Description
The report includes topics like inventory types, postponement.
Postponement as a Strategy in Channel
Introduction
Inventory management in channel is a perennial issue of conflict. In a traditional channel, where we face a manufacturer, his branch, the distributor and the retailer, channel inventory is a complex matter. The manager (of the company) has the responsibility of not only managing his inventory but also monitoring and managing the inventories at the distributor and retailer level. Needless to say, he has no authority in the last two cases but only the responsibility. And, there are certain interesting but tricky situations that arise in this regard. Suppose the branch maintains inventory appropriately (meaning it never goes stock-out when a distributor places an order) and it finds that a distributor is under-stocked. The natural tendency is to ask the distributor to increase his stocks. This is against the interests of the distributor who tries to minimize his stocks, if not optimize. Obviously, there is a clash of interests. It is not uncommon to witness situations when the manager's efficiency becomes a source of complacency for the distributor who may maintain a precarious level of inventory bordering on stock-out. This note is an attempt to consider certain issues in inventory management in channels broadly, and focus on a specific method of inventoryoptimization, viz., postponement.
Inventory Types
Interestingly, when we use the phrase channel, we include the branch office too to get a total view, since the branch office's practices may vary from the corporate preferences, thus affecting channel management considerably. For example, the corporate office may like the branches to carry large inventory while the branch may prefer the opposite, to show a better operating-income statement. And, if the branches operate on profit-center basis, the conflict can be well understood. Inventory in a channel is held for various purposes and accordingly inventory types have been identified. They are as follows 1: A. Pipeline inventory B. Cyclical Inventory C. Buffer D. Seasonal Inventory E. Speculative Inventory Not all members in the channel carry all types of inventories, even if the type is applicable to the product category. This is due to differing perceptions about the need for the same.
© 2002, Prof. R. C. Natarajan, TAPMI, Manipal, Karnataka. For more discussion on inventory management, read Inventory Management - An Introduction by Prof. R.Rajagopalan, TAPMI.
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Cost of Inventory
Cost of Inventory holding includes the following: Cost of funds required for the stocks Cost of storage such as warehouse, insurance, maintenance of temperature / humidity, security etc. Cost of additional transportation due to storing at a point, including loading and unloading charges Cost of aging of stock due to storage (especially in food products and medicines) Cost of change of quality (deterioration) in fresh or perishable products due to handing and transshipment Holding inventory at as many places as possible enhances the organization's capacity to provide customer-service. Customer service includes: Meeting the order in time and in sufficient quantity Providing the variety and/or the packing sought by the consumer Ability to provide back-up support such as installation, training and after-sales service Needless to say that in the absence of these services, the customer will, in all probability, switch brands, adding to cost of stock-out.2 Thus, inventory policy and planning encompass decisions pertaining to channel-capacity as well.
Order Quantity and Frequency
An area where exists considerable conflict is the frequency of ordering and quantity to be ordered. Typically, a lower member3 wants his supplier (an upper member) to supply as frequently as possible and minimum quantity every time, whereas the upper member prefers to supply maximum stocks in as limited number of deliveries as possible. While in theory we study that the economic order quantity is a function of inventory-carrying cost, ordering cost and annual demand,4 following EOQ has its own difficulties in a channel. Some such situations where difficulties arise are as follows: a. Normally, the manufacturer finds shipment of large quantities - one truckload in practice - more economical than a "part-load". Thus they may prefer that the branch or the
2 It may be seen that the term stock-out is used rather broadly in this context to include the services that go with the product as well. In the realm of channel management, this interpretation will be more useful than to confine to the product alone. 3 The terms lower and upper are used to denote conceptually the channel flow from manufacturer (uppermost) and consumer (lowermost) without any value-loading. 4
You may recall that
EOQ = 2AD I
where, D is the periodic demand, A is the ordering cost per order and I is the inventory carrying cost per unit per period expressed as percentage of the value of the stock
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distributor order in truckloads. This may not go well with the EOQ of the branch / distributor. b. Preference by the manufacturer for larger orders may lead them to queue the larger orders first and waitlist the smaller orders. The resultant delay may make it impossible for such channel partners to plan their EOQ effectively. In both the cases of (a) and (b), those channel partners who place smaller orders are at a disadvantage. c. In cases where transportation is outsourced, the transport contractors may service full truckloads faster than smaller batches. As in the case of (b), this too may cause delays. d. In many organizations, salesforce incentives are linked to sales. Thus, they may prefer their distributors to lift more stocks than EOQ to fulfil their incentive-norms. In such cases, there is a systemic resistance for inventory-optimization in the channel. e. Some channel members (distributors or retailers) may attempt to minimize their inventory of a specific brand with a view to gaining funds for more profitable brands (may be of other organizations). In this case, EOQ cannot be practised. Such instances lead to inter-distributor transfers in times of emergent demand thus adding further to the cost of logistics. f. It is not uncommon among organizations to witness situations where the branch dumps inventory on distributors to show low inventory with itself. This practice is known as pseudo inventory reduction. When we talk of inventory-optimization, we consider the inventory in the whole channel and not at one stage at the cost of another. g. On certain occasions, a sporadic spike in demand could cause a ripple effect on the inventory policies, which may result in escalation of inventory-holdings across the channel. This phenomenon, known as bullwhip effect is a common occurrence in channels of distribution.5 When such a phenomenon occurs, it is difficult to rearrange the ordering-holding combination to set it on EOQ mode. h. Whenever the channel leader announces a sales promotion activity, the demand spikes up. By and large, this encourages only "forward buy", thus giving a false sense of demand escalation. This leads to excess stocking by the channel members at one time and stocking much lower stock at another time. These can hardly be termed as EOQ, though in the given context, the quantities may be optimal. The event invariably starts off a chain reaction whereby the next few orders become highly volatile. i. In those products that have unpredictable demand, very slow movement, but very high value of expected order(s), the concept of EOQ cannot be applied directly due to D in the formula for EOQ being unknown. In products such as magazines or newspapers, excess production and excess stocking is a part of the industry practice due to the involvement of advertising revenues. This is because it is better to hold a higher inventory than to lose sales due to stock-out. If the excess prints are sold, the publisher gets the MRP less the transportation cost and the channel commission. On the contrary, if the excess prints are unsold, the publisher loses only the variable cost of the unsold stock, which is very low, in addition to a miniscule transportation cost. So, the excess cost is worth the risk.
j.
For a detailed account of bullwhip effect, read my note Bullwhip Effect in Supply Chain, 2002, TAPMI, Manipal, Karnataka
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To overcome the problem of over-stocking or under stocking, organizations have innovated a method known as postponement. This is outlined below.
Postponement: An Inventory Reduction Technique
Postponement denotes shifting the product-completion closer to the time and/or place of purchase. This improves responsiveness to consumer-needs. To implement postponement, the production-process should be such as to enable resequencing, the major process should be common for all variants and the product should be capable of modularization. Postponement is not a new concept. It has been followed by bicycles industry for a long time. Normally, bicycle companies transport their products in batches of unassembled parts. This serves two logistical purposes: 1. Packaging of homogeneous components enables shipment of larger quantities thus offering economies of scale. 2. Assembled finished products are susceptible to damage in transit. Apart from these logistical benefits, postponement offers an important marketing benefit to the organization, viz., delayed differentiation. This means that the manufacturer is able to delay the complete the production of the product to suit the specific requirement of a specific consumer. So, in the bicycle example, the consumer's need for a bicycle with preferred specifications such as dynamo-operated headlight, a rear-view mirror, a seat with 6" escalation, a front seat, a rear seat with cushion etc. can be fitted at the dealer's premises before delivering to the consumer. Such a customization cannot be feasible at a centralized factory. In recent times, postponement has been extensively used to benefit the consumers by the paint industry. (Shah et al, 1999) Asian Paints in mid-seventies pioneered the computerized color-scheme selection in India. Under this system, in each of the Sales Points (meaning the distribution centers) spread across the country, a tinting machine was made available. The dealers were sold those fast moving variants, anyway. In addition, the specific color combination preferred by the consumer was recorded by the computer and the Sales Point, which carried the base liquid, added the stainers to generate the preferred paint for the consumer. Thus the consumer's specific need was met in less than 48 hours6 in most cases. This implied that the hub had to carry a predictable volume of base fluid and minimum quantities of stainers. Contrast it with a situation when this strategy was not existent. The company would have either forced its dealers to stock large number of shades of paints, a huge block of funds in the channel, or the consumer would have had to wait for a minimum two weeks to get his/her preferred shade. Yet another example of Benetton's postponement strategy is cited. Benetton, in fashion garment business, overcame the problem of forecasting the demand by resequencing the dyeing-knitting sequence to knitting-dyeing sequence. The dyeing would be completed once the consumer demand for shades at the season would be known. Based on the retail orders, the company dyed the already knitted garments appropriately and shipped them. This is an example of postponement till purchase (or sale), instead of postponement by place.
This time-period was as reported in 2002. With improved technology, the customer’s waiting time would fall drastically in due course.
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When the conditions mentioned in the first paragraph of this section are fulfilled, postponement optimizes both the carrying cost and the value of inventory carried. This is illustrated through an exercise at the end of this section. At an intuitive level, it is easy to understand certain benefits that postponement offers. They are reflected in the following costs:7 Inventory Holding Costs: These are the costs of holding more or less inventory at the regional warehouse including the cost of pipeline inventory Transportation Costs: These are the costs of shipping goods from the centralized warehouse to the regional warehouse. Processing Costs: These are the costs of processing such as manufacturing, assembling, packaging and labeling. Lead-time Costs: These are the costs of lost customers due to their unwillingness to wait for the product to be formed at the postponed stage. While assessing these costs under postponement, the comparison is made for form postponement8 vis-à-vis anticipatory production-cum-shipment. For this purpose, we classify form postponement into four types: Labeling Postponement: This is adopted when an organization manufactures the same product under different brand names. For example, if an organization manufactures orange squash in bottles for different large departmental stores, this method of postponement will come handy. It can be understood that the orders from the departmental stores, (let us call the four departmental stores A, B, C and D) may vary from time to time. If the organization decides to keep labeled stock in anticipation of the respective stocks, then it has to have much more stocks. On the contrary, if the organization keeps unlabelled bottles filled with squash, then, as and when the store’s orders come in, labeling can be done. In this way, the organization’s need for inventory to be maintained is low. However, since labeling will be done for smaller quantity depending on the store’s order, the economy of scale will be low and so the labeling cost will be higher. Further, if the store is not efficient enough to maintain adequate base inventory, the lead-time may cause the store to lose some of its customers of squash. Therefore, the stock out cost is higher in this case. Packaging Postponement: This is relevant when an organization has many sizes of the same products sold in different areas. A fall out of this condition is the complexity involved in tracking sales and forecasting demand for production planning. Invariably, this ends up in such a production quantity that is either in excess of the optimal inventory or below it. In such situations, an organization may well postpone its packaging, by shipping the product in bulk to the regional warehouses.
This section has been suitably adapted from Walter Zinn and Donald Bowersox, Planning Physical Distribution with the Principle of Postponement, Journal of Business Logistics, Vol.9, Number 2, pp.117-135.
7 8 We specifically consider form postponement and do not concern much with time postponement in this section. Time postponement implies production and shipping of stocks after receiving customer-orders. This primarily helps in shifting business risk to the customer and has the disadvantages of increased production costs due to diseconomies of smaller scale, increased stock out costs due to longer delivery time, reduced inventory costs due to smaller inventory at centralized warehouse and increased transportations costs due to less than truckload (LTL) shipment to customer.
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Depending upon the local orders for different pack sizes, the regional warehouse can pack the product in the requisite sizes in requisite Figure 1 quantities. This reduces inventory-holding costs since the holding will be in bulk volume that can be minimal. It Desk Top A Desk Top B also reduces transport costs since transporting bulk volume is cheaper per unit than transporting in packed units. C MP 2 C The compactness of the bulk MP 1 volume offers economy of space to reduce transportation costs.
Assembly Postponement: This can come handy when the customers have varied preferences for the configuration of the product. As mentioned earlier, computers and bicycles fall under this category. The organization merely procures/manufactures components of the final products and ships them to the regional warehouses in parts. This allows compact packing of the individual parts, thus offering economy of truck space, in addition to reducing the extent of damages considerably as compared to the case of transporting finished products. Thus, the transport cost per unit reduces considerably. However, the assembling costs will increase due to less quantity being assembled in response to customer orders. The resultant delivery time lag may also turn some customers off to competitors and thus the stock out costs are higher. In all the above cases, it should be remembered that all types of form postponement offer the company the ability to respond to the customers’ variety-preferences much better than an anticipatory system can offer. The counteractive effect is the loss in speed of response leading to loss of customers due to lead-time.
Illustration 9
A computer manufacturer has two products of Desk Top computers, A and B. These two products use different micro-processors (denoted by MP 1 and MP 2). All other components are common (denoted by C). Thus, the structures of the two products can be shown as in Figure 1. The value of the products includes the cost of MP, C and the assembling expenses. Let us take that the cost of assembling for each of these products is Rs.1000 per unit. The other two costs for the two products are as given below: Item Cost of MP per unit Cost of C per unit Total Cost per unit Desk Top A Rs. 12000 per MP 1 Rs. 30000 Rs. 43000 Desk Top B Rs. 11000 per MP 2 Rs. 30000 Rs.42000
Suitably adapted from Janat Shah and Balram Avittathur. 1999. “Improving Supply Chain Performance Through Postponement Strategy”, Management Review, IIM-B, June. p. 11.
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Now the company has two options of material-flow: Centralized assembly and despatch of finished goods (let us call it base-case) Figure 2
Regional stock-point 1 Central warehouse Central warehouse Regional stock-point 1
Regional stock-point 2 Base-case Material Flow
Regional stock-point 2 Postponement Material Flow
Finished Product Material Flow Assembly Operation Components Material Flow
Postponement material flow These two options are shown in the Figure 2. Let us say we have been given the following data on demand patterns for these two products. The demands for A and B follow a normal distribution, with mean demands per period of 1000 and 600 units respectively, and standard deviations per period of 400 and 300 respectively. The lead-time for inventory-replenishment - time taken by the Regional Stock Points (RSPs) from ordering to receipt of stocks - is 3 periods. There is no uncertainty in lead-time. The organization wants a service level of 98 %. This means, in 98% of the cases, when it faces an order, it will not go stock-out. The inventory carrying cost per desktop is Rs. 645 and Rs.630 per unit per period for A and B respectively. The ordering cost is given to be Rs.435000 for each variety. (This is a ballpark figure taking into account all the direct costs involved in placing an order, inspection, approvals etc.)
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Given these data, it is easy to find out the economic order quantity (EOQ) using the formula shown in the footnote on page 2 for each of these products as 1161 units of A and 910 units of B. Now, we find out the inventory carrying costs for these two products, worked out in Appendix A as a total of Rs.14,51,985 per period. The value of inventory held will be Rs.9,70,09,000. Now, we consider postponement. Under postponement, we need to transfer the microprocessors and common components to the RSPs. The demands will be as follows: Mean demand of common components (C) Mean demand of MP 1(used in product A) Mean demand of MP 2(used in product B) Standard deviation for C 10 Standard deviation for MP 1 Standard deviation for MP 2 1000+600 1600 1000 600 500 400 300
Now, we set out to find the average inventories for these three input materials. This is done in Appendix B, where we find that the inventory carrying cost works out to Rs.12,67,380 (a gain of Rs.1,84,605 per period) and the value of average inventory held is Rs.8,44,92,000 (a reduction of Rs.1,25,17,000). This illustration proves quantitatively that under suitable conditions mentioned in the theory before, postponement works out better than centralized assembling / manufacturing.
Issues in Postponement
As mentioned in page 4, there are certain prerequisites for postponement to work. Once they are fulfilled, certain other aspects of managing postponement have to be considered. These are a. Postponement is different from simple stocking and selling. It involves a part of manufacturing. Therefore the personnel at the postponement-point should be trained appropriately for maintaining the standards. b. When the organization shifts from centralized manufacturing to postponed completion process, the benefits should be effectively communicated to the consumers. If this is not done, the channel member, who is now a part of the manufacturing process, is left to feel that the extra efforts do not make significant difference to the consumer. It should be remembered that a traditional distributor is only a reseller and to convert him to become a part-manufacturer implies a major paradigm shift on his part. The shift should yield results, the bottomline. c. The company should be willing to disclose a part of their manufacturing process to the distributors so as to enable postponement. d. The channel members should be willing to disclose their demand details to the parent organization for effective forecasting of components - both common and
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2 2 We know that ? xy = ? x + ? y + cov (x, y) . We have made a simple assumption that the covariance of xy is
zero. Then, the combined standard deviation becomes ? xy = 1600 + 900 = 500
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area-specific. This implies that the trust between the two partners should be of the highest order. e. The organization should be willing to rethink periodically about the non-moving components rather than allow them to rot at the distributor's warehouse. A mutually agreed policy on this issue is essential. f. There should be a mutual agreement on standards of production and the methods of verification and ensuring. g. With postponement, there is a clear-cut division of labor. The organization will specialize in component manufacture and the channel will specialize in assembly and vending.
Postponement and Speculation
It is interesting to note that postponement is the converse of speculation. Speculation shifts the risk to the organization whereas postponement shifts it away from it. Speculation implies that changes in the form and movement of goods should be made at the earliest possible, (read at the manufacturer's plant) so as to reduce the costs of marketing. It is true that this can give economies of scale to an organization and reduces the cost or sorting and transportation. So, one should weigh both the possibilities before choosing between them.
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Postponement: A Mathematical Treatment 11
We have seen in the previous section the costs-benefits of different types of postponement. In this section, we shall specifically see the following: Is there an optimal level of postponement that minimizes the total cost of inventory holding and lead-time? (Proposition # 1) If there is an optimal level of postponement, how does it change with increased level of product customization? (Proposition # 2) Let us denote total costs by CT, Lead-time costs by CL and Inventory Holding Costs by CI. Then, (1) CT=CL+CI All these costs are functions of postponement. That is, for every level of postponement, there is a corresponding, unique level of these costs. However, how are these costs related to the level of postponement? From the previous equation, we can derive, (2)
?C T ?C L ?C I = + ?p ?p ?p
Further differentiating the above derivative, we get (3)
? 2C T ?p 2 = ? 2C L ?p 2 + ? 2C I ?p 2
As we saw in the previous section, ceteris paribus, postponement increases the chance of loss of customers due to increase in waiting time. Therefore, (4)
?C L >0 ?p
Also, it is understandable that beyond a certain level of postponement, the customers may not like to wait at all and therefore they may, en masse, shift over to competition. Thus, the CL is an increasingly increasing function. So, (5)
? 2C L ?p 2 >0
The other component of (1), viz., CI , as we have seen in the previous section, decreases with increased postponement.12 So, (6)
?C I <0 ?p
11 This section is suitably adapted from Matthew A. Waller, Pratibha A. Dhabolkar and Julie J. Gentry, “Postponement, Product Customization and Market-Oriented Supply Chain Management”, Journal of Business Logistics, Vol.21. No.2, 2000, pp.133-159
This is because under postponement, one needs to keep less of finished inventory, whose cost is always higher than the cost of components. In addition, the total quantity of common components to be kept in inventory will also be reduced.
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Also, it is understandable that the gain in inventory cost cannot not be indefinite. There must exist a particular level below which CI will not decrease despite increase in postponement. Therefore, it is easy to perceive the function as a decreasingly decreasing function. Hence, (7) From (3), (5) and (7), it can be seen that (8)
? 2C T ?p 2 = ? 2C L ?p 2 + ? 2C I ?p 2 >0 ? 2C I ?p 2 >0
That is, CT is a non-linear function of p that attains minimum at a specific level of postponement. If we denote that level by p*, the optimal level of postponement at which the total cost is minimum, then, it is easy to understand its existence as in Graph 1 below. Next, we try to see how p* changes due to different degrees of product customization. Intuitively, it is understandable that increased product customization involves storing lager varieties of components to meet the different custom-needs of customers. Hence, inventory-holding costs (of parts) will be higher. This can be shown by the notation, (9)
?C I >0 ?PC
Graph 1
C
CT
CL
CI 0 p* p
Moreover, with increased product customization, customers will not mind waiting for delivery. So, the lead-time costs reduce. Therefore ( 10 ) Now, ( 11 )
?p * ?p * ?C I ?p * ?C L ={ x } +{ x }, ?PC ?C I ?PC ?C L ?PC ?C L <0 ?PC
since p* will be affected by PC via CI and CL. To understand what happens to p* in this process, let us look at Graph 2.
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Graph 2 The thicker lines pertain to lower level of product customization and the dotted lines pertain to higher level of product customization. As explained by (9) and (10) in the previous page, higher PC leads to higher CI and therefore the curve shifts upwards to the right of the thicker line. Similarly, higher PC results in lower CL and therefore the curve shifts downward to the right. This means that when the curve CI shifts to the right, p* shifts to the right as well. That is, ( 12 )
?p * >0 ?C I
C CT CL CTa CLa
CIa
CI 0 p* p* * p
Intuitively, this means that with higher inventory holding costs, the cost-optimizing level of postponement is higher, since higher level of postponement offers greater savings in CI. Similarly, when the curve CL shifts to the right (meaning a reduction in CL), p* shifts to the right too. That is, lower the lead-time costs, higher is the level of postponement that optimizes total costs. This implies, ( 13 )
?p * <0 ?C L
Intuitively, this means that with lower lead-time costs, the opportunity to reduce total costs further by increasing postponement level exists and this warrants an increase in postponement level to reach the optimum. These two curves, CIa and CLa add up to give the curve CTa (all three dotted curves). The curve CTa is to the right of the curve CT, implying a shift of the optimal level of p* to the right, that is higher, at p**. This means that with increased product customization, the optimal level of postponement is higher. This can be proved mathematically as well. In (11), we have two expressions on the right-hand side, as follows:
?p * ?C I ?p * ?C L ?p * ={ x } +{ x } ?C I ?PC ?C L ?PC ?PC (A) (B)
From (9) and (12), expression (A) is positive. From (10) and (13), (B) is positive. Therefore,
?p * ?C I ?p * ?C L ?p * ={ x } +{ x }>0 ?C I ?PC ?C L ?PC ?PC
This concludes the proposition #2 that increased customization (PC) warrants higher p*.
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Reference
Shah, Janat & Balram Avittathur. 1999. Improving Supply Chain Performance Through Postponement Strategy, Management Review, IIM-B, June. pp. 5-13 Waller, Matthew A., Pratibha A.Dabholkar and Julie J. Gentry, 2000. Postponement, product Customization and market-oriented Supply Chain Management, Journal of Business Logistics, Vol. 21, No. 2. pp 133-159. Zinn, Walter and Donald J. Bowersox, 1988. Planning Physical Distribution with the Principle of Postponement, Journal of Business Logistics, Vol. 9, No. 2. pp. 117-135.
Recommended Readings Bucklin, Louis P. 1965. Postponement, Speculation and the Structures of Distribution Channels, Journal of Marketing Research, February. pp. 26 - 31 Feitzinger, Edward and Hau L. Lee. 1997. Mass Customization at Hewlett-Packard: The Power of Postponement, Harvard Business Review, Jan-Feb. pp. 116 - 121 Lee, Hau L. and Corey Billington. 1993. Material Management in Decentralized Supply Chain, Operations Research, Vol. 41, No. 5, Sep-Oct. pp. 835 - 847 Simchi-Levi, David, Philip Kaminsky and Edith Simchi-Levi. 2000. Designing and Managing the Supply Chain, McGraw Hill. pp 167-195.
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APPENDIX A I. TO FIND THE REORDER POINT & LEADTIME BUFFER FOR DESKTOP-A UNDER POSTPONEMENT CONDITION Given Demand follows normal distribution. Mean Demand Std. Deviation Lead-time = 1000 units per period = 400 units = 3 periods Figure a
Service Expectations = 98 % Since lead-time is 3 periods, we need to carry stocks to manage three periods, with buffer. This means,
x
= 3000
2%
s = 400 ?3 = 693.
By using the normal distribution table Z = 2.05 3000 for 98% confidence level, we find that X = 4421 z=2.05, as shown in Figure-a. Solving the equation for X, we get the value X = 4421 units. This is the reorder point for the firm and the Lead-time + buffer stock is 1421 units. This is sketched in the Figure-b. Figure b Now, we can set on to Quantity (Units) find out the cost of inventory holding for this company for the Reorder point 4421 product A. This is done by taking the average stock and multiplying the inventory carrying 3000 cost. units We know that in a case where the buffer is 1421 Buffer + Lead-time stock and the order quantity is 1421 1161, the average inventory is given by 1421+(1161/2) = 2002. 0 Time Therefore, the inventory carrying cost for product A is Rs.12,91,290 per period. Now, we shall find the inventory carrying cost for product B. 14
II.
TO FIND THE REORDER POINT & LEADTIME BUFFER FOR DESKTOP-B UNDER POSTPONEMENT CONDITION Given Demand follows normal distribution. Mean Demand Std. Deviation Lead-time = 600 units per period = 300 units = 3 periods Figure c
Service Expectations = 98 % Since lead-time is 3 periods, we need to carry stocks to manage three periods, with buffer. This means,
x = 1800
s = 300 ?3 = 520.
By using the normal distribution table for 98% confidence level, we find Z = Z = 2.05 2.05, as shown in Figure-c. Solving 1800 the equation for X, we get the value X X = 2866 = 2866 units. This is the reorder point for the firm and the Lead-time + buffer stock is 1066 units. This is sketched in the Figure-d. Now, we can set on to find out the cost of inventory holding for this company for the product B. This is done by taking the Quantity (Units) Figure d average stock and multiplying the inventory carrying cost.
2866
Reorder point
2%
1800 units
We know that in a case where the buffer is 1066 and the order quantity is 910, the average inventory is given by 1066+(910/2) = 1521.
Buffer + Lead-time stock
1066
So, the inventory carrying cost for product B is Rs.9,58,230 per period.
Time
0
The total cost for A & B is Rs.22,50,150.
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APPENDIX B Using similar technique as in Appendix A, we can find that Buffer is 1775 and the reorder point is 6575 for C Buffer is 1421 and the reorder point is 4421for MP 1 Buffer is 1066 and the reorder point is 2866 for MP 2 We know from the given data that the total ordering cost for the RSP is Rs.8,70,000. We can apportion this amount among C, MP 1 and MP 2 either on the basis of the cost of these items ( 57%, 23 % and 21 %) or on the basis of the mean demand (50 %, 31 % and 19%). This is done because we have no historical data on the orders placed for these materials. I. Ordering costs are apportioned in the ratio of costs. This gives us the ordering costs as Components ordering cost MP 1 ordering cost MP 2 ordering cost QC QMP1 QMP2 = = = 1878 1491 1153 Rs. 4,95,900 Rs. 2,00,100 Rs. 1,82,700
On the basis of these, the EOQs are found to be
Average Inventory is calculated by the formula Buffer +(Q/2), which gives us Components 2714 MP1 MP2 2167 1643
The inventory carrying costs per period will be (2714 x 450 + 2167 x 180 + 1643 x 165) which works out to Rs. 18,82,455. The cost of inventory will be (2714 x 30000 + 2167 x 12000 + 1643 x 11000) which works out to Rs.12,54,97,000. II. Ordering costs are apportioned in the ratio of mean demand. This gives us the ordering costs as Components ordering cost MP 1 ordering cost MP 2 ordering cost QC = 1759 Rs. 4,35,000 Rs. 2,69,700 Rs. 1,56,600
On the basis of these, the EOQs are found to be
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QMP1 QMP2
= =
1731 1067
Average Inventory is calculated by the formula Buffer +(Q/2), which gives us Components 2655 MP1 MP2 2287 1600
The inventory carrying costs per period will be (2655 x 450 + 2287 x 180 + 1600 x 165) which works out to Rs. 18,70,410. The cost of inventory will be (2655 x 30000 + 2287 x 12000 + 1600 x 11000) which works out to Rs.12,46,94,000.
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doc_637858331.pdf
The report includes topics like inventory types, postponement.
Postponement as a Strategy in Channel
Introduction
Inventory management in channel is a perennial issue of conflict. In a traditional channel, where we face a manufacturer, his branch, the distributor and the retailer, channel inventory is a complex matter. The manager (of the company) has the responsibility of not only managing his inventory but also monitoring and managing the inventories at the distributor and retailer level. Needless to say, he has no authority in the last two cases but only the responsibility. And, there are certain interesting but tricky situations that arise in this regard. Suppose the branch maintains inventory appropriately (meaning it never goes stock-out when a distributor places an order) and it finds that a distributor is under-stocked. The natural tendency is to ask the distributor to increase his stocks. This is against the interests of the distributor who tries to minimize his stocks, if not optimize. Obviously, there is a clash of interests. It is not uncommon to witness situations when the manager's efficiency becomes a source of complacency for the distributor who may maintain a precarious level of inventory bordering on stock-out. This note is an attempt to consider certain issues in inventory management in channels broadly, and focus on a specific method of inventoryoptimization, viz., postponement.
Inventory Types
Interestingly, when we use the phrase channel, we include the branch office too to get a total view, since the branch office's practices may vary from the corporate preferences, thus affecting channel management considerably. For example, the corporate office may like the branches to carry large inventory while the branch may prefer the opposite, to show a better operating-income statement. And, if the branches operate on profit-center basis, the conflict can be well understood. Inventory in a channel is held for various purposes and accordingly inventory types have been identified. They are as follows 1: A. Pipeline inventory B. Cyclical Inventory C. Buffer D. Seasonal Inventory E. Speculative Inventory Not all members in the channel carry all types of inventories, even if the type is applicable to the product category. This is due to differing perceptions about the need for the same.
© 2002, Prof. R. C. Natarajan, TAPMI, Manipal, Karnataka. For more discussion on inventory management, read Inventory Management - An Introduction by Prof. R.Rajagopalan, TAPMI.
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Cost of Inventory
Cost of Inventory holding includes the following: Cost of funds required for the stocks Cost of storage such as warehouse, insurance, maintenance of temperature / humidity, security etc. Cost of additional transportation due to storing at a point, including loading and unloading charges Cost of aging of stock due to storage (especially in food products and medicines) Cost of change of quality (deterioration) in fresh or perishable products due to handing and transshipment Holding inventory at as many places as possible enhances the organization's capacity to provide customer-service. Customer service includes: Meeting the order in time and in sufficient quantity Providing the variety and/or the packing sought by the consumer Ability to provide back-up support such as installation, training and after-sales service Needless to say that in the absence of these services, the customer will, in all probability, switch brands, adding to cost of stock-out.2 Thus, inventory policy and planning encompass decisions pertaining to channel-capacity as well.
Order Quantity and Frequency
An area where exists considerable conflict is the frequency of ordering and quantity to be ordered. Typically, a lower member3 wants his supplier (an upper member) to supply as frequently as possible and minimum quantity every time, whereas the upper member prefers to supply maximum stocks in as limited number of deliveries as possible. While in theory we study that the economic order quantity is a function of inventory-carrying cost, ordering cost and annual demand,4 following EOQ has its own difficulties in a channel. Some such situations where difficulties arise are as follows: a. Normally, the manufacturer finds shipment of large quantities - one truckload in practice - more economical than a "part-load". Thus they may prefer that the branch or the
2 It may be seen that the term stock-out is used rather broadly in this context to include the services that go with the product as well. In the realm of channel management, this interpretation will be more useful than to confine to the product alone. 3 The terms lower and upper are used to denote conceptually the channel flow from manufacturer (uppermost) and consumer (lowermost) without any value-loading. 4
You may recall that
EOQ = 2AD I
where, D is the periodic demand, A is the ordering cost per order and I is the inventory carrying cost per unit per period expressed as percentage of the value of the stock
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distributor order in truckloads. This may not go well with the EOQ of the branch / distributor. b. Preference by the manufacturer for larger orders may lead them to queue the larger orders first and waitlist the smaller orders. The resultant delay may make it impossible for such channel partners to plan their EOQ effectively. In both the cases of (a) and (b), those channel partners who place smaller orders are at a disadvantage. c. In cases where transportation is outsourced, the transport contractors may service full truckloads faster than smaller batches. As in the case of (b), this too may cause delays. d. In many organizations, salesforce incentives are linked to sales. Thus, they may prefer their distributors to lift more stocks than EOQ to fulfil their incentive-norms. In such cases, there is a systemic resistance for inventory-optimization in the channel. e. Some channel members (distributors or retailers) may attempt to minimize their inventory of a specific brand with a view to gaining funds for more profitable brands (may be of other organizations). In this case, EOQ cannot be practised. Such instances lead to inter-distributor transfers in times of emergent demand thus adding further to the cost of logistics. f. It is not uncommon among organizations to witness situations where the branch dumps inventory on distributors to show low inventory with itself. This practice is known as pseudo inventory reduction. When we talk of inventory-optimization, we consider the inventory in the whole channel and not at one stage at the cost of another. g. On certain occasions, a sporadic spike in demand could cause a ripple effect on the inventory policies, which may result in escalation of inventory-holdings across the channel. This phenomenon, known as bullwhip effect is a common occurrence in channels of distribution.5 When such a phenomenon occurs, it is difficult to rearrange the ordering-holding combination to set it on EOQ mode. h. Whenever the channel leader announces a sales promotion activity, the demand spikes up. By and large, this encourages only "forward buy", thus giving a false sense of demand escalation. This leads to excess stocking by the channel members at one time and stocking much lower stock at another time. These can hardly be termed as EOQ, though in the given context, the quantities may be optimal. The event invariably starts off a chain reaction whereby the next few orders become highly volatile. i. In those products that have unpredictable demand, very slow movement, but very high value of expected order(s), the concept of EOQ cannot be applied directly due to D in the formula for EOQ being unknown. In products such as magazines or newspapers, excess production and excess stocking is a part of the industry practice due to the involvement of advertising revenues. This is because it is better to hold a higher inventory than to lose sales due to stock-out. If the excess prints are sold, the publisher gets the MRP less the transportation cost and the channel commission. On the contrary, if the excess prints are unsold, the publisher loses only the variable cost of the unsold stock, which is very low, in addition to a miniscule transportation cost. So, the excess cost is worth the risk.
j.
For a detailed account of bullwhip effect, read my note Bullwhip Effect in Supply Chain, 2002, TAPMI, Manipal, Karnataka
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To overcome the problem of over-stocking or under stocking, organizations have innovated a method known as postponement. This is outlined below.
Postponement: An Inventory Reduction Technique
Postponement denotes shifting the product-completion closer to the time and/or place of purchase. This improves responsiveness to consumer-needs. To implement postponement, the production-process should be such as to enable resequencing, the major process should be common for all variants and the product should be capable of modularization. Postponement is not a new concept. It has been followed by bicycles industry for a long time. Normally, bicycle companies transport their products in batches of unassembled parts. This serves two logistical purposes: 1. Packaging of homogeneous components enables shipment of larger quantities thus offering economies of scale. 2. Assembled finished products are susceptible to damage in transit. Apart from these logistical benefits, postponement offers an important marketing benefit to the organization, viz., delayed differentiation. This means that the manufacturer is able to delay the complete the production of the product to suit the specific requirement of a specific consumer. So, in the bicycle example, the consumer's need for a bicycle with preferred specifications such as dynamo-operated headlight, a rear-view mirror, a seat with 6" escalation, a front seat, a rear seat with cushion etc. can be fitted at the dealer's premises before delivering to the consumer. Such a customization cannot be feasible at a centralized factory. In recent times, postponement has been extensively used to benefit the consumers by the paint industry. (Shah et al, 1999) Asian Paints in mid-seventies pioneered the computerized color-scheme selection in India. Under this system, in each of the Sales Points (meaning the distribution centers) spread across the country, a tinting machine was made available. The dealers were sold those fast moving variants, anyway. In addition, the specific color combination preferred by the consumer was recorded by the computer and the Sales Point, which carried the base liquid, added the stainers to generate the preferred paint for the consumer. Thus the consumer's specific need was met in less than 48 hours6 in most cases. This implied that the hub had to carry a predictable volume of base fluid and minimum quantities of stainers. Contrast it with a situation when this strategy was not existent. The company would have either forced its dealers to stock large number of shades of paints, a huge block of funds in the channel, or the consumer would have had to wait for a minimum two weeks to get his/her preferred shade. Yet another example of Benetton's postponement strategy is cited. Benetton, in fashion garment business, overcame the problem of forecasting the demand by resequencing the dyeing-knitting sequence to knitting-dyeing sequence. The dyeing would be completed once the consumer demand for shades at the season would be known. Based on the retail orders, the company dyed the already knitted garments appropriately and shipped them. This is an example of postponement till purchase (or sale), instead of postponement by place.
This time-period was as reported in 2002. With improved technology, the customer’s waiting time would fall drastically in due course.
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When the conditions mentioned in the first paragraph of this section are fulfilled, postponement optimizes both the carrying cost and the value of inventory carried. This is illustrated through an exercise at the end of this section. At an intuitive level, it is easy to understand certain benefits that postponement offers. They are reflected in the following costs:7 Inventory Holding Costs: These are the costs of holding more or less inventory at the regional warehouse including the cost of pipeline inventory Transportation Costs: These are the costs of shipping goods from the centralized warehouse to the regional warehouse. Processing Costs: These are the costs of processing such as manufacturing, assembling, packaging and labeling. Lead-time Costs: These are the costs of lost customers due to their unwillingness to wait for the product to be formed at the postponed stage. While assessing these costs under postponement, the comparison is made for form postponement8 vis-à-vis anticipatory production-cum-shipment. For this purpose, we classify form postponement into four types: Labeling Postponement: This is adopted when an organization manufactures the same product under different brand names. For example, if an organization manufactures orange squash in bottles for different large departmental stores, this method of postponement will come handy. It can be understood that the orders from the departmental stores, (let us call the four departmental stores A, B, C and D) may vary from time to time. If the organization decides to keep labeled stock in anticipation of the respective stocks, then it has to have much more stocks. On the contrary, if the organization keeps unlabelled bottles filled with squash, then, as and when the store’s orders come in, labeling can be done. In this way, the organization’s need for inventory to be maintained is low. However, since labeling will be done for smaller quantity depending on the store’s order, the economy of scale will be low and so the labeling cost will be higher. Further, if the store is not efficient enough to maintain adequate base inventory, the lead-time may cause the store to lose some of its customers of squash. Therefore, the stock out cost is higher in this case. Packaging Postponement: This is relevant when an organization has many sizes of the same products sold in different areas. A fall out of this condition is the complexity involved in tracking sales and forecasting demand for production planning. Invariably, this ends up in such a production quantity that is either in excess of the optimal inventory or below it. In such situations, an organization may well postpone its packaging, by shipping the product in bulk to the regional warehouses.
This section has been suitably adapted from Walter Zinn and Donald Bowersox, Planning Physical Distribution with the Principle of Postponement, Journal of Business Logistics, Vol.9, Number 2, pp.117-135.
7 8 We specifically consider form postponement and do not concern much with time postponement in this section. Time postponement implies production and shipping of stocks after receiving customer-orders. This primarily helps in shifting business risk to the customer and has the disadvantages of increased production costs due to diseconomies of smaller scale, increased stock out costs due to longer delivery time, reduced inventory costs due to smaller inventory at centralized warehouse and increased transportations costs due to less than truckload (LTL) shipment to customer.
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Depending upon the local orders for different pack sizes, the regional warehouse can pack the product in the requisite sizes in requisite Figure 1 quantities. This reduces inventory-holding costs since the holding will be in bulk volume that can be minimal. It Desk Top A Desk Top B also reduces transport costs since transporting bulk volume is cheaper per unit than transporting in packed units. C MP 2 C The compactness of the bulk MP 1 volume offers economy of space to reduce transportation costs.
Assembly Postponement: This can come handy when the customers have varied preferences for the configuration of the product. As mentioned earlier, computers and bicycles fall under this category. The organization merely procures/manufactures components of the final products and ships them to the regional warehouses in parts. This allows compact packing of the individual parts, thus offering economy of truck space, in addition to reducing the extent of damages considerably as compared to the case of transporting finished products. Thus, the transport cost per unit reduces considerably. However, the assembling costs will increase due to less quantity being assembled in response to customer orders. The resultant delivery time lag may also turn some customers off to competitors and thus the stock out costs are higher. In all the above cases, it should be remembered that all types of form postponement offer the company the ability to respond to the customers’ variety-preferences much better than an anticipatory system can offer. The counteractive effect is the loss in speed of response leading to loss of customers due to lead-time.
Illustration 9
A computer manufacturer has two products of Desk Top computers, A and B. These two products use different micro-processors (denoted by MP 1 and MP 2). All other components are common (denoted by C). Thus, the structures of the two products can be shown as in Figure 1. The value of the products includes the cost of MP, C and the assembling expenses. Let us take that the cost of assembling for each of these products is Rs.1000 per unit. The other two costs for the two products are as given below: Item Cost of MP per unit Cost of C per unit Total Cost per unit Desk Top A Rs. 12000 per MP 1 Rs. 30000 Rs. 43000 Desk Top B Rs. 11000 per MP 2 Rs. 30000 Rs.42000
Suitably adapted from Janat Shah and Balram Avittathur. 1999. “Improving Supply Chain Performance Through Postponement Strategy”, Management Review, IIM-B, June. p. 11.
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Now the company has two options of material-flow: Centralized assembly and despatch of finished goods (let us call it base-case) Figure 2
Regional stock-point 1 Central warehouse Central warehouse Regional stock-point 1
Regional stock-point 2 Base-case Material Flow
Regional stock-point 2 Postponement Material Flow
Finished Product Material Flow Assembly Operation Components Material Flow
Postponement material flow These two options are shown in the Figure 2. Let us say we have been given the following data on demand patterns for these two products. The demands for A and B follow a normal distribution, with mean demands per period of 1000 and 600 units respectively, and standard deviations per period of 400 and 300 respectively. The lead-time for inventory-replenishment - time taken by the Regional Stock Points (RSPs) from ordering to receipt of stocks - is 3 periods. There is no uncertainty in lead-time. The organization wants a service level of 98 %. This means, in 98% of the cases, when it faces an order, it will not go stock-out. The inventory carrying cost per desktop is Rs. 645 and Rs.630 per unit per period for A and B respectively. The ordering cost is given to be Rs.435000 for each variety. (This is a ballpark figure taking into account all the direct costs involved in placing an order, inspection, approvals etc.)
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Given these data, it is easy to find out the economic order quantity (EOQ) using the formula shown in the footnote on page 2 for each of these products as 1161 units of A and 910 units of B. Now, we find out the inventory carrying costs for these two products, worked out in Appendix A as a total of Rs.14,51,985 per period. The value of inventory held will be Rs.9,70,09,000. Now, we consider postponement. Under postponement, we need to transfer the microprocessors and common components to the RSPs. The demands will be as follows: Mean demand of common components (C) Mean demand of MP 1(used in product A) Mean demand of MP 2(used in product B) Standard deviation for C 10 Standard deviation for MP 1 Standard deviation for MP 2 1000+600 1600 1000 600 500 400 300
Now, we set out to find the average inventories for these three input materials. This is done in Appendix B, where we find that the inventory carrying cost works out to Rs.12,67,380 (a gain of Rs.1,84,605 per period) and the value of average inventory held is Rs.8,44,92,000 (a reduction of Rs.1,25,17,000). This illustration proves quantitatively that under suitable conditions mentioned in the theory before, postponement works out better than centralized assembling / manufacturing.
Issues in Postponement
As mentioned in page 4, there are certain prerequisites for postponement to work. Once they are fulfilled, certain other aspects of managing postponement have to be considered. These are a. Postponement is different from simple stocking and selling. It involves a part of manufacturing. Therefore the personnel at the postponement-point should be trained appropriately for maintaining the standards. b. When the organization shifts from centralized manufacturing to postponed completion process, the benefits should be effectively communicated to the consumers. If this is not done, the channel member, who is now a part of the manufacturing process, is left to feel that the extra efforts do not make significant difference to the consumer. It should be remembered that a traditional distributor is only a reseller and to convert him to become a part-manufacturer implies a major paradigm shift on his part. The shift should yield results, the bottomline. c. The company should be willing to disclose a part of their manufacturing process to the distributors so as to enable postponement. d. The channel members should be willing to disclose their demand details to the parent organization for effective forecasting of components - both common and
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2 2 We know that ? xy = ? x + ? y + cov (x, y) . We have made a simple assumption that the covariance of xy is
zero. Then, the combined standard deviation becomes ? xy = 1600 + 900 = 500
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area-specific. This implies that the trust between the two partners should be of the highest order. e. The organization should be willing to rethink periodically about the non-moving components rather than allow them to rot at the distributor's warehouse. A mutually agreed policy on this issue is essential. f. There should be a mutual agreement on standards of production and the methods of verification and ensuring. g. With postponement, there is a clear-cut division of labor. The organization will specialize in component manufacture and the channel will specialize in assembly and vending.
Postponement and Speculation
It is interesting to note that postponement is the converse of speculation. Speculation shifts the risk to the organization whereas postponement shifts it away from it. Speculation implies that changes in the form and movement of goods should be made at the earliest possible, (read at the manufacturer's plant) so as to reduce the costs of marketing. It is true that this can give economies of scale to an organization and reduces the cost or sorting and transportation. So, one should weigh both the possibilities before choosing between them.
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Postponement: A Mathematical Treatment 11
We have seen in the previous section the costs-benefits of different types of postponement. In this section, we shall specifically see the following: Is there an optimal level of postponement that minimizes the total cost of inventory holding and lead-time? (Proposition # 1) If there is an optimal level of postponement, how does it change with increased level of product customization? (Proposition # 2) Let us denote total costs by CT, Lead-time costs by CL and Inventory Holding Costs by CI. Then, (1) CT=CL+CI All these costs are functions of postponement. That is, for every level of postponement, there is a corresponding, unique level of these costs. However, how are these costs related to the level of postponement? From the previous equation, we can derive, (2)
?C T ?C L ?C I = + ?p ?p ?p
Further differentiating the above derivative, we get (3)
? 2C T ?p 2 = ? 2C L ?p 2 + ? 2C I ?p 2
As we saw in the previous section, ceteris paribus, postponement increases the chance of loss of customers due to increase in waiting time. Therefore, (4)
?C L >0 ?p
Also, it is understandable that beyond a certain level of postponement, the customers may not like to wait at all and therefore they may, en masse, shift over to competition. Thus, the CL is an increasingly increasing function. So, (5)
? 2C L ?p 2 >0
The other component of (1), viz., CI , as we have seen in the previous section, decreases with increased postponement.12 So, (6)
?C I <0 ?p
11 This section is suitably adapted from Matthew A. Waller, Pratibha A. Dhabolkar and Julie J. Gentry, “Postponement, Product Customization and Market-Oriented Supply Chain Management”, Journal of Business Logistics, Vol.21. No.2, 2000, pp.133-159
This is because under postponement, one needs to keep less of finished inventory, whose cost is always higher than the cost of components. In addition, the total quantity of common components to be kept in inventory will also be reduced.
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Also, it is understandable that the gain in inventory cost cannot not be indefinite. There must exist a particular level below which CI will not decrease despite increase in postponement. Therefore, it is easy to perceive the function as a decreasingly decreasing function. Hence, (7) From (3), (5) and (7), it can be seen that (8)
? 2C T ?p 2 = ? 2C L ?p 2 + ? 2C I ?p 2 >0 ? 2C I ?p 2 >0
That is, CT is a non-linear function of p that attains minimum at a specific level of postponement. If we denote that level by p*, the optimal level of postponement at which the total cost is minimum, then, it is easy to understand its existence as in Graph 1 below. Next, we try to see how p* changes due to different degrees of product customization. Intuitively, it is understandable that increased product customization involves storing lager varieties of components to meet the different custom-needs of customers. Hence, inventory-holding costs (of parts) will be higher. This can be shown by the notation, (9)
?C I >0 ?PC
Graph 1
C
CT
CL
CI 0 p* p
Moreover, with increased product customization, customers will not mind waiting for delivery. So