market concentration were taken into account. Additionally, a new category of action
was introduced in this study as a determinant of firm performance—supply chain
actions. The impact of supply chain activities on operational performance objectives
has been studied in the extant literature. Studies investigating the impact on financial
performance, however, are often limited to survey-based data and do not consider
other factors, such as market-based activities, that may account for performance
gains. These limitations were addressed in this study using secondary data and
market-related performance factors, finding that firms in the grocery industry did
realize a higher growth in sales when engaged in a higher number of supply chain
actions. The results suggest that supply chain activities provide financial
performance benefits in addition to the operational benefits often associated with
supply chain management.
Supply chain diversity was shown to be a liability in the grocery industry with
higher levels of diversity resulting in negative sales growth. Because some supply
chain activities require considerable capital investment, a few well chosen supply
chain activities might be the best way to expend limited resources in the grocery
industry.
The exploratory study provided insight to the different strategies firms
employed in the grocery industry. With respect to market-based actions, the results
of the exploratory study were consistent with the regression analysis. Firms
employing a competitive strategy focused on market-related activities realized higher
126
than average sales growth. When market-based actions were coupled with supply
chain actions in a balanced strategy, however, the higher-than-average performance
benefit vanished. While there was no clear competitive advantage to supply chain-
only or balanced strategies as a group, these firms did realize average levels of sales
growth compared to all firms in the dataset. This was not necessarily inconsistent
with the regression analysis. The positive relationship between supply chain actions
and sales growth found in the regression analysis captured the marginal contribution
of the total number of actions. This is not to say that those same firms did not also
engage in market-based activities. On the other hand, the cluster analysis considered
only the portfolio of actions, not the magnitude of actions.
The exploratory study found that large and mid-sized firms employed
different strategies in order to compete effectively in the marketplace. Large firms,
with greater access to resources, focused on market-related strategies and were
engaged in more organizational change actions. Mid-sized firms tended to compete
effectively by focusing on supply chain-only or balanced strategies.
7.4. Future Research
Considering the 10 disaggregated action categories were useful in the
exploratory study, a natural extension to the research is a more rigorous analysis of
the 10 action categories using the panel data statistical techniques. This might help to
understand whether the relationship between supply chain actions and performance
differs depending on the type of action, specifically internal and external actions. It
might also help explain the negative relationship between supply chain diversity and
sales growth. Furthermore, the exploratory study might provide the foundation to
127
examine specific interactions among the disaggregated actions. For example,
organizational change and marketing actions describe the firms in group B2 (see
figure 9). It would be interesting to examine how the interaction of organizational
change and marketing actions compares with marketing-dominated strategies (e.g.,
group B4, figure 9). Furthermore, firms that emphasized marketing actions also
committed some of their resources to material flow activities.
Another consideration not examined in this study was the lagged relationship
between supply chain actions and performance or sales growth. In this study both
types of actions, market-based and supply chain, were considered to affect
performance in the next time period. Specifically, actions in year t were hypothesized
to impact performance in year t + 1. However, many supply chain actions require
significant capital expenditures which might lengthen the payback period. Thus,
efficiency gains accrued through supply chain management programs may not
translate into immediate performance benefits. Future research should then consider
longer time lags between supply chain actions and performance, particularly
profitability.
7.5. Limitations
There were several limitations in this study which should be noted. This study
used a structured content method which relied heavily on electronic search and did
not independently code each article. Thus, while it is possible that a documented
action was mis-represented in this process, the consistency of the coding was
considered very high due to the expert indexing practices of Thomson Gale.
Furthermore, reliance on an external coding schema helped to reduce researcher bias.
128
Variable measurement might also limit the results of this study. The percent
change in sales as the dependent variable is a viable growth measure, but in this
sample it had much less variability than the absolute change in sales. To mitigate the
affect of firm size on the absolute change in sales, control variables were added. An
alternate approach, not investigated, might be to standardize all variables with respect
to firm size, thereby eliminating the need for size-related control variables. Finally,
some variables were highly correlated, such as market-based and supply chain
actions. While multi-collinearity did not appear to be a problem when examining the
variance inflation factors, the high correlation might imply the measurement of some
common firm characteristic. However, theoretical distinctions between market-based
and supply chain activities remain with the former aimed at capturing customers and
the latter geared toward cost-saving and efficiency goals, at least in the short term.
The small sample of firms with financial performance data severely limited
this study in terms of the impact of market-based and supply chain actions on
profitability. While profitability is also a function of cost, the inclusion of cost-
related factors, such as the cost of goods sold, did not change the results of the
analysis. Nevertheless, greater effort is needed to increase the number of firms with
financial performance data and to perhaps respecify the model in terms of inclusive
variables or variable measurement.


129
Appendices
Appendix 1. Derivation of Full (R, T) Policy
The total cost equation for the Full (R, T) policy is given in equation (5) and
rewritten in this appendix for clarity as equation (25).
( ) ( )
( )
| |
2

i i k i i k i
i i i
i k i
C nc TF
TC T PD G D P G D
T
K E X R
F P G S
T
+
= + + + +
>
+ + +
? ? ?
?
?
(25)

The order interval,
Full
T , in equation (26) is found by setting equal to zero the
first derivative of the total cost function with respect to T, as shown below, and
solving for T, where safety stock,
( )
ˆ
i i i T L
S R X
+
= ? .
( )
( )
( )
| |
( ) | | ( ) ( )
( ) ( )
( ) | | ( ) ( ) ( )
| |
2
2
1
1
1
2
2

2
0
i i k i i k i
T T
i i i
i k i
i i i i k i T T T T
i k i i i T
i i i i k i i k i T T
i i i T
C nc TF
PD G D P G D
T
TC T
K E X R
F P G S
T
TF
TC T C nc K E X R P G D
F P G R LX TX
F
TC T C nc K E X R P G D F P G X
C nc K E X R
? ?
? ?
? ? ?
? ? ?
?
?
?
?
+ (
+ + + +
(
( =
>
(
+ + +
(
¸ ¸
= + + > + +
+ + ? ?
= ? + + > + + ? +
= ? + + >
? ? ?
?
?
? ?
?
? ? ?
( ) ( ) ( )
2
i k i i k i
F
P G D F P G X + + ? +
? ? ?

| | ( ) ( ) ( )
2
2
2
i i i i k i i k i T
C nc K E X R F P G D F P G X + + > = + ? +
? ? ?

| | ( )
( ) ( )
2
2
2
i i i
Full
i k i i k i
C nc K E X R
T
F P G D F P G X
+ + >
=
+ ? +
?
? ?

130
| | ( )
( ) ( )
2
2
i i i
FULL
i k i i k i
C nc K E X R
T
F P G D F P G X
+ + >
=
+ ? +
?
? ?
(26)
The probability of a stockout for each item, i, is found by taking the first
derivative of the cost function for safety stock in equation (25) with respect to the
base stock level,
i
R , as shown below.
( ) ( )
( ) ( )
| |
( ) ( )
( )
( )
| |
( ) ( )
( ) ( )
ˆ
0
i
i i
i i i
i i i
i
i
i i i R
i i i
i i k i R R
K E X R
i i k i i T L R R R T
K
i k i i T
K
i i i k T
P X R TC S
K E X R
TC S F P G S
T
TC S F P G R X
F P G P X R
P X R F P G
?
?
? ?
? ?
>
? ? ?
+ ? ? ?
> =
( >
= + +
(
¸ ¸
= + ? +
= + ? >
> = +


( )
( )
i k
i i
i
TF P G
P X R
K
+
> = (27)
131
Appendix 2. Comparing Models: Full (R, T) and Truck (R, T) Policies
The total cost functions for the Full (R, T) policy, equation (5), and the Truck
(R, T) heuristic, equation (10), differ only in their transportation rates. The Full
policy uses the unit shipping rate,
k
G , from equation (4), corresponding to the
shipping quantity,
k Full i
Q T D =
?
. In the Truck heuristic, the truckload unit shipping
rate,
0
G , is used, corresponding to a shipment size equal to the truck capacity,
t
Q .
By redefining the transportation function,
k
G , it can be shown that the Truck (R, T)
heuristic is simply a special case of the Full (R, T) policy.
The transportation function for
k
G can be redefined by first noting that the
unit transportation rate varies from the minimum TL rate,
0
G , to the maximum LTL
rate,
1
G , such that
0 1 k
G G G ? ? . Let,
k
J be the additional cost in transportation (per
shipment) associated with shipping quantity
k
Q at a rate other than the TL rate,
0
G .
This can be written as, ( )
0 k k k
J Q G G = ? . For example, if the shipping quantity is
850 units, the appropriate shipping rate from table 3 is
( ) ( )
1000
2 0 850
3.00
t
Q
Q
G G = = ,
where
2
$3.529/ G unit = . The actual shipment cost for 850 units is ( )
2
850 G =
$3, 000 . However, if the 850 units could have been shipped at the lower TL rate, the
total shipment would have cost ( )
0
850 $2, 550 G = . The added cost for not shipping
all 850 units at the TL rate is ( ) ( )
0
850 3.527 3.00 $450
k k k
J Q G G = ? = ? = , or the
difference between the actual shipping cost ($3,000) and the cost had all units shipped
at the TL rate ($2,550).
132
The transportation function,
k
G , can then be rewritten in equation (28) as a
function of the TL rate and an added cost per unit associated with shipping any
quantity other than truck capacity.
0
k
k
J
k Q
G G = + (28)

k
J is a maximum value at the less-than-truckload weight break and a
minimum value( ) 0
k
J = when the shipping quantity equals the full truck capacity,
t
Q
(or a positive integer multiple of
t
Q ). It is now possible to replace the transportation
function,
k
G , in the total cost equation of the Full (R, T) policy with equation (28), as
shown below.
( )
( ) ( )
( )
| |
0 0
0
2

k k
k k
k
k
J J
Full
Full i i i i i Q Q
Full
J i i i
i i Q
Full
T F C nc
TC T PD G D P G D
T
K E X R
F P G S
T
+
= + + + + + +
>
+ + + +
? ? ?
?
?


Thus, when the shipping quantity,
k
Q , equals truck capacity, the added
shipment cost,
k
J , equals zero and the total cost function for the Full (R, T) policy
equals the total cost function for the Truck (R, T) heuristic.
133
Appendix 3. Visual Basic Module in Excel 2003
Option Base 1
Dim item_demand(10, 5) As Double '[item i][1] = annual demand
'[item i][2] = average daily demand (mean)
'[item i][3] = stdev of daily demand (stdev)
'[item i][4] = expected demand during L+T
'[item i][5] = stdev of expected dmd during L+T
Dim num_items As Integer 'Number of stock-keeping units
Dim num_factors As Integer 'Number of factors
Dim item_costs(10, 2) As Double '[item i][1] = purchase p, item i
'[item i][2] = shortage cost, item i
Dim item_levels(10, 5) As Double '[item i][1] = Base stock level, item i
'[item i][2] = safety stock level, item i
'[item i][3] = probability of stockout, item i
'[item i][4] = z-value, item i
'[item i][5] = expected stockout quantity, item i
Dim shortage_cost(10) As Double 'array for shortage cost per unit, factor levels
Dim shortage As Double 'assign from array for each iteration
Dim major_order_cost(3) As Double 'array for major order cost, factor levels
Dim major_order As Double 'assign from array for each iteration
Dim minor_order_cost(3) As Double 'array for minor order cost, line item cost, factor
levels
Dim minor_order As Double 'assign from array for each iteration
Dim holding_fraction(3) As Double 'array for holding fraction, factor levels
Dim holding As Double 'assign from array for each iteration
Dim mean_lead_time As Double 'average lead time
Dim stdev_lead_time As Double 'standard deviation of lead time
Dim truck_unit_capacity As Double 'in units (Qt)
Dim TL_unit_rate As Double 'truckload transportation rate per unit
Dim LTL_unit_rate As Double 'less-than-truckload transportation rate per unit
Dim unit_shipment_rate As Double 'unit shipping rate associated with order quantity Qk
Dim order_quantity_Qk As Double 'Total order quantity, Qk
Dim annual_purchase_cost As Currency 'total annual purchase cost
Dim annual_trans_cost As Currency 'total annual cost of transportation
Dim annual_order_cost As Currency 'total annual cost of ordering
Dim annual_holding_cost_cycle As Currency 'total annual holding cost of cycle stock
Dim annual_holding_cost_safety As Currency 'total annual holding cost of safety stock
Dim annual_holding_cost_total As Currency ‘total annual holding cost: cycle + safety stock
Dim annual_shortage_cost As Currency 'total annual shortage costs
Dim total_annual_inventory_cost As Currency 'total annual cost of inventory
Dim break1_lower, break1_upper, break2_lower, break2_upper As Double
Dim break3_lower, break3_upper, break4_lower, break4_upper As Double
Dim break5_lower, break5_upper, break6_lower, break6_upper As Double
Dim break7_lower, break7_upper, break8_lower, break8_upper As Double
Dim break9_lower, break9_upper As Double
Dim A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T As Integer 'columns
134

Dim factor, indexrows_a, indexrows_b, indexrows_c, indexrows_d As Integer
Dim index_i, index_j, index_k, index_p, index_l As Integer
Dim Graph_Qk As Long

Sub MainBaseModel() 'Main Program Routine 'Sets Input Parameters and Calls
'subroutines
indexrows_a = 2 'initialize to 2
nd
row for output
indexrows_b = 2
indexrows_c = 2
indexrows_d = 2
A = 1 'Set columns
B = 2
C = 3
D = 4
E = 5
F = 6
G = 7
H = 8
I = 9
J = 10
K = 11
L = 12
M = 13
N = 14
O = 15
P = 16
Q = 17
R = 18
S = 19
T = 20
num_items = Worksheets("Input Parameters").Cells(2, F).Value 'Set Number of Items
num_factors = Worksheets("Input Parameters").Cells(2, A).Value 'Set Number of Factors
rateschedule 'call sub-routine to set rate
'schedule
factor = 0

For index_i = 1 To num_factors 'set Major Order Cost
major_order_cost(index_i) = Worksheets("Input Parameters").Cells(index_i + 1, B).Value
major_order = major_order_cost(index_i)
For index_j = 1 To num_factors 'set Minor Order Cost
minor_order_cost(index_j) = Worksheets("Input Parameters").Cells(index_j + 1, C).Value
minor_order = minor_order_cost(index_j)
For index_k = 1 To num_factors 'Set Holding Fraction
holding_fraction(index_k) = Worksheets("Input Parameters").Cells(index_k + 1,D).Value
holding = holding_fraction(index_k)
For index_p = 1 To num_factors 'Set shortage unit Cost
shortage_cost(index_p) = Worksheets("Input Parameters").Cells(index_p + 1, E).Value
shortage = shortage_cost(index_p)
initialize 'Initialize variables
135
baseline 'Calculate BaseLine
Next index_p 'Select Next Shortage Unit Cost
Next index_k 'Select Next Holding Fraction
Next index_j 'Select Next Minor Order Cost
Next index_i 'Select Next Major Order Cost

Graph_Qk = 10 'graph transportation rates

For index_l = 1 To 10000
Worksheets("Graph_Rates").Cells(index_l + 1, A).Value = Graph_Qk
order_quantity_Qk = Graph_Qk
unitshipmentrate 'Get unit shipping rate
Worksheets("Graph_Rates").Cells(index_l + 1, B).Value = unit_shipment_rate
Worksheets("Graph_Rates").Cells(index_l + 1, C).Value = Graph_Qk * unit_shipment_rate
Graph_Qk = Graph_Qk + 10
Next index_l

End Sub

Sub initialize() 'Initialize variables

Dim item As Integer

factor = factor + 1 'full factorial design
Worksheets("Out_Base").Cells(factor + 1, A).Value = factor
Worksheets("Out_Base").Cells(factor + 1, B).Value = major_order
Worksheets("Out_Base").Cells(factor + 1, C).Value = minor_order
Worksheets("Out_Base").Cells(factor + 1, D).Value = holding
Worksheets("Out_Base").Cells(factor + 1, E).Value = shortage

For item = 1 To num_items 'fill array - attributes
item_demand(item, 1) = Worksheets("Item Input").Cells(item + 1, B).Value 'annual demand, i
item_demand(item, 2) = Worksheets("Item Input").Cells(item + 1, C).Value 'avg daily demand, i
item_demand(item, 3) = Worksheets("Item Input").Cells(item + 1, D).Value 'SD daily demand, i
item_costs(item, 1) = Worksheets("Item Input").Cells(item + 1, E).Value 'purchase price, i
item_costs(item, 2) = shortage 'shortage cost, i
'Print Current Values to Output File
Worksheets("Out_Base_Item").Cells(indexrows_a, A).Value = factor
Worksheets("Out_Base_Item").Cells(indexrows_a, B).Value = item
Worksheets("Out_Base_Item").Cells(indexrows_a, C).Value = item_demand(item, 1)
Worksheets("Out_Base_Item").Cells(indexrows_a, D).Value = item_demand(item, 2)
Worksheets("Out_Base_Item").Cells(indexrows_a, E).Value = item_demand(item, 3)
Worksheets("Out_Base_Item").Cells(indexrows_a, F).Value = item_costs(item, 1)
Worksheets("Out_Base_Item").Cells(indexrows_a, G).Value = item_costs(item, 2)
indexrows_a = indexrows_a + 1
Next item

136

mean_lead_time = Worksheets("Input Parameters").Cells(2, G).Value
stdev_lead_time = Worksheets("Input Parameters").Cells(2, H).Value
annual_purchase_cost = 0 'initialize
annual_trans_cost = 0 'initialize
annual_order_cost = 0 'initialize
annual_holding_cost_cycle = 0 'initialize
annual_holding_cost_safety = 0 'initialize
annual_shortage_cost = 0 'initialize
total_annual_inventory_cost = 0 'initialize

End Sub

Sub baseline() 'Calculate Order Interval for Baseline Model

Dim index_r, index_s As Integer
Dim PtimesD As Double
Dim SumPtimesD As Double
Dim PplusG As Double
Dim PplusGtimesD As Double
Dim numerator As Double
Dim denominator As Double
Dim order_interval As Double
Dim t_days As Double
Dim order_cycles As Double
Dim total_annual_demand As Double
Dim holding_safetystock As Double
Dim total_shortage_cost As Double
Dim safetystock As Double
Dim term_a, term_b, term_c, term_d, term_e As Double
holding_safetystock = 0 'initialize
total_annual_demand = 0 'initialize
total_shortage_cost = 0 'initialize

For index_r = 1 To num_items
total_annual_demand = total_annual_demand + item_demand(index_r, 1)
PtimesD = item_costs(index_r, 1) * item_demand(index_r, 1)
Worksheets("Out_Base_Item").Cells(indexrows_b, H).Value = PtimesD
SumPtimesD = SumPtimesD + PtimesD
indexrows_b = indexrows_b + 1
Next index_r

numerator = 2 * (major_order + num_items * minor_order)
denominator = holding * SumPtimesD
order_interval = Sqr(numerator / denominator)
t_days = order_interval * 365
order_cycles = 1 / order_interval

137

Worksheets("Out_Base").Cells(indexrows_d, F).Value = numerator
Worksheets("Out_Base").Cells(indexrows_d, G).Value = denominator
Worksheets("Out_Base").Cells(indexrows_d, H).Value = order_interval
Worksheets("Out_Base").Cells(indexrows_d, I).Value = t_days
Worksheets("Out_Base").Cells(indexrows_d, J).Value = order_cycles

'Calculate Order Qty, Safety Stock, and Expected Stockout
order_quantity_Qk = order_interval * total_annual_demand
order_quantity_Qk = Round(order_quantity_Qk, 0)
Worksheets("Out_Base").Cells(indexrows_d, K).Value = order_quantity_Qk
unitshipmentrate 'Determine unit shipping
rate
Worksheets("Out_Base").Cells(indexrows_d, L).Value = unit_shipment_rate

For index_s = 1 To num_items
' Calculate expected and Stdev of demand during L+T
term_a = mean_lead_time * item_demand(index_s, 2)
' L× X
i

term_b = order_interval * 365 * item_demand(index_s, 2)
' T × X
i

item_demand(index_s, 4) = term_a + term_b
'
( )
ˆ
i T+L
X
Worksheets("Out_Base_Item").Cells(indexrows_c, I).Value =_
item_demand(index_s, 4)
term_c = mean_lead_time * item_demand(index_s, 3) ^ 2
'
2
X
i
L ? ×
term_d = order_interval * 365 * item_demand(index_s, 3) ^ 2
'
2
X
i
T ? ×
term_e = item_demand(index_s, 2) ^ 2 * stdev_lead_time ^ 2
'
2
L
2
X ×?
i

item_demand(index_s, 5) = Sqr(term_c + term_d + term_e)
'
( ) i L T
?
+

Worksheets("Out_Base_Item").Cells(indexrows_c, J).Value =item_demand(index_s, 5)
'Calculate Safety Stock, stockout probability and Stockout quantity
item_levels(index_s, 3) = (order_interval * holding *_
item_costs(index_s, 1)) / item_costs(index_s, 2)
' ( ) P X >R
i i

If item_levels(index_s, 3) >= 1 Then item_levels(index_s, 3) = 0.99999
Worksheets("Out_Base_Item").Cells(indexrows_c, K).Value = item_levels(index_s, 3)
Worksheets("Out_Base_Item").Cells(indexrows_c, L).FormulaR1C1 =_
"=norminv(1-RC[-1],0,1)"
item_levels(index_s, 4) = Worksheets("Out_Base_Item")._
Cells(indexrows_c, L).Value
'
i
Z
item_levels(index_s, 2) = item_levels(index_s, 4) *_
item_demand(index_s, 5)
'
( ) i i L T
Safety Stock = Z ?
+

safetystock = item_levels(index_s, 2)
If item_levels(index_s, 2) < 0 Then item_levels(index_s, 2) = 0
Worksheets("Out_Base_Item").Cells(indexrows_c, M).Value = item_levels(index_s, 2)
holding_safetystock = holding_safetystock + holding *_
item_costs(index_s, 1) * item_levels(index_s, 2)
item_levels(index_s, 1) = item_demand(index_s, 4) + safetystock 'Base stock level, R
i

138

Worksheets("Out_Base_Item").Cells(indexrows_c, N).Value = item_levels(index_s, 1)
Worksheets("Out_Base_Item").Cells(indexrows_c, O).FormulaR1C1 = _
"=RC[-5]*(NORMDIST(RC[-3],0,1,0)-RC[-3]*_
(1-NORMDIST(RC[-3],0,1,1)))"
item_levels(index_s, 5) = Worksheets("Out_Base_Item")._
Cells(indexrows_c, O).Value
'
i i
E X R ( >
¸ ¸

total_shortage_cost = total_shortage_cost + item_costs(index_s, 2) *_
item_levels(index_s, 5)
indexrows_c = indexrows_c + 1
Next index_s

'Calculate Costs
annual_purchase_cost = SumPtimesD
annual_trans_cost = unit_shipment_rate * total_annual_demand
annual_order_cost = (major_order + num_items * minor_order) / order_interval
annual_holding_cost_cycle = 0.5 * order_interval * holding * SumPtimesD
annual_holding_cost_safety = holding_safetystock
annual_shortage_cost = total_shortage_cost / order_interval
total_annual_inventory_cost = annual_purchase_cost + annual_trans_cost + annual_order_cost _
+ annual_holding_cost_cycle + annual_holding_cost_safety _
+ annual_shortage_cost

Worksheets("Out_Base").Cells(indexrows_d, M).Value = annual_purchase_cost
Worksheets("Out_Base").Cells(indexrows_d, N).Value = annual_trans_cost
Worksheets("Out_Base").Cells(indexrows_d, O).Value = annual_order_cost
Worksheets("Out_Base").Cells(indexrows_d, P).Value = annual_holding_cost_cycle
Worksheets("Out_Base").Cells(indexrows_d, Q).Value = annual_holding_cost_safety
Worksheets("Out_Base").Cells(indexrows_d, R).Value = annual_holding_cost_cycle_
+ annual_holding_cost_safety
Worksheets("Out_Base").Cells(indexrows_d, S).Value = annual_shortage_cost
Worksheets("Out_Base").Cells(indexrows_d, T).Value = total_annual_inventory_cost
indexrows_d = indexrows_d + 1
End Sub

Sub MainBaseActualModel() 'Main Program Routine

indexrows_a = 2 'initialize rows to row 2 for output
indexrows_b = 2
indexrows_c = 2
indexrows_d = 2
A = 1 'Set columns
B = 2
C = 3
D = 4
E = 5
F = 6
G = 7
H = 8
I = 9
139
J = 10
K = 11
L = 12
M = 13
N = 14
O = 15
P = 16
Q = 17
R = 18
S = 19
T = 20
U = 21
V = 22
W = 23
X = 24
num_items = Worksheets("Input Parameters").Cells(2, F).Value 'Set Number of Items
num_factors = Worksheets("Input Parameters").Cells(2, A).Value 'Set Number of Factors
rateschedule 'set Rate Schedule
factor = 0

For index_i = 1 To num_factors 'set Major Order Cost
major_order_cost(index_i) = Worksheets("Input Parameters").Cells(index_i + 1, B).Value
major_order = major_order_cost(index_i)
For index_j = 1 To num_factors 'set Minor Order Cost
minor_order_cost(index_j) = Worksheets("Input Parameters").Cells(index_j + 1, C).Value
minor_order = minor_order_cost(index_j)
For index_k = 1 To num_factors 'Set Holding Fraction
holding_fraction(index_k) = Worksheets("Input Parameters").Cells(index_k + 1, D).Value
holding = holding_fraction(index_k)
For index_p = 1 To num_factors 'Set shortage unit Cost
shortage_cost(index_p) = Worksheets("Input Parameters").Cells(index_p + 1, E).Value
shortage = shortage_cost(index_p)
initialize 'Initialize variables
baselineactual 'adj holding costs (P+Gk)
Next index_p 'Select Next Shortage Unit Cost
Next index_k 'Select Next Holding Fraction
Next index_j 'Select Next Minor Order Cost
Next index_i 'Select Next Major Order Cost
End Sub

Sub initialize() 'Initialize variables

Dim item As Integer

factor = factor + 1 'full factorial design
Worksheets("Out_BaseActual").Cells(factor + 1, A).Value = factor
Worksheets("Out_BaseActual").Cells(factor + 1, B).Value = major_order
Worksheets("Out_BaseActual").Cells(factor + 1, C).Value = minor_order
Worksheets("Out_BaseActual").Cells(factor + 1, D).Value = holding
Worksheets("Out_BaseActual").Cells(factor + 1, E).Value = shortage
140

For item = 1 To num_items 'fill array attributes
item_demand(item, 1) = Worksheets("Item Input").Cells(item + 1, B).Value 'annual demand, i
item_demand(item, 2) = Worksheets("Item Input").Cells(item + 1, C).Value 'avg daily demand, i
item_demand(item, 3) = Worksheets("Item Input").Cells(item + 1, D).Value 'sd daily demand, i
item_costs(item, 1) = Worksheets("Item Input").Cells(item + 1, E).Value 'purchase price, i
item_costs(item, 2) = shortage 'shortage cost, i
'Print Current Values to Output File
Worksheets("Out_BaseActual_Item").Cells(indexrows_a, A).Value = factor
Worksheets("Out_BaseActual_Item").Cells(indexrows_a, B).Value = item
Worksheets("Out_BaseActual_Item").Cells(indexrows_a, C).Value = item_demand(item, 1)
Worksheets("Out_BaseActual_Item").Cells(indexrows_a, D).Value = item_demand(item, 2)
Worksheets("Out_BaseActual_Item").Cells(indexrows_a, E).Value = item_demand(item, 3)
Worksheets("Out_BaseActual_Item").Cells(indexrows_a, F).Value = item_costs(item, 1)
Worksheets("Out_BaseActual_Item").Cells(indexrows_a, G).Value = item_costs(item, 2)
indexrows_a = indexrows_a + 1
Next item

mean_lead_time = Worksheets("Input Parameters").Cells(2, G).Value
stdev_lead_time = Worksheets("Input Parameters").Cells(2, H).Value
annual_purchase_cost = 0 'total annual purchase cost
annual_trans_cost = 0 'total annual cost of transportation
annual_order_cost = 0 'total annual cost of ordering
annual_holding_cost_cycle = 0 'total annual holding cost cycle stock
annual_holding_cost_safety = 0 'total annual holding cost safety stock
annual_shortage_cost = 0 'total annual shortage costs
total_annual_inventory_cost = 0 'total annual cost of inventory

End Sub

Sub baselineactual() 'Calculate Order Interval for Baseline Model with true holding costs

Dim index_r, index_s As Integer
Dim PtimesD As Double
Dim SumPtimesD As Double
Dim PplusG As Double
Dim PplusGtimesD As Double
Dim SumPplusGtimesD As Double
Dim numerator As Double
Dim denominator As Double
Dim order_interval As Double
Dim t_days As Double
Dim order_cycles As Double
Dim total_annual_demand As Double
Dim holding_safetystock As Double
Dim total_shortage_cost As Double
Dim safetystock As Double
Dim term_a, term_b, term_c, term_d, term_e As Double

141

holding_safetystock = 0 'initialize
total_annual_demand = 0 'initialize
total_shortage_cost = 0 'initialize
PplusGtimesD = 0 'initialize
SumPplusGtimesD = 0 'initialize

For index_r = 1 To num_items 'Calculate T based on input parameters
total_annual_demand = total_annual_demand + item_demand(index_r, 1)
PtimesD = item_costs(index_r, 1) * item_demand(index_r, 1)
Worksheets("Out_BaseActual_Item").Cells(indexrows_b, H).Value = PtimesD
SumPtimesD = SumPtimesD + PtimesD
indexrows_b = indexrows_b + 1
Next index_r

numerator = 2 * (major_order + num_items * minor_order)
denominator = holding * SumPtimesD
order_interval = Sqr(numerator / denominator)
t_days = order_interval * 365
order_cycles = 1 / order_interval
Worksheets("Out_BaseActual").Cells(indexrows_d, F).Value = numerator
Worksheets("Out_BaseActual").Cells(indexrows_d, G).Value = denominator
Worksheets("Out_BaseActual").Cells(indexrows_d, H).Value = order_interval
Worksheets("Out_BaseActual").Cells(indexrows_d, I).Value = t_days
Worksheets("Out_BaseActual").Cells(indexrows_d, J).Value = order_cycles
'Calculate Order Qty, Safety Stock, and Expected Stockout

order_quantity_Qk = order_interval * total_annual_demand
order_quantity_Qk = Round(order_quantity_Qk, 0)
Worksheets("Out_BaseActual").Cells(indexrows_d, K).Value = order_quantity_Qk
unitshipmentrate 'Determine unit shipping rate
Worksheets("Out_BaseActual").Cells(indexrows_d, L).Value = unit_shipment_rate

For index_s = 1 To num_items
' Calculate expected and Stdev of demand during L+T
term_a = mean_lead_time * item_demand(index_s, 2)
' L× X
i

term_b = order_interval * 365 * item_demand(index_s, 2)
' T × X
i

item_demand(index_s, 4) = term_a + term_b
'
( )
ˆ
i T+L
X
Worksheets("Out_BaseActual_Item").Cells(indexrows_c, I).Value = item_demand(index_s, 4)
term_c = mean_lead_time * item_demand(index_s, 3) ^ 2
'
2
X
i
L ? ×
term_d = order_interval * 365 * item_demand(index_s, 3) ^ 2
'
2
X
i
T ? ×
term_e = item_demand(index_s, 2) ^ 2 * stdev_lead_time ^ 2
'
2
i
2
L
×? X
item_demand(index_s, 5) = Sqr(term_c + term_d + term_e)
'
( ) i L T
?
+

Worksheets("Out_BaseActual_Item").Cells(indexrows_c, J).Value = item_demand(index_s, 5)

142
'Calculate Safety Stock, stockout probability and Stockout quantity
item_levels(index_s, 3) = (order_interval * holding * (item_costs(index_s, 1) +_
unit_shipment_rate)) / item_costs(index_s, 2)
' ( ) P X >R
i i

If item_levels(index_s, 3) >= 1 Then item_levels(index_s, 3) = 0.99999
Worksheets("Out_BaseActual_Item").Cells(indexrows_c, K).Value = item_levels(index_s, 3)
Worksheets("Out_BaseActual_Item").Cells(indexrows_c, L).FormulaR1C1 =_
"=norminv(1-RC[-1],0,1)"
item_levels(index_s, 4) = Worksheets("Out_BaseActual_Item")._
Cells(indexrows_c, L).Value
'
i
Z
item_levels(index_s, 2) = item_levels(index_s, 4) * _
item_demand(index_s, 5)
'
( ) i i L T
Safety Stock = Z ?
+

safetystock = item_levels(index_s, 2)
If item_levels(index_s, 2) < 0 Then item_levels(index_s, 2) = 0
Worksheets("Out_BaseActual_Item").Cells(indexrows_c, M).Value = item_levels(index_s, 2)
holding_safetystock = holding_safetystock + holding * (item_costs(index_s, 1) +_
unit_shipment_rate) * item_levels(index_s, 2)
item_levels(index_s, 1) = item_demand(index_s, 4) + safetystock 'Base stock level, R
i

Worksheets("Out_BaseActual_Item").Cells(indexrows_c, N).Value = item_levels(index_s, 1)
Worksheets("Out_BaseActual_Item").Cells(indexrows_c, O).FormulaR1C1 = _
"=RC[-5]*(NORMDIST(RC[-3],0,1,0)-RC[-3]*_
(1-NORMDIST(RC[-3],0,1,1)))"
item_levels(index_s, 5) = Worksheets("Out_BaseActual_Item")._
Cells(indexrows_c, O).Value
'
i i
E X R ( >
¸ ¸

total_shortage_cost = total_shortage_cost + item_costs(index_s, 2) * item_levels(index_s, 5)

indexrows_c = indexrows_c + 1

PplusGtimesD = (item_costs(index_s, 1) + unit_shipment_rate) * item_demand(index_s, 1)
SumPplusGtimesD = SumPplusGtimesD + PplusGtimesD
Next index_s

'Calculate Costs
annual_purchase_cost = SumPtimesD
annual_trans_cost = unit_shipment_rate * total_annual_demand
annual_order_cost = (major_order + num_items * minor_order) / order_interval
annual_holding_cost_cycle = 0.5 * order_interval * holding *
SumPplusGtimesD

annual_holding_cost_safety = holding_safetystock
annual_shortage_cost = total_shortage_cost / order_interval
total_annual_inventory_cost = annual_purchase_cost + annual_trans_cost + annual_order_cost _
+ annual_holding_cost_cycle + annual_holding_cost_safety _
+ annual_shortage_cost
Worksheets("Out_BaseActual").Cells(indexrows_d, M).Value = annual_purchase_cost
Worksheets("Out_BaseActual").Cells(indexrows_d, N).Value = annual_trans_cost
Worksheets("Out_BaseActual").Cells(indexrows_d, O).Value = annual_order_cost
Worksheets("Out_BaseActual").Cells(indexrows_d, P).Value = annual_holding_cost_cycle
Worksheets("Out_BaseActual").Cells(indexrows_d, Q).Value = annual_holding_cost_safety
Worksheets("Out_BaseActual").Cells(indexrows_d, R).Value = annual_holding_cost_cycle_
+ annual_holding_cost_safety
Worksheets("Out_BaseActual").Cells(indexrows_d, S).Value = annual_shortage_cost
143
Worksheets("Out_BaseActual").Cells(indexrows_d, T).Value = total_annual_inventory_cost
Worksheets("Overview").Cells(indexrows_d, U).Value = t_days
Worksheets("Overview").Cells(indexrows_d, V).Value = order_quantity_Qk
Worksheets("Overview").Cells(indexrows_d, W).Value = unit_shipment_rate
Worksheets("Overview").Cells(indexrows_d, X).Value = total_annual_inventory_cost
indexrows_d = indexrows_d + 1
End Sub

Sub MainFullModel() 'Main Program Routine

indexrows_a = 2 'initialize to row 2 for output
indexrows_b = 2
indexrows_c = 2
indexrows_d = 2
indexrows_e = 2
indexrows_f = 2
A = 1 'Set columns
B = 2
C = 3
D = 4
E = 5
F = 6
G = 7
H = 8
I = 9
J = 10
K = 11
L = 12
M = 13
N = 14
O = 15
P = 16
Q = 17
R = 18
S = 19
T = 20
num_items = Worksheets("Input Parameters").Cells(2, F).Value 'Set Number of Items
num_factors = Worksheets("Input Parameters").Cells(2, A).Value 'Set Number of Factors
rateschedule 'set Rate Schedule
factor = 0

For index_i = 1 To num_factors 'set Major Order Cost
major_order_cost(index_i) = Worksheets("Input Parameters").Cells(index_i + 1, B).Value
major_order = major_order_cost(index_i)
For index_j = 1 To num_factors 'set Minor Order Cost
minor_order_cost(index_j) = Worksheets("Input Parameters").Cells(index_j + 1, C).Value
minor_order = minor_order_cost(index_j)
For index_k = 1 To num_factors 'Set Holding Fraction
holding_fraction(index_k) = Worksheets("Input Parameters").Cells(index_k + 1, D).Value
holding = holding_fraction(index_k)
144
For index_p = 1 To num_factors 'Set shortage unit Cost
shortage_cost(index_p) = Worksheets("Input Parameters").Cells(index_p + 1, E).Value
shortage = shortage_cost(index_p)
initialize 'Initialize variables
full 'Calculate Full Model
Next index_p 'Select Next Shortage Unit Cost
Next index_k 'Select Next Holding Fraction
Next index_j 'Select Next Minor Order Cost
Next index_i 'Select Next Major Order Cost

End Sub

Sub initialize() 'Initialize variables

Dim item As Integer
total_annual_demand = 0 'initialize
factor = factor + 1 'full factorial design
Worksheets("Out_Full").Cells(factor + 1, A).Value = factor
Worksheets("Out_Full").Cells(factor + 1, B).Value = major_order
Worksheets("Out_Full").Cells(factor + 1, C).Value = minor_order
Worksheets("Out_Full").Cells(factor + 1, D).Value = holding
Worksheets("Out_Full").Cells(factor + 1, E).Value = shortage

For item = 1 To num_items 'fill array with item attributes
item_demand(item, 1) = Worksheets("Item Input").Cells(item + 1, B).Value 'ann dmd, item i
item_demand(item, 2) = Worksheets("Item Input").Cells(item + 1, C).Value 'daily dmd, item i
item_demand(item, 3) = Worksheets("Item Input").Cells(item + 1, D).Value 'sd daily dmd, i
item_costs(item, 1) = Worksheets("Item Input").Cells(item + 1, E).Value 'purch p, item i
item_costs(item, 2) = shortage 'short cost, i
total_annual_demand = total_annual_demand + item_demand(item, 1)
'Print Current Values to Output File
Worksheets("Out_Full_Item").Cells(indexrows_a, A).Value = factor
Worksheets("Out_Full_Item").Cells(indexrows_a, B).Value = item
Worksheets("Out_Full_Item").Cells(indexrows_a, C).Value = item_demand(item, 1)
Worksheets("Out_Full_Item").Cells(indexrows_a, D).Value = item_demand(item, 2)
Worksheets("Out_Full_Item").Cells(indexrows_a, E).Value = item_demand(item, 3)
Worksheets("Out_Full_Item").Cells(indexrows_a, F).Value = item_costs(item, 1)
Worksheets("Out_Full_Item").Cells(indexrows_a, G).Value = item_costs(item, 2)
indexrows_a = indexrows_a + 1
Next item

mean_lead_time = Worksheets("Input Parameters").Cells(2, G).Value
stdev_lead_time = Worksheets("Input Parameters").Cells(2, H).Value

annual_purchase_cost = 0 'total annual purchase cost
annual_trans_cost = 0 'total annual cost of trans
annual_order_cost = 0 'total annual cost of ordering
annual_holding_cost_cycle = 0 'total annual holding cost of cycle stock
145

annual_holding_cost_safety = 0 'total annual holding cost of safety stock
annual_shortage_cost = 0 'total annual shortage costs
total_annual_inventory_cost = 0 'total annual cost of inventory

End Sub


Sub full() 'Calculate Order Interval for Full Model

Dim index_r, index_s, index_t As Integer
Dim t_days As Double
Dim order_cycles As Double

iterativesolution 'Call Sub – iterative solution for T
search 'Call Sub – T with MIN(Annual Cost)

t_days = optimal_order_interval * 365 'With Optimal T, Calc relevant variables
order_cycles = 1 / optimal_order_interval
unitshipmentrate 'Call Sub - Get unit shipping rate

'Output to worksheet
Worksheets("Out_Full").Cells(indexrows_b, F).Value = optimal_order_interval
Worksheets("Out_Full").Cells(indexrows_b, G).Value = t_days
Worksheets("Out_Full").Cells(indexrows_b, H).Value = order_cycles
Worksheets("Out_Full").Cells(indexrows_b, I).Value = order_quantity_Qk
Worksheets("Out_Full").Cells(indexrows_b, J).Value = unit_shipment_rate

calcPplusGvalues 'Call Subroutine
calclevels 'Call Subroutine
calcannualcosts 'Call Subroutine

For index_s = 1 To num_items
'Output to worksheet
Worksheets("Out_Full_Item").Cells(indexrows_c, H).Value = PplusG
Worksheets("Out_Full_Item").Cells(indexrows_c, I).Value = item_demand(index_s, 4)
Worksheets("Out_Full_Item").Cells(indexrows_c, J).Value = item_demand(index_s, 5)
Worksheets("Out_Full_Item").Cells(indexrows_c, K).Value = item_levels(index_s, 3)
Worksheets("Out_Full_Item").Cells(indexrows_c, L).Value = item_levels(index_s, 4)
Worksheets("Out_Full_Item").Cells(indexrows_c, M).Value = item_levels(index_s, 2)
Worksheets("Out_Full_Item").Cells(indexrows_c, N).Value = item_levels(index_s, 1)
Worksheets("Out_Full_Item").Cells(indexrows_c, O).Value = item_levels(index_s, 5)
indexrows_c = indexrows_c + 1
Next index_s

Worksheets("Out_Full").Cells(indexrows_b, K).Value = annual_purchase_cost
Worksheets("Out_Full").Cells(indexrows_b, L).Value = annual_trans_cost
Worksheets("Out_Full").Cells(indexrows_b, M).Value = annual_order_cost
Worksheets("Out_Full").Cells(indexrows_b, N).Value = annual_holding_cost_cycle
Worksheets("Out_Full").Cells(indexrows_b, O).Value = annual_holding_cost_safety
146
Worksheets("Out_Full").Cells(indexrows_b, P).Value = annual_holding_cost_cycle +_
annual_holding_cost_safety
Worksheets("Out_Full").Cells(indexrows_b, Q).Value = annual_shortage_cost
Worksheets("Out_Full").Cells(indexrows_b, R).Value = total_annual_inventory_cost
Worksheets("Overview").Cells(indexrows_b, M).Value = t_days
Worksheets("Overview").Cells(indexrows_b, N).Value = order_quantity_Qk
Worksheets("Overview").Cells(indexrows_b, O).Value = unit_shipment_rate
Worksheets("Overview").Cells(indexrows_b, P).Value = total_annual_inventory_cost
indexrows_b = indexrows_b + 1

End Sub

Sub iterativesolution()

Dim numerator As Double
Dim denominator As Double
Dim iterations As Long
Dim new_order_interval As Double
Dim T_interval(50000) As Double
total_shortage_cost = 0 'initialize
iterations = 2
T_interval(1) = 0
T_interval(2) = 0.02 'starting point for iterative solution

Do Until Round(T_interval(iterations), 5) = Round(T_interval(iterations - 1), 5)
'Iterative solution for Order Interval
order_quantity_Qk = T_interval(iterations) * total_annual_demand
order_quantity_Qk = Round(order_quantity_Qk, 0)
unitshipmentrate 'Determine unit shipping rate
calcPplusGvalues 'Call sub for calculations
'Calculate New Order Interval
numerator = 2 * (major_order + num_items * minor_order + total_shortage_cost)
denominator = (holding * SumPplusGtimesD) - (2 * holding * SumPplusGtimesdailydemand)
new_order_interval = Sqr(numerator / denominator)
'Call sub to calculate item levels
current_order_interval = new_order_interval 'set order interval for sub routines
calclevels
iterations = iterations + 1 'Next iteration
T_interval(iterations) = new_order_interval
Loop

current_order_interval = new_order_interval
calcannualcosts 'Calculate Costs

End Sub

Sub search() 'Using current_order_interval return the optimal_order_interval

147

Dim index As Integer
Dim total_cost(100000) As Double
Dim T_interval(100000) As Double
Dim Qk(100000) As Integer

index = 1
Qk(index) = Round(order_quantity_Qk, 0)
'Set for Subroutines
current_order_interval = Qk(index) / total_annual_demand
order_quantity_Qk = Qk(index)
'Call Subroutines
unitshipmentrate
calcPplusGvalues
calclevels
calcannualcosts
'Set Total Inv Cost for Comparison
total_cost(index) = total_annual_inventory_cost
index = index + 1 'increment for first comparison
Qk(index) = Qk(index - 1) + 1
'Set for Subroutines
current_order_interval = Qk(index) / total_annual_demand
order_quantity_Qk = Qk(index)
'Call Subroutines
unitshipmentrate
calcPplusGvalues
calclevels
calcannualcosts
'Set Total Inv Cost for Comparison
total_cost(index) = total_annual_inventory_cost

'local search in one direction
If total_cost(index) < total_cost(index - 1) Then
Do While total_cost(index) < total_cost(index - 1)
'Increment Qk and calculate relevant variables
index = index + 1
Qk(index) = Qk(index - 1) + 1
'Set for Subroutines
current_order_interval = Qk(index) / total_annual_demand
order_quantity_Qk = Qk(index)
'Call Subroutines
unitshipmentrate
calcPplusGvalues
calclevels
calcannualcosts
'Set Total Inv Cost for Comparison
total_cost(index) = total_annual_inventory_cost
Loop
Else
If total_cost(index) > total_cost(index - 1) Then
148
'Reset index for search in other direction
index = 1
index = index + 1
Qk(index) = Qk(index - 1) - 1 'Search in other direction
'Set for Subroutines
current_order_interval = Qk(index) / total_annual_demand
order_quantity_Qk = Qk(index)
'Call Subroutines
unitshipmentrate
calcPplusGvalues
calclevels
calcannualcosts
'Set Total Inv Cost for Comparison
total_cost(index) = total_annual_inventory_cost
'local search in other direction
Do While total_cost(index) < total_cost(index - 1)
index = index + 1 'Decrement Qk & calc relevant variables
Qk(index) = Qk(index - 1) - 1
current_order_interval = Qk(index) / total_annual_demand
order_quantity_Qk = Qk(index)
unitshipmentrate 'Call Subroutines
calcPplusGvalues
calclevels
calcannualcosts
total_cost(index) = total_annual_inventory_cost 'Set Total Inv Cost for Comparison
Loop
End If
End If

Qk_search = Qk(index - 1)
TCost_search = total_cost(index - 1)
searchweightbreaks 'compare search results w/ wt breaks
order_quantity_Qk = Qk_search 'Final Order Quantity & Interval
current_order_interval = order_quantity_Qk / total_annual_demand
optimal_order_interval = current_order_interval

End Sub

Sub searchweightbreaks()

Dim Q_break(10) As Long, index_w As Integer, total_cost(10) As Currency

Q_break(1) = break1_upper
Q_break(2) = break2_upper
Q_break(3) = break3_upper
Q_break(4) = break4_upper
Q_break(5) = break5_upper
Q_break(6) = break6_upper
Q_break(7) = break7_upper
Q_break(8) = break8_upper
149
Q_break(9) = break9_upper

For index_w = 1 To 9
current_order_interval = Q_break(index_w) / total_annual_demand
order_quantity_Qk = Q_break(index_w)
unitshipmentrate 'Call Subroutines
calcPplusGvalues
calclevels
calcannualcosts
total_cost(index_w) =
total_annual_inventory_cost
'Set Total Inv Cost for Comparison
If total_cost(index_w) < TCost_search Then
Qk_search = Q_break(index_w)
TCost_search = total_cost(index_w)
End If
Next index_w

End Sub

Sub calcPplusGvalues()

Dim index_s As Integer
SumPplusGtimesD = 0 'initialize
SumPplusGtimesdailydemand = 0
SumPtimesD = 0

For index_s = 1 To num_items
PtimesD = item_costs(index_s, 1) * item_demand(index_s, 1)
SumPtimesD = SumPtimesD + PtimesD
PplusG = item_costs(index_s, 1) + unit_shipment_rate
PplusGtimesD = PplusG * item_demand(index_s, 1)
SumPplusGtimesD = SumPplusGtimesD + PplusGtimesD
PplusGtimesdailydemand = PplusG * item_demand(index_s, 2)
SumPplusGtimesdailydemand = SumPplusGtimesdailydemand + PplusGtimesdailydemand
Next index_s

End Sub

Sub MainTruckModel() 'Main Program Routine
'Sets Input Parameters and Calls subroutines
indexrows_a = 2 'initialize to row 2 for output
indexrows_b = 2
indexrows_c = 2
A = 1 'Set columns
B = 2
C = 3
D = 4
E = 5
F = 6
G = 7
150
H = 8
I = 9
J = 10
K = 11
L = 12
M = 13
N = 14
O = 15
P = 16
Q = 17
R = 18
S = 19
T = 20
num_items = Worksheets("Input Parameters").Cells(2, F).Value 'Set Number of Items
num_factors = Worksheets("Input Parameters").Cells(2, A).Value 'Set Number of Factors
rateschedule 'Set Rate Schedule
factor = 0

For index_i = 1 To num_factors 'set Major Order Cost
major_order_cost(index_i) = Worksheets("Input Parameters").Cells(index_i + 1, B).Value
major_order = major_order_cost(index_i)
For index_j = 1 To num_factors 'set Minor Order Cost
minor_order_cost(index_j) = Worksheets("Input Parameters").Cells(index_j + 1, C).Value
minor_order = minor_order_cost(index_j)
For index_k = 1 To num_factors 'Set Holding Fraction
holding_fraction(index_k) = Worksheets("Input Parameters").Cells(index_k + 1, D).Value
holding = holding_fraction(index_k)
For index_p = 1 To num_factors 'Set shortage unit Cost
shortage_cost(index_p) = Worksheets("Input Parameters").Cells(index_p + 1, E).Value
shortage = shortage_cost(index_p)
initialize 'Initialize variables
truck 'Calculate Truck Model
Next index_p 'Select Next Shortage Unit Cost
Next index_k 'Select Next Holding Fraction
Next index_j 'Select Next Minor Order Cost
Next index_i 'Select Next Major Order Cost

End Sub
Public Sub initialize() 'Initialize variables
Dim item As Integer
factor = factor + 1 'full factorial design
Worksheets("Out_Truck").Cells(factor + 1, A).Value = factor
Worksheets("Out_Truck").Cells(factor + 1, B).Value = major_order
Worksheets("Out_Truck").Cells(factor + 1, C).Value = minor_order
Worksheets("Out_Truck").Cells(factor + 1, D).Value = holding
Worksheets("Out_Truck").Cells(factor + 1, E).Value = shortage

For item = 1 To num_items 'fill array with item attributes
item_demand(item, 1) = Worksheets("Item Input")._
Cells(item + 1, B).Value
'assign annual demand, item i
151
item_demand(item, 2) = Worksheets("Item Input")._
Cells(item + 1, C).Value
'assign avg daily demand, item i
item_demand(item, 3) = Worksheets("Item Input")._
Cells(item + 1, D).Value
'assign sd daily demand, item i
item_costs(item, 1) = Worksheets("Item Input")._
Cells(item + 1, E).Value
'assign purchase price for item i
item_costs(item, 2) = shortage 'assign shortage cost for item i
'Print Current Values to Output File
Worksheets("Out_Truck_Item").Cells(indexrows_a, A).Value = factor
Worksheets("Out_Truck_Item").Cells(indexrows_a, B).Value = item
Worksheets("Out_Truck_Item").Cells(indexrows_a, C).Value = item_demand(item, 1)
Worksheets("Out_Truck_Item").Cells(indexrows_a, D).Value = item_demand(item, 2)
Worksheets("Out_Truck_Item").Cells(indexrows_a, E).Value = item_demand(item, 3)
Worksheets("Out_Truck_Item").Cells(indexrows_a, F).Value = item_costs(item, 1)
Worksheets("Out_Truck_Item").Cells(indexrows_a, G).Value = item_costs(item, 2)
indexrows_a = indexrows_a + 1
Next item

mean_lead_time = Worksheets("Input Parameters").Cells(2, G).Value
stdev_lead_time = Worksheets("Input Parameters").Cells(2, H).Value

Worksheets("Overview").Cells(factor + 1, A).Value = factor
Worksheets("Overview").Cells(factor + 1, B).Value = major_order
Worksheets("Overview").Cells(factor + 1, C).Value = minor_order
Worksheets("Overview").Cells(factor + 1, D).Value = holding
Worksheets("Overview").Cells(factor + 1, E).Value = shortage
Worksheets("Overview").Cells(factor + 1, K).Value =
mean_lead_time

Worksheets("Overview").Cells(factor + 1, L).Value =
stdev_lead_time


annual_purchase_cost = 0 'total annual purchase cost
annual_trans_cost = 0 'total annual cost of transportation
annual_order_cost = 0 'total annual cost of ordering
annual_holding_cost_cycle = 0 'total annual holding cost of cycle stock
annual_holding_cost_safety = 0 'total annual holding cost of safety stock
annual_shortage_cost = 0 'total annual shortage costs
total_annual_inventory_cost = 0 'total annual cost of inventory

End Sub

Sub truck() 'Calculate Order Interval for Truck Model

Dim order_interval As Double
Dim index_r, index_s As Integer
Dim t_days As Double
Dim order_cycles As Double
Dim PplusG As Double
Dim SumPplusGtimesD As Double
Dim SumPtimesD As Double
Dim term_a, term_b, term_c, term_d, term_e As Double

152
Dim total_annual_demand As Double
Dim holding_safetystock As Double
Dim total_shortage_cost As Double
Dim safetystock As Double

holding_safetystock = 0 'initialize
total_annual_demand = 0 'initialize
total_shortage_cost = 0 'initialize

For index_r = 1 To num_items
total_annual_demand = total_annual_demand + item_demand(index_r, 1)
Next index_r

'Calculate order interval, order quantity, unit shipping rate
order_interval = truck_unit_capacity / total_annual_demand
t_days = order_interval * 365
order_cycles = 1 / order_interval
order_quantity_Qk = Round((order_interval *
total_annual_demand), 0)

unit_shipment_rate = TL_unit_rate

Worksheets("Out_Truck").Cells(indexrows_b, F).Value = order_interval 'Output to worksheet
Worksheets("Out_Truck").Cells(indexrows_b, G).Value = t_days
Worksheets("Out_Truck").Cells(indexrows_b, H).Value = order_cycles
Worksheets("Out_Truck").Cells(indexrows_b, I).Value = order_quantity_Qk
Worksheets("Out_Truck").Cells(indexrows_b, J).Value = unit_shipment_rate

For index_s = 1 To num_items
'Calculate P+G0 and Sum(P+G0)*D
PplusG = item_costs(index_s, 1) + unit_shipment_rate
SumPtimesD = SumPtimesD + item_costs(index_s, 1) * item_demand(index_s, 1)
SumPplusGtimesD = SumPplusGtimesD + PplusG * item_demand(index_s, 1)
Worksheets("Out_Truck_Item").Cells(indexrows_c, H).Value = PplusG
'Calculate expected and Stdev of demand during L+T
term_a = mean_lead_time * item_demand(index_s, 2)
' L× X
i

term_b = order_interval * 365 * item_demand(index_s, 2)
' T × X
i

item_demand(index_s, 4) = term_a + term_b
'
( )
ˆ
i T+L
X
Worksheets("Out_Truck_Item").Cells(indexrows_c, I).Value = item_demand(index_s, 4)
term_c = mean_lead_time * item_demand(index_s, 3) ^ 2
'
2
X
i
L ? ×
term_d = order_interval * 365 * item_demand(index_s, 3) ^ 2
'
2
X
i
T ? ×
term_e = item_demand(index_s, 2) ^ 2 * stdev_lead_time ^ 2
'
2
L
2
X ×?
i

item_demand(index_s, 5) = Sqr(term_c + term_d + term_e)
'
( ) i L T
?
+

Worksheets("Out_Truck_Item").Cells(indexrows_c, J).Value = item_demand(index_s, 5)
'Calculate stockout probability, Stockout quantity, Safety Stock, and Base Stock Level
item_levels(index_s, 3) = (order_interval * holding * PplusG)/item_costs(index_s, 2)
' ( ) P X >R
i i

153
If item_levels(index_s, 3) >= 1 Then item_levels(index_s, 3) = 0.99999
Worksheets("Out_Truck_Item").Cells(indexrows_c, K).Value = item_levels(index_s, 3)
Worksheets("Out_Truck_Item").Cells(indexrows_c, L).FormulaR1C1 _
= "=norminv(1-RC[-1],0,1)"
item_levels(index_s, 4) = Worksheets("Out_Truck_Item")._
Cells(indexrows_c, L).Value
'
i
Z
item_levels(index_s, 2) = item_levels(index_s, 4) * _
item_demand(index_s, 5)
'
( ) i i L T
Safety Stock = Z ?
+

safetystock = item_levels(index_s, 2)
If item_levels(index_s, 2) < 0 Then item_levels(index_s, 2) _
= 0
'Set to zero for purpose of holding
cost
Worksheets("Out_Truck_Item").Cells(indexrows_c, M).Value = item_levels(index_s, 2)
holding_safetystock = holding_safetystock + holding * PplusG * item_levels(index_s, 2)
item_levels(index_s, 1) = item_demand(index_s, 4) + safetystock 'Base stock level, R
i

Worksheets("Out_Truck_Item").Cells(indexrows_c, N).Value = item_levels(index_s, 1)
Worksheets("Out_Truck_Item").Cells(indexrows_c, O).FormulaR1C1 = _
"=RC[-5]*(NORMDIST(RC[-3],0,1,0)-RC[-3]*(1-NORMDIST(RC[-3],0,1,1)))"
item_levels(index_s, 5) = Worksheets("Out_Truck_Item")._
Cells(indexrows_c, O).Value
'
i i
E X R ( >
¸ ¸

total_shortage_cost = total_shortage_cost + item_costs(index_s, 2) * item_levels(index_s, 5)
indexrows_c = indexrows_c + 1
Next index_s

annual_purchase_cost = SumPtimesD 'Calculate Costs
annual_trans_cost = unit_shipment_rate * total_annual_demand
annual_order_cost = (major_order + num_items * minor_order) / order_interval
annual_holding_cost_cycle = 0.5 * order_interval * holding * SumPplusGtimesD
annual_holding_cost_safety = holding_safetystock
annual_shortage_cost = total_shortage_cost / order_interval
total_annual_inventory_cost = annual_purchase_cost + annual_trans_cost + annual_order_cost _
+ annual_holding_cost_cycle + annual_holding_cost_safety _
+ annual_shortage_cost
Worksheets("Out_Truck").Cells(indexrows_b, K).Value = annual_purchase_cost
Worksheets("Out_Truck").Cells(indexrows_b, L).Value = annual_trans_cost
Worksheets("Out_Truck").Cells(indexrows_b, M).Value = annual_order_cost
Worksheets("Out_Truck").Cells(indexrows_b, N).Value = annual_holding_cost_cycle
Worksheets("Out_Truck").Cells(indexrows_b, O).Value = annual_holding_cost_safety
Worksheets("Out_Truck").Cells(indexrows_b, P).Value = annual_holding_cost_cycle +_
annual_holding_cost_safety
Worksheets("Out_Truck").Cells(indexrows_b, Q).Value = annual_shortage_cost
Worksheets("Out_Truck").Cells(indexrows_b, R).Value = total_annual_inventory_cost

'write key parameters to Model Comparison Overview WorkSheet
'get number items
Worksheets("Overview").Cells(indexrows_b, F).Value = Worksheets("Input_
Parameters").Cells(2, F).Value
'get avg item weight
Worksheets("Overview").Cells(indexrows_b, G).Value = Worksheets("Input_
Parameters").Cells(2, I).Value
154

'get TL unit rate
Worksheets("Overview").Cells(indexrows_b, H).Value = Worksheets("Rates").Cells(2, D).Value
'get LTL unit rate
Worksheets("Overview").Cells(indexrows_b, I).Value = Worksheets("Rates").Cells(2, E).Value
'get truck capacity
Worksheets("Overview").Cells(indexrows_b, J).Value = Worksheets("Input _
Parameters").Cells(2, L).Value
Worksheets("Overview").Cells(indexrows_b, Q).Value = t_days
Worksheets("Overview").Cells(indexrows_b, R).Value = order_quantity_Qk
Worksheets("Overview").Cells(indexrows_b, S).Value = unit_shipment_rate
Worksheets("Overview").Cells(indexrows_b, T).Value = total_annual_inventory_cost
indexrows_b = indexrows_b + 1

End Sub

Sub calclevels()

Dim index_t As Integer, term_a, term_b, term_c, term_d, term_e As Double, safetystock As Double
total_shortage_cost = 0 'initialize
holding_safetystock = 0

For index_t = 1 To num_items
'Calculate expected and Stdev of demand during L+T
term_a = mean_lead_time * item_demand(index_t, 2)
' L× X
i

term_b = current_order_interval * 365 * item_demand(index_t, 2)
' T × X
i

item_demand(index_t, 4) = term_a + term_b
'
( )
ˆ
i T+L
X
term_c = mean_lead_time * item_demand(index_t, 3) ^ 2
'
2
X
i
L ? ×
term_d = current_order_interval * 365 * item_demand(index_t, 3) ^2
'
2
X
i
T ? ×
term_e = item_demand(index_t, 2) ^ 2 * stdev_lead_time ^ 2
'
2
L
2
X ×?
i

item_demand(index_t, 5) = Sqr(term_c + term_d + term_e)
'
( ) i L T
?
+


'Calculate Safety Stock, stockout probability and Stockout quantity
PplusG = item_costs(index_t, 1) + unit_shipment_rate
' ( ) P X >R
i i

item_levels(index_t, 3) = (current_order_interval * holding * PplusG) / item_costs(index_t, 2)
If item_levels(index_t, 3) >= 1 Then item_levels(index_t, 3) = 0.99999
'holding cell to calculate Z & E[X>R]
Worksheets("Out_Full_Item").Cells(3, Q).Value = item_levels(index_t, 3)
Worksheets("Out_Full_Item").Cells(3, R).FormulaR1C1 = "=norminv(1-RC[-1],0,1)"
'
i
Z
item_levels(index_t, 4) = Worksheets("Out_Full_Item").Cells(3, R).Value
item_levels(index_t, 2) = item_levels(index_t, 4) * item_demand(index_t, 5)
'
( ) i i L T
Safety Stock = Z ?
+
safetystock = item_levels(index_t, 2)
If item_levels(index_t, 2) < 0 Then item_levels(index_t, 2) = 0
155
holding_safetystock = holding_safetystock + holding * PplusG * item_levels(index_t, 2)
item_levels(index_t, 1) = item_demand(index_t, 4) + safetystock 'Base stock level, R
i

Worksheets("Out_Full_Item").Cells(3, P).Value = item_demand(index_t, 5)
'
i i
E X R ( >
¸ ¸

Worksheets("Out_Full_Item").Cells(3, S).FormulaR1C1 = _
"=RC[-3]*(NORMDIST(RC[-1],0,1,0)-RC[-1]*(1-NORMDIST(RC[-1],0,1,1)))"
item_levels(index_t, 5) = Worksheets("Out_Full_Item").Cells(3, S).Value
total_shortage_cost = total_shortage_cost + item_costs(index_t, 2) * item_levels(index_t, 5)
Next index_t

End Sub

Sub calcannualcosts()

annual_purchase_cost = SumPtimesD
annual_trans_cost = unit_shipment_rate * total_annual_demand
annual_order_cost = (major_order + num_items * minor_order) / current_order_interval
annual_holding_cost_cycle = 0.5 * current_order_interval * holding * SumPplusGtimesD
annual_holding_cost_safety = holding_safetystock
annual_shortage_cost = total_shortage_cost / current_order_interval
total_annual_inventory_cost = annual_purchase_cost + annual_trans_cost + annual_order_cost _
+ annual_holding_cost_cycle + annual_holding_cost_safety _
+ annual_shortage_cost

End Sub

Sub rateschedule() 'Determine Freight Rate Schedule

Dim TL_freight_rate As Double '$/cwt
Dim LTL_freight_rate As Double '$/cwt
Dim truck_lbs_capacity As Double 'in pounds
Dim truck_cwt_capacity As Double 'in cwt
Dim weight_break_cwt As Double 'in cwt
Dim weight_break_unit As Double 'in units
Dim item_weight As Double 'average weight of all items
'assume items are equal
'get input values
item_weight = Worksheets("Input Parameters").Cells(2, I).Value
TL_freight_rate = Worksheets("Input Parameters").Cells(2, J).Value
LTL_freight_rate = Worksheets("Input Parameters").Cells(2, K).Value
truck_lbs_capacity = Worksheets("Input Parameters").Cells(2, L).Value

'calculate rates per unit
TL_unit_rate = TL_freight_rate * item_weight / 100
LTL_unit_rate = LTL_freight_rate * item_weight / 100
Worksheets("Rates").Cells(2, 2).Value = TL_freight_rate
Worksheets("Rates").Cells(2, 3).Value = LTL_freight_rate
Worksheets("Rates").Cells(2, 4).Value = TL_unit_rate
Worksheets("Rates").Cells(2, 5).Value = LTL_unit_rate
Worksheets("Rates").Cells(4, 2).Value = truck_lbs_capacity
156

'calculate truck capacity and wt breaks
truck_cwt_capacity = truck_lbs_capacity / 100 '1cwt = 100 lbs.
weight_break_cwt = truck_cwt_capacity * (TL_freight_rate / LTL_freight_rate)
Worksheets("Rates").Cells(5, 2).Value = truck_cwt_capacity
Worksheets("Rates").Cells(8, 2).Value = weight_break_cwt
weight_break_unit = Round((weight_break_cwt * 100 / item_weight), 0)
truck_unit_capacity = Round((truck_lbs_capacity / item_weight), 0) 'Qt
Worksheets("Rates").Cells(6, 2).Value = truck_unit_capacity
Worksheets("Rates").Cells(9, 2).Value = weight_break_unit

'Set upper & lower unit break points
break1_lower = 1
break1_upper = weight_break_unit
Worksheets("Rates").Cells(13, 2).Value = break1_lower
Worksheets("Rates").Cells(13, 3).Value = break1_upper
break2_lower = break1_upper + 1
break2_upper = truck_unit_capacity
Worksheets("Rates").Cells(14, 2).Value = break2_lower
Worksheets("Rates").Cells(14, 3).Value = break2_upper
break3_lower = break2_upper + 1
break3_upper = break2_upper + weight_break_unit
Worksheets("Rates").Cells(15, 2).Value = break3_lower
Worksheets("Rates").Cells(15, 3).Value = break3_upper
break4_lower = break3_upper + 1
break4_upper = 2 * truck_unit_capacity
Worksheets("Rates").Cells(16, 2).Value = break4_lower
Worksheets("Rates").Cells(16, 3).Value = break4_upper
break5_lower = break4_upper + 1
break5_upper = break4_upper + weight_break_unit
Worksheets("Rates").Cells(17, 2).Value = break5_lower
Worksheets("Rates").Cells(17, 3).Value = break5_upper
break6_lower = break5_upper + 1
break6_upper = 3 * truck_unit_capacity
Worksheets("Rates").Cells(18, 2).Value = break6_lower
Worksheets("Rates").Cells(18, 3).Value = break6_upper
break7_lower = break6_upper + 1
break7_upper = break6_upper + weight_break_unit
Worksheets("Rates").Cells(19, 2).Value = break7_lower
Worksheets("Rates").Cells(19, 3).Value = break7_upper
break8_lower = break7_upper + 1
break8_upper = 4 * truck_unit_capacity
Worksheets("Rates").Cells(20, 2).Value = break8_lower
Worksheets("Rates").Cells(20, 3).Value = break8_upper
break9_lower = break8_upper + 1
break9_upper = break8_upper + weight_break_unit
Worksheets("Rates").Cells(21, 2).Value = break9_lower
Worksheets("Rates").Cells(21, 3).Value = break9_upper

End Sub
157

Sub unitshipmentrate()
unit_shipment_rate = 0 'initialize
Select Case order_quantity_Qk 'Select Case calculate unit shipping rate

Case break1_lower To break1_upper
unit_shipment_rate = LTL_unit_rate
Case break2_lower To break2_upper
unit_shipment_rate = (truck_unit_capacity / order_quantity_Qk) * TL_unit_rate
Case break3_lower To break3_upper
unit_shipment_rate = (truck_unit_capacity / order_quantity_Qk) * _
(TL_unit_rate - LTL_unit_rate) + LTL_unit_rate
Case break4_lower To break4_upper
unit_shipment_rate = 2 * (truck_unit_capacity / order_quantity_Qk) * TL_unit_rate
Case break5_lower To break5_upper
unit_shipment_rate = 2 * (truck_unit_capacity / order_quantity_Qk) * _
(TL_unit_rate - LTL_unit_rate) + LTL_unit_rate
Case break6_lower To break6_upper
unit_shipment_rate = 3 * (truck_unit_capacity / order_quantity_Qk) * TL_unit_rate
Case break7_lower To break7_upper
unit_shipment_rate = 3 * (truck_unit_capacity / order_quantity_Qk) * _
(TL_unit_rate - LTL_unit_rate) + LTL_unit_ rate
Case break8_lower To break8_upper
unit_shipment_rate = 4 * (truck_unit_capacity / order_quantity_Qk) * TL_unit_rate
Case break9_lower To break9_upper
unit_shipment_rate = 4 * (truck_unit_capacity / order_quantity_Qk) * _
(TL_unit_rate - LTL_unit_rate) + LTL_unit_rate
Case Else
unit_shipment_rate = 0
End Select
End Sub
Appendix 4. Grocery Item Demand Characteristics
Item Description Mean SD
Annual
Demand
Purchase
Price
Shortage
Cost Probability Distribution MSE
2
?
p-value K-S p-value
1 Silk Soy Milk Plain 9.55 3.21 3,486 2.17 0.67 NORM (9.55, 3.18) 0.017 2.600 0.467
2 Jiffy Corn Muffin Mix 14.30 8.49 5,220 0.32 0.06 2+WEIB (13.3, 1.34) 0.009 2.580 0.284 0.077 >0.15
3 Pills Grands Golden Corn 5.84 3.04 2,132 1.23 0.39 NORM (5.84, 3.01) 0.020 4.530 0.035 0.043 >0.15
4 Hunts Spad Sce Four Cheese 8.39 4.79 3,062 0.85 0.13 NORM (8.39, 4.74) 0.013 5.750 0.059 0.136 >0.15
5 Lnl Cottage Chse Sc 1% 6.27 2.70 2,289 1.52 0.77 TRIA ( 2, 4.57, 14) 0.034 7.820 0.050 0.102 >0.15
6 Whiskas Temptations Seafood 5.41 2.62 1,975 1.04 0.15 2+11*BETA (0.863, 1.92) 0.013 4.280 0.127 0.155 >0.15
7 Gerber Rice Cereal 3.22 1.84 1,175 1.43 0.17 NORM (3.22, 1.82) 0.035 11.200 0.005 0.116 >0.15
8 Overlake Blueberries 10.00 4.48 3,650 1.40 0.51 2+17*BETA ( 1.22, 1.37) 0.017 5.960 0.120 0.065 >0.15
9 Whiskas Bits O Beef Dinner 13.50 6.51 4,928 0.51 0.08 NORM (13.5, 6.44) 0.004 0.915 0.367 0.064 >0.15
10 Fancy Feast Flaked Salm Wfish 7.41 4.48 2,705 0.40 0.03 2+EXPO(5.41) 0.014 2.770 0.250 0.133 >0.15
11 Musselman Apple Juice 14.30 11.80 5,220 1.48 0.53 3+GAMM(10.8, 1.05) 0.027 6.810 0.009 0.144 >0.15
12 Ortega Soft Taco Dinner Kit 5.31 3.40 1,938 1.84 0.59 0.999+13*BETA(0.742, 1.49) 0.007 2.250 0.524 0.139 >0.15
13 Shake Bake Chicken 7.27 3.50 2,654 1.48 0.40 NORM(7.27, 3.46) 0.019 6.880 0.009 0.113 >0.15
14 Hunt Tomato Paste 7.59 4.30 2,770 0.96 0.03 NORM(7.59, 4.25) 0.040 12.100 <0.005 0.106 >0.15
15 Combo Cheddar Cheese Pretzel 6.14 4.35 2,241 1.31 0.47 0.999+EXPO(5.14) 0.022 4.280 0.126 0.187 0.049
16 Breakstone Sour Cream 19.20 4.42 7,008 0.78 0.31 6+22*BETA(2.96, 1.99) 0.008 1.100 0.587 0.081 >0.15
17 Shurfine California Blend 10.80 4.83 3,942 0.83 0.65 NORM(10.8, 4.78) 0.011 2.500 0.122 0.119 >0.15
18 Campbell Cream Chicken Soup 15.60 7.45 5,694 0.87 0.11 3+36*BETA(1.52, 2.81) 0.005 1.170 0.565 0.070 >0.15
19 Greens Scooter Crunch 18.00 8.22 6,570 1.15 0.56 4+31*BETA(1.14, 1.38) 0.016 5.760 0.134 0.080 >0.15
20 Pedigree Choice Chkn Rice 8.41 4.21 3,070 0.56 0.09 NORM(8.41, 4.16) 0.023 5.890 0.017 0.139 >0.15
21 Shurfine Yellow Amer Cheese 25.80 18.00 9,417 1.90 0.79 5+WEIB(22.1, 1.2) 0.044 11.000 <0.005 0.178 0.075
22 Int Delite French Vanilla 11.10 4.15 4,052 1.15 0.43 4+23*BETA(1.71, 3.84) 0.009 1.560 0.224 0.152 >0.15
23 Pills Btrmlk Biscuits 7.51 3.73 2,741 1.97 0.94 NORM(7.51, 3.69) 0.011 1.640 0.215 0.088 >0.15
24 Cole Mini Garlic Bread 15.90 5.71 5,804 0.96 0.47 TRIA(7, 11.3, 27) 0.012 7.460 0.061 0.145 >0.15
25 Tetley Tea Bags Decaf 7.24 2.96 2,643 2.03 0.41 TRIA(0.999, 7.5, 14) 0.005 2.180 0.541 0.123 >0.15

Item Description Mean SD
Annual
Demand
Purchase
Price
Shortage
Cost Probability Distribution MSE
2
?
p-value K-S p-value
26 Pillsbury Grands Flaky 7.47 3.85 2,727 0.88 0.41 NORM(7.47, 3.81) 0.038 6.850 0.009 0.081 >0.15
27 Shultz Fun Tas Stixs 7.88 3.02 2,876 0.72 0.24 TRIA(2, 6.65, 15) 0.009 2.460 0.487 0.117 >0.15
28 Breakstone Sour Cream Reg 50.10 33.10 18,287 1.31 0.47 15+EXPO(35.1) 0.002 0.314 0.600 0.211 0.019
29 Kraft Shred Mozz Cheese skim 15.80 12.70 5,767 1.83 0.76 3+LOGN(24.3, 78) 0.011 2.510 <0.005 0.194 0.038
30 Fancy Feast Tend Liver & Chkn 9.82 5.79 3,584 0.40 0.03 0.999+30*BETA(1.35, 3.23) 0.019 5.150 0.024 0.091 >0.15
31 Stouf Homestyle Chicken 4.69 2.36 1,712 3.19 1.35 NORM(4.69, 2.34) 0.063 14.600 <0.005 0.069 >0.15
32 Trop Twst Strawbery Kiwi Cycl 4.45 3.10 1,624 1.97 0.27 0.999+16*BETA(0.757, 2.75) 0.004 0.397 0.541 0.189 0.047
33 Bounty Big White Blancos 16.40 5.18 5,986 1.59 0.10 8+20*BETA(1.09, 1.53) 0.026 9.050 0.030 0.086 >0.15
34 Domino Dark Brown Sugar 8.00 6.07 2,920 0.58 0.10 2+EXPO(6) 0.008 2.380 0.322 0.107 >0.15
35 Budget Lt Spec Sel Rigat Broc 7.59 4.03 2,770 0.71 0.33 0.999+17*BETA(1.25, 1.97) 0.022 1.060 0.113 0.082 >0.15
36 Era Liq Reg Cp 16 Use 4.25 1.82 1,551 2.51 0.48 TRIA(0.999, 4.5, 8) 0.020 4.680 0.210 0.111 >0.15
37 Shake Bake Original Pork 10.90 5.03 3,979 1.48 0.41 2+25*BETA(1.66, 3) 0.011 3.350 0.203 0.086 >0.15
38 Heluva Gd French Onion Dip 4.49 2.68 1,639 2.38 0.98 0.999+8*BETA(0.521, 0.674) 0.006 2.780 0.600 0.213 0.018
39 Old El Paso Refried Beans Ff 5.20 2.76 1,898 0.95 0.22 0.999+ERLA (2.1, 2) 0.007 3.850 0.162 0.124 >0.15
40 Alpo Prime Slices W Beef 7.71 5.22 2,814 0.53 0.07 0.999+WEIB(7.13, 1.23) 0.021 5.330 0.074 0.095 >0.15
41 Fancy Feast Ocean Fish 8.75 6.10 3,194 0.40 0.03 0.999+23*BETA(0.732, 1.44) 0.004 1.500 0.688 0.151 >0.15
42 Frenchs Mustard Squeeze 10.00 4.35 3,650 0.74 0.16 2+17*BETA(1.32, 1.48) 0.013 4.470 0.225 0.080 >0.15
43 Cherry Man Maraschino Cherry 6.51 3.46 2,376 1.00 0.25 NORM(6.51, 3.43) 0.035 8.120 <0.005 0.096 >0.15
44 Fancy Feast Cod Sole Shrimp 13.20 5.83 4,818 0.40 0.03 NORM(13.2, 5.77) 0.058 11.100 <0.005 0.168 0.103
45 Black Pearl Ripe Olive Small 6.20 3.04 2,263 1.02 0.58 NORM(6.2, 3.01) 0.017 5.910 0.053 0.067 >0.15
46 Kraft Nat Mild Ched Chunk 11.00 6.03 4,015 1.70 0.75 3+ERLA(4.02, 2) 0.047 7.490 0.007 0.184 0.057
47 York Peppermint Miniatures 4.04 2.00 1,475 2.48 0.79 0.999+9*BETA(1.19, 2.34) 0.033 12.300 <0.005 0.126 >0.15
48 SF Sweet Garden Peas 8.41 4.16 3,070 0.34 0.09 NORM(8.41, 4.12) 0.011 2.940 0.090 0.091 >0.15
49 Morton Iodized Salt 9.31 3.99 3,398 0.38 0.04 3+15*BETA(1.03, 1.41) 0.001 0.306 >0.75 0.093 >0.15
50 SF Double Duos Cookies 4.59 2.60 1,675 1.61 0.57 0.999+12*BETA(1.04, 2.43) 0.031 9.270 0.010 0.126 >0.15
51 Crisco Oil 4.27 2.28 1,559 1.99 0.30 0.999+11*BETA(1.15, 2.71) 0.004 2.640 0.275 0.119 >0.15
52 Shurfine Sour Cream 24.10 7.04 8,797 0.55 0.24 TRIA(12, 19.1, 45) 0.016 4.300 0.237 0.085 >0.15
53 Pills Grands Flky Buttermilk 12.20 6.21 4,453 1.23 0.39 TRIA(0.999, 7.21, 30) 0.007 1.410 0.707 0.081 >0.15
Item Description Mean SD
Annual
Demand
Purchas
e Price
Shortage
Cost Probability Distribution MSE
2
?
p-value K-S p-value
54 Lol Whip Butter Aa Salt Bowl 7.55 2.56 2,756 1.44 0.65 3+12*BETA(1.58, 2.58) 0.011 3.060 0.227 0.134 >0.15
55 Campbell Hmstyl Chick Noodle 12.00 5.57 4,380 1.09 0.14 0.999+25*BETA(1.74, 2.22) 0.018 4.280 0.126 0.081 >0.15
56 Lipton Onion Soup Mix 2 Pk 13.50 5.09 4,928 1.10 0.26 5+WEIB(9.24, 1.49) 0.018 4.320 0.235 0.161 0.129
57 Friskies Salmon Dinner 14.10 6.54 5,147 0.33 0.04 0.999+33*BETA(2.03, 3.07) 0.004 0.647 0.445 0.088 >0.15
58 Fancy Feast Flaked Trout 13.30 6.19 4,855 0.40 0.03 4+ERLA(4.66, 2) 0.009 2.310 0.334 0.078 >0.15
59 Skippy Snk Bar Pbtr Marsh 6 P 2.80 1.47 1,022 2.21 0.52 NORM(2.8, 1.46) 0.011 3.710 0.173 0.110 >0.15
60 Welchs Strawberry Breeze Cktl 4.39 2.12 1,602 1.67 0.66 NORM(4.39, 2.1) 0.023 6.520 0.040 0.056 >0.15
61 Dannon Lacreme Straw 6.67 2.73 2,435 1.45 0.71 TRIA(0.99, 5.29, 13) 0.030 8.310 0.042 0.142 >0.15
62 Eggo Homestyle Waffles 28.40 8.10 10,366 1.35 0.53 NORM(28.4, 8.02) 0.012 4.380 0.039 0.167 0.107
63 Jello Inst Van Pudding 10.50 5.97 3,833 0.64 0.08 0.999+ERLA(4.73, 2) 0.011 2.170 0.358 0.090 >0.15
64 Clear Choice Cal Fr Peach 9.08 5.09 3,314 0.46 0.06 0.999+22*BETA(1.23, 2.12) 0.034 11.900 <0.005 0.102 >0.15
65 King Syrup Glass 8.45 3.45 3,084 1.16 0.31 TRIA(0.999, 7.35, 17) 0.013 3.150 0.387 0.080 >0.15
66 Shurfine Shredded Cheddar 39.60 22.60 14,454 1.33 0.61 13+117*BETA(0.842, 2.86) 0.017 5.280 0.023 0.126 >0.15
67 Pills H Jack Pancakes 6.00 2.68 2,190 1.46 0.66 0.999+11*BETA(1.44, 1.73) 0.013 4.560 0.218 0.105 >0.15
68 Dart Nat Plas Drink Cup 16oz 10.40 3.45 3,796 0.75 0.25 NORM(10.4, 3.41) 0.006 2.020 0.385 0.068 >0.15
69 Sf Margarine Quarters 12.80 7.55 4,672 0.46 0.22 TRIA(0.999, 8.29, 35) 0.017 3.440 0.346 0.172 0.090
70 Scott 1000 Bath Tissue Wht 6.43 2.47 2,347 3.91 0.25 TRIA(0.999, 6.29, 12) 0.031 11.600 0.009 0.092 >0.15
71 White Paper Plates 150 Ct 10.60 3.79 3,869 1.47 0.48 2+17*BETA(12.04, 1.99) 0.007 1.760 0.433 0.108 >0.15
72 Kid Cuisine Chicken Nugget 21.20 6.17 7,738 1.31 0.47 TRIA(10, 17.5, 36) 0.026 7.850 0.049 0.096 >0.15
73 Shurfine Squeeze Mustard 5.16 2.49 1,883 0.73 0.25 2+10*BETA(0.782, 1.7) 0.005 0.645 0.728 0.147 >0.15
74 Sf Orange Soda 2 Liter 5.02 2.12 1,832 0.62 0.16 UNIF(0.999, 9) 0.014 5.140 0.528 0.132 >0.15
75 Heinz Squeeze Ketchup 9.80 10.60 3,577 1.12 0.35 2+78*BETA(0.389, 3.5) 0.021 11.500 <0.005 0.436 <0.01
76 Bumble Bee Solid White Water 28.60 7.43 10,439 2.56 0.46 NORM(28.6, 7.36) 0.015 4.080 0.045 0.110 >0.15
77 Smart Balance 67% Spread Bowl 13.60 4.37 4,964 1.33 0.47 NORM(13.6, 4.33) 0.009 1.880 0.189 0.068 >0.15
78 Sf Grape Juice 7.25 4.87 2,646 2.00 0.63 2+EXPO(5.26) 0.034 5.920 0.053 0.161 0.133
79 Nestle Chunky Singles 7.39 5.64 2,697 0.34 0.15 0.999+EXPO(6.39) 0.027 5.650 0.063 0.198 0.033
80 Oreida Shoestring Fries 12.50 4.68 4,563 1.69 0.70 TRIA(5, 9.29, 25) 0.016 2.660 0.458 0.102 >0.15

Item Description Mean SD
Annual
Demand
Purchas
e Price
Shortage
Cost Probability Distribution MSE
2
?
p-value K-S p-value
81 Shurfine Straw Preserves 3.51 1.63 1,281 1.78 0.80 TRIA(0.999, 2.29, 7) 0.004 0.789 >0.75 0.152 >0.15
82 Sf Plastic Wrap 12 4.75 2.28 1,734 0.75 0.36 0.999+8*BETA(0.969, 1.1) 0.014 4.480 0.361 0.108 >0.15
83 Sf Baby Lima Beans 17.70 6.37 6,461 1.00 0.44 6+26*BETA(1.41, 1.71) 0.002 0.540 >0.75 0.083 >0.15
84 Friskies Chicken & Salmon 11.30 5.81 4,125 0.33 0.04 NORM(11.3, 5.76) 0.015 2.690 0.267 0.076 >0.15
85 Campbell Beef Broth 9.24 4.30 3,373 0.76 0.11 NORM(9.24, 4.25) 0.026 7.090 0.030 0.081 >0.15
86 Kraft 3 Cheese Mac & Cheese 11.10 4.37 4,052 0.83 0.08 NORM(11.1, 4.33) 0.015 1.920 0.404 0.108 >0.15
87 Reynolds Wrap Heavy Duty Foil 10.00 5.83 3,650 1.83 0.54 3+35*BETA(0.958, 3.82) 0.017 3.940 0.048 0.156 >0.15
88 Oreida Golden Crinkle Fries 24.30 7.16 8,870 1.69 0.71 NORM(24.3, 7.09) 0.021 4.050 0.046 0.092 >0.15
89 Glad Drawstring Tall Kit 4.35 2.02 1,588 3.29 0.68 NORM(4.35, 2) 0.032 12.200 <0.005 0.081 >0.15
90 Bounty White Towels(C) 13.70 3.95 5,001 0.91 0.25 TRIA(4, 14.9, 21) 0.015 2.310 0.511 0.109 >0.15
91 Frigo Ricotta Cheese P/Skim 8.47 3.55 3,092 1.60 0.97 3+16*BETA(1.22, 2.35) 0.009 4.340 0.122 0.091 >0.15
92 Green Giant White Shoepeg Corn 8.67 4.23 3,165 0.81 0.14 NORM(8.67, 4.19) 0.009 3.260 0.210 0.066 >0.15
93 Starbucks Brkfst Blnd W B Cof 3.16 1.60 1,153 6.03 0.94 NORM(3.16, 1.59) 0.013 4.900 0.089 0.095 >0.15
94 White Paper Plates 9 12.90 4.16 4,709 0.98 0.41 TRIA(4, 11.7, 23) 0.011 1.660 0.654 0.099 >0.15
95 Friskies Prime Filet Ckn Gvy 13.70 6.55 5,001 0.33 0.04 NORM(13.7, 6.49) 0.013 2.170 0.158 0.098 >0.15
96 Heinz Tomato Ketchup 12.30 7.72 4,490 1.86 0.12 2+WEIB(11.1, 1.34) 0.031 7.460 0.007 0.103 >0.15
97 Swanson Pancakes & Sausage 9.35 3.83 3,413 1.04 0.51 NORM(9.35, 3.79) 0.019 4.530 0.036 0.108 >0.15
98 Popsicle Creamsicle Orang Ras 5.27 3.56 1,924 1.54 0.94 0.999+14*BETA(0.699, 1.59) 0.012 4.300 0.125 0.164 0.120
99 Popsicle Fudgesicle Sf 7.31 4.14 2,668 1.78 0.95 0.999+16*BETA(1.01, 1.56) 0.008 2.670 0.457 0.070 >0.15
100 Frigo P Skim Mozzarella Ball 6.57 3.91 2,398 2.65 1.42 0.999+16*BETA(0.978, 1.83) 0.002 0.649 0.727 0.111 >0.15
162

Appendix 5. Supply Chain Actions Source Publications
Title Frequency Description
Advantage Monthly Published by the Food Marketing Institute. Provides
news and information about issues, programs,
business trends and developments.
Progressive Grocer Monthly Strategic publication serving upper management in the
supermarket industry. Trends in store development,
technology, marketing, logistics, international
retailing, human resources, and consumer purchasing
patterns.
Frozen Food Age Monthly Devoted to retail, manufacturing, and logistics
decision-makers in the frozen and refrigerated food
industry.
Grocery Headquarters Monthly Reporting on issues, trends and strategies involved in
the operation of food retailers, including
developments throughout the distribution chain.
Food Logistics Monthly Articles and benchmark research in the areas of
warehousing, material handling, transportation and
information management.
PROMO Magazine Serves marketing professionals at consumer product
and service companies, retail chains, and Internet
businesses.
Supermarket News Weekly Nationally circulated weekly trade magazine for the
food distribution industry.
Supermarket Business Monthly Reporting on issues affecting the supermarket industry
Food & Drug Packaging Monthly Reporting on packaging issues
163

Appendix 6. Supply Chain Actions
Action
Type BCRC Category
Total Number
of Actions 2000 2001 2002 2003 2004
SC Alliance 323 194 85 14 5 25
SC Buildings and Facilities 8,220 745 1080 1334 2361 2700
SC Capacity 318 0 39 0 5 274
SC Contracting
7,303
883 1702 1312 1894 1512
SC Customer Relations
1,191
5 5 30 74 1077
SC Distribution
4,433
364 523 916 2129 501
SC E-Commerce
311
137 67 20 10 77
SC Equipment and Supplies
2,815
420 625 744 654 372
SC Information Management
1,193
147 15 221 505 305
SC Inventory
263
5 47 59 92 60
SC Labeling
4,318
549 292 1228 1545 704
SC Logistics
1,010
84 83 282 369 192
SC Outsourcing
191
1 30 61 48 51
SC Packaging
1,025
86 108 163 333 335
SC Partnerships
679
50 40 195 116 278
SC Product Development
722
32 35 117 295 243
SC Purchasing
818
205 55 265 140 153
SC Quality Management
386
0 47 118 109 112
SC Service Development
70
0 0 0 0 70
SC Storage
91
19 11 15 20 26
SC Suppliers
1,700
171 158 506 689 176
SC Technology
4,217
396 260 1081 1420 1060
SC Transportation
344
18 72 97 92 65
SC Warehousing
4,309
612 894 897 1202 704
Totals: 46,250 7,123 8,274 11,677 16,110 13,076
164

Appendix 7. Market-Based Actions
Action
Type BCRC Category
Total Number
of Articles 2000 2001 2002 2003 2004
MB Acquisition 13,693 2180 2351 3287 3245 2630
MB Advertising 2,219 301 604 575 373 366
MB Competition 6,469 725 640 1538 1737 1829
MB Design & Construction 483 50 41 86 174 132
MB Divestment
11,475
1717 1961 2768 2798 2231
MB Downsize
248
30 0 20 80 118
MB Endorsements
93
5 25 18 45 0
MB Environmental Policy
50
10 5 35 0 0
MB Facility Closure
562
0 0 4 0 558
MB Franchise
250
73 21 79 27 50
MB Green Market
30
10 0 0 0 20
MB Growth
3,085
215 242 1076 649 903
MB Innovation
777
50 35 371 175 146
MB Investment
2,489
131 494 612 709 543
MB Investor Relations
269
15 13 61 80 100
MB Joint Venture
302
53 75 49 115 10
MB Labor Relations
3,327
50 135 472 1094 1576
MB Licensing Agreements
183
30 20 49 54 30
MB Location
1,259
149 171 234 448 257
MB Market Research
355
0 5 55 50 245
MB Market Share
4,017
389 651 711 1094 1172
MB Market Size
190
0 0 30 20 140
MB Marketing
42,219
5583 6064 10910 10690 8972
MB Marketing Agreements
90
0 0 10 10 70
MB Mediation
709
0 24 55 115 515
MB Mergers
12,535
2048 2160 2914 2977 2436
MB Negotiation
918
0 44 112 212 550
MB Organization Formation
40
0 0 0 5 35
MB Prices and Rates
7,526
873 769 2101 2283 1500
MB Product Defects and Recalls
254
45 15 69 70 55
MB Product Discontinuation
165
0 0 85 70 10
MB Product Enhancement
321
0 0 122 169 30
MB Product Introduction
1,846
106 89 358 908 385
MB Property
435
39 158 88 88 62
MB Public Relations
461
88 60 168 70 75
MB Remodeling
619
63 107 142 90 217
MB Renovation
466
15 100 124 70 157
MB Reorganization
991
55 63 70 119 684
MB Restructuring
1,038
112 139 88 86 613
MB Service Discontinuation
50
0 0 0 20 30
MB Service Enhancement
251
0 0 0 0 251
MB Service Introduction
432
0 5 6 55 366
MB Target Marketing
854
10 205 98 263 278
Totals: 124,045 17,220 19,492 31,652 33,340 32,351
165

Disclaimer

The views expressed in this dissertation are those of the author and do not
reflect the official policy or position of the United States Air Force, Department of
Defense, or the U.S. Government.
166

References
Afuah, A. 2001. Dynamic Boundaries of the Firm: Are Firms Better Off Being
Vertically Integrated in the Face of a Technological Change? Academy of
Management Journal, 44(6): 1121-1228.
Agnese, J. 2005. Supermarkets & Drugstores. In E. M. Bossong-Martines (Ed.),
Standard & Poor's Industry Surveys: 36.
Aldenderfer, M. S. and Blashfield, R. K. (Eds.). 1984. Cluster Analysis. Newbury
Park: Sage Publications.
Anderson, M. G. and Katz, P. B. 1998. Strategic sourcing. International Journal of
Logistics Management, 9(1): 1.
Atkins, D. R. and Iyogun, P. O. 1988. Periodic Versus 'Can-Order' Policies For
Coordinated Multi-Item Inventory Systems. Management Science, 34(6): 791.
Bearing Point. 2003. Inventory Management 2003: An Overview. Chain Store Age,
Dec 2003: 3A-11A.
Bensaou, M. and Anderson, E. 1999. Buyer-Supplier Relations in Industrial Markets:
When do Buyers Risk Making Idiosyncratic Investments? Organization Science,
10(14): 460-481.
Buffa, F. P. and Reynolds, J. I. 1977. The Inventory-Transport Model With
Sensitivity Analysis by Indifference Curves. Transportation Journal, 17(2): 83.
Butner, K. 2005. The GMA 2005 Logistics Survey. Supply chain performance in
food, grocery and consumer products: 29: IBM Business Consulting Services.
Cachon, G. 2001. Managing a Retailer's Shelf Space, Inventory, and Transportation.
Manufacturing & Service Operations Management, 3(3): 211-229.
Cetinkaya, S. and Lee, C.-Y. 2000. Stock Replenishment and Shipment Scheduling
for Vendor-Managed Inventory Systems. Management Science, 46(2): 217-232.
167

Chen, M.-J. and Hambrick, D. 1995. Speed, Stealth, and Selective Attach: How
Small Firms Differ from Large Firms in Competitive Behavior. Academy of
Management Journal, 38(2): 453-482.
Cool, K. and Henderson, J. 1998. Power and Firm Profitability in Supply Chains:
French Manufacturing Industry in 1993. Strategic Management Journal, 19: 909-926.
Copacino, W. C. 1997. Supply Chain Management The Basics and Beyond. Boca
Raton, FL: St. Lucie Press.
Corsten, D. and Gruen, T. 2003. Desperately seeking shelf availability: an
examination of the extent, the causes, and the efforts to address retail out-of stocks.
International Journal of Retail & Distribution Management, 31(12): 605-617.
Currie, N. 2005. USB Q-Series Report: Do supermarkets have a future?, The
Progressive Grocer, 72nd Annual Report of the Grocery Industry:: 62-79.
Droge, C. L. M. and Germain, R. 2000. The Relationship of Electronic Data
Interchange with Inventory and Financial Performance. Journal of Business Logistics,
21(2): 209-230.
Fazel, F. 1997. A comparative analysis of inventory costs of JIT and EOQ
purchasing. International Journal of Physical Distribution & Logistics Management,
27(8): 496-504.
Federgruen, A., Groenevelt, H., and Tijms, H. C. 1984. Coordinated Replenishments
in a Multi-Item Inventory System with Compound Poisson Demands. Management
Science, 30(3): 344.
Fernie, J. 1999. Relationships in the Supply Chain, Logistics and Retail Management:
23-46. Boca Raton, LF: CRC Press.
Ferrier, W. J., Smith, K. G., and Grimm, C. M. 1999. The Role of Competitive Action
in Market Share Erosion and Industry Dethronement: A Study of Industry Leaders
and Challengers. Academy of Management Journal, 42(4): 372-388.
Ferrier, W. J. and Lee, H. 2002. Strategic Aggressiveness, Variation, and Surprise:
How the Sequential Pattern of Competitive Rivalry Influences Stock Market Returns.
Journal of Managerial Issues, 14(2): 162-180.
168

Frankel, R., Goldsby, T. J., and Whipple, J. M. 2002. Grocery industry collaboration
in the wake of ECR. International Journal of Logistics Management; Ponte Vedra
Beach, 13(1): 57.
Frohlich, M. T. and Westbrook, R. A. 2001. Arcs of integration: an international
study of supply chain strategies. Journal of Operations Management, 19: 185-200.
Gale, T. Grocery Stores; http://galenet.galegroup.com/servlet/BCRC, 2005.
Gale, T. Content Solutions; http://www.gale.com/bizdev/content.htm.
Greene, W. H. 2003. Econometric Analysis (Fifth ed.). Delhi/India: Pearson
Education Inc.
Grimm, C. M. and Smith, K. G. 1997. Strategy as Action. Industry Rivalry and
Coordination. Cincinnati, Ohio: South-Western College Publishing.
Gulati, R. 1998. Alliances and Networks. Strategic Management Journal, 19: 293-
317.
Hair, J. F., Anderson, R. E., Tatham, R. L., and Black, W. C. 1998. Multivariate Data
Analysis (5th ed.). Upper Saddle River, New Jersey: Prentice Hall.
Hannan, M. T. and Freeman, J. 1984. Structural Inertia and Organizational Change.
American Sociology Review, 49: 149-164.
Hansen, G. S. and Wernerfelt, B. 1989. Determinants of Firm Performance: The
Relative Importance of Economic and Organizational Factors. Strategic Management
Journal, 10(5): 399-411.
Hines, P., Rich, N., Bicheno, J., Brunt, D., and al, e. 1998. Value stream management.
International Journal of Logistics Management, 9(1): 25.
Houlihan, J. B. 1985. International Supply Chain Management. International Journal
of Physical Distribution and Materials Management, 15(1): 22-38.
169

Hult, G. T. M., Ketchen, D. J., and Nichols, E. 2002. An Examination of Cultural
Competitiveness and Order Fulfillment Cycle Time Within Supply Chains. Academy
of Management Journal, 45(3): 577-586.
Hult, G. T. M., Ketchen, D. J., and Slater, S. F. 2004. Information Processing,
Knowledge Development, and Strategic Supply Chain Performance. Academy of
Management Journal, 47(2): 241-253.
Ireland, R. B., Hitt, M. A., and Vaidyanath, D. 2002. Alliance Management as a
Source of Competitive Advantage. Journal of Management, 28(3): 413-446.
Jacobson, R. 1992. The "Austrian" School of Strategy. Academy of Management
Journal, 17(4): 782-807.
Jauch, L. R., Osborn, R. N., and Martin, T. N. 1980. Structured Content Analysis of
Cases: A Complementary Method for Organizational Research. Academy of
Management Review, 5(4): 517-525.
Keaton, M. H. 1994. A New Functional Approximation to the Standard Normal Loss
Integral. Production and Inventory Management, 35(2): 58-61.
Kinsey, J. and Senauer, B. 1996. Consumer Trends and Changing Food Retailing
Formats. American Journal of Agricultural Economics, 78(5): 1187-1191.
Kotabe, M., Martin, X., and Domoto, H. 2003. Gaining From Vertical Partnerships:
Knowledge Transfer, Relationship Duration, and Supplier Performance
Improvements in the U.S. and Japanese Automotive Industries. Strategic
Management Journal, 24: 293-316.
Kurnia, S. and Johnston, R. B. 2003. Adoption of efficient consumer response: key
issues and challenges in Australia. Supply Chain Management: An International
Journal, 8(3): 251-262.
Law, A. M. and Kelton, W. D. 2000. Simulation Modeling and Analysis (Third ed.).
Singapore: McGraw Hill Companies.
Lee, H., Smith, K. G., Grimm, C. M., and Schomburg, A. 2000. Timing, Order and
Durability of New Product Advantages with Imitation. Strategic Management
Journal, 21: 23-30.
170

Lee, H. L., Padmanabhan, V., and Whang, S. 1997. Information Distortion in a
Supply Chain: The Bullwhip Effect. Management Science, 43(4): 546-558.
Lynch, D. F., Keller, S. B., and Ozment, J. 2000. The Effects of Logistics Capabilities
and Strategy on Firm Performance. Journal of Business Logistics, 21(2): 47-67.
Madhok, A. 2002. Reassessing The Fundamentals And Beyond: Ronald Coase, The
Transaction Cost and Resource-Based Theories of the Firm and The Institutional
Structure of Production. Strategic Management Journal, 23: 535-550.
Majumdar, S. K. and Ramaswamy, V. 1994. Explaining Downstream Integration.
Managerial and Decision Economics, 15(2): 119-129.
Mathews, R. 2005. True Believers, The Progressive Grocer, 72nd Annual Report of
the Grocery Industry:: 80-82.
McTaggart, J. and Heller, W. 2005. Forces of Change, The Progressive Grocer, 72nd
Annual Report of the Grocery Industry:: 48-60.
Mentzer, J. T., DeWitt, W., Keebler, J. S., Min, S., Nix, N. W., Smith, C. D., and
Zacharia, Z. G. 2001a. Defining Supply Chain Management. Journal of Business
Logistics, 22(2): 1-23.
Mentzer, J. T., Flint, D. J., and Hult, G. T. M. 2001b. Logistics service quality as a
segment-customized process. Journal of Marketing, 65(4): 82-104.
Microsoft. Description of the NORMSDIST function in Excel 2003, Article ID:
827369; http://support.mocrosoft.com/kb/827369; January 11, 2006.
Morash, E. A. 2001. Supply Chain Strategies, Capabilities, and Performance.
Transportation Journal, 41(1): 37-54.
Mudambi, R. and Helper, S. 1998. The 'Close But Adversarial' Model of Supplier
Relations in the U.S. Auto Industry. Strategic Management Journal, 19: 775-792.
Nielsen, C. and Larsen, C. 2005. An analytical study of the Q(s,S) policy applied to
the joint replenishment problem. European Journal of Operational Research, 163(3):
721-732.
171

Pantumsinchai, P. 1992. A Comparison of Three Joint Ordering Inventory Policies.
Decision Sciences, 23(1): 111.
Pindyck, R. S. and Rubinfeld, D. L. 1998. Econometric Models and Economic
Forecasts (4th ed.). Boston: Irwin McGraw-Hill.
Porter, M. 1990. The Competitive Advantage of Nations, The Competitive Advantage
of Nations: 73-93: Free Press.
Porter, M. E. 1980. Competitive Strategy. New York: The Free Press.
Rabinovich, E. and Evers, P. T. 2002. Enterprise-wide adoption patterns of inventory
management practices and information systems. Transportation Research Part E, 38:
389-404.
Randall, T. and Ulrich, K. 2001. Product Variety, Supply Chain Structure, and Firm
Performance: Analysis of the U.S. Bicycle Industry. Management Science, 47(12):
1588-1604.
Rao, U. S. 2003. Properties of the Periodic Review (R, T) Inventory Control Policy
for Stationary, Stochastic Demand. Manufacturing & Service Operations
Management, 5(1): 37-53.
Ricks, J. E. 1997. Electronically developed theory and procedure for distribution
channel management via electronic data interchange linkage. Logistics Information
Management, 10(1): 20-27.
Ross, S. 2002. A First Course in Probability (Sixth ed.). Upper Saddle River, New
Jersey: Prentice hall.
Russell, R. M. and Krajewski, L. J. 1991. Optimal Purchase and Transportation Cost
Lot Sizing for a Single Item. Decision Sciences, 22(4): 940-952.
Scott, C. and Westbrook, R. 1991. New Strategic Tools for Supply Chain
Management. International Journal of Physical Distribution & Logistics Management,
21(1): 23-33.
172

Shaffer, B., Quasney, T. J., and Grimm, C. M. 2000. Firm Level Performance
Implication of Nonmarket Actions. Business and Society, 39(2): 126-143.
Shin, H., Collier, D. A., and Wilson, D. D. 2000. Supply Management Orientation
and Supplier/Buyer Performance. Journal of Operations Management, 18: 317-333.
Silver, E. A. and Peterson, R. 1979. Decision Systems for Inventory Management and
Production Planning. New York: John Wiley & Sons.
Silver, E. A. 1981. Operations Research in Inventory Management: A Review and
Critique. Operations Research, 29(4): 628-645.
Smith, K., Grimm, C., Gannon, M., and Chen, M. 1991. Organizational Information
Processing, Competitive Responses, and Performance in the U.S. Domestic Airlines
Industry. Academy of Management Journal, 34: 60-85.
Smith, K., Grimm, C., Young, G., and Wally, S. 1997. Strategic Groups and rivalrous
firm behavior. Towards a reconciliation. Strategic Management Journal, 18: 149-157.
Smith, K. G., Ferrier, W. J., and Ndorfor, H. 2001. Competitive Dynamics Research:
Critique and Future Directions, Handbook of Strategic Management. Oxford, UK:
Blackwell Publishers, Ltd.
Stock, G. N., Gries, J. P., and Kasarda, J. D. 2000. Enterprise Logistics and Supply
Chain Structure: The Role of Fit. Journal of Operations Management, 18: 531-547.
Stock, J. R. 1997. Applying theories from other disciplines to logistics. International
Journal of Physical Distribution & Logistics Management, 27(9/10): 515-539.
Swink, M. 1999. Threats to new product manufacturability and the effects of
development team integration processes. Journal of Operations Management, 17:
691-709.
Tan, K. C., Handfield, R. B., and Krause, D. R. 1998. Enhancing the firm's
performance through quality and supply base management: an empirical study.,
International Journal of Production Research, Vol. 36: 2813-2837: Taylor & Francis
Ltd.
173

Tan, K. C. 2002. Supply chain management: Practices, concerns, and performance
issues. Journal of Supply Chain Management, 38(1): 42.
Tan, K. C., Lyman, S. B., and Wisner, J. D. 2002. Supply chain management: A
strategic perspective. International Journal of Operations & Production Management,
22(5/6): 614.
Tarnowski, J. and Heller, W. 2004. The Super 50, The Progressive Grocer, Vol. May.
Tarnowski, J. 2005. Executive Insight Series: Technology and the Independent
Grocer. Progressive Grocer, February 1, 2005.
Teece, D. J., Pisano, G., and Shuen, A. 1997. Dynamic Capabilities and Strategic
Management. Strategic Management Journal, 18(7): 509-533.
Tersine, R. J. 1994. Principles of Inventory and Materials Management. Upper Saddle
River NJ: PTR Prentice Hall.
The Progressive Grocer. 2003. 70th Annual Report of the Grocer Industry, Marketing
Guidebook: The Bluebook of Supermarket Distribution: 16-30: Trade Dimensions
and The Progressive Grocer.
The Progressive Grocer. 2005. Staying Alive: Channel blurring isn't a fad.
Supermarkets are going to fight harder to remain relevant, and winning will require
radical changes. Is the industry ready to do what it takes to fix itself?, The
Progressive Grocer, 72nd Annual Report of the Grocery Industry:: 47.
Trade Dimensions. 2005. Market Scope: The Desktop Guide to Supermarket Share.
In T. Donato & K. Pluchino (Eds.). Wilton, CT: Trade Dimensions International, Inc.
U.S. Census Bureau. 2005. Annual Benchmark Report for Retail Trade and Food
Services: January 1992 Through February 2005, Current Business Reports, Series
BR/04-A: 96. Washington DC.
Vickery, S. K., Droge, C. L. M., Yeomans, J. M., and Markland, R. E. 1995. Time-
Based Competition in the Furniture Industry. Production and Inventory Management
Journal, Fourth Quarter: 14-21.
174

Viswanathan, S. 1997. Note. Periodic Review (s, S) Policies for Joint Replenishment
Inventory Systems. Management Science, 43(10): 1447-1454.
Walker, G. and Weber, D. 1984. A Transaction Cost Approach to Make-or-Buy
Decisions. Administrative Science Quarterly, 29(3): 373-391.
Ward, P. T. and Duray, R. 2000. Manufacturing strategy in context: environment,
competitive strategy and manufacturing strategy. Journal of Operations Management,
18: 123-138.
Weber, R. P. 1985. Series: Quantitative Applications in the Social Sciences. Basic
Content Analysis. Beverly Hills: Sage Publications.
Whiteoak, P. 1999. Rethinking Efficient Replenishment in the Grocery Sector,
Logistics and Retail Management: 110-140. Boca Raton, LF: CRC Press.
Williamson, O. E. 1975. Markets and Hierarchies: Analysis and Antitrust
Implications. A Study in the Economics of Internal Organization. New York: The
Free Press.
Williamson, O. E. 1998. The Institutions of Governance. American Economic
Review, 88(2): 75-79.
Williamson, O. E. 1999. Strategy Research: Governance and Competence
Perspectives. Strategic Management Journal, 20: 1087-1108.
Wisner, J. D. and Tan, K. C. 2000. Supply Chain Management and its Impact on
Purchasing. Journal of Supply Chain Management, 36(4): 33-42.
Zinn, W. and Liu, P. C. 2001. Consumer Response to Retail Stockouts. Journal of
Business Logistics, 22(1): 49-71.


doc_641102959.pdf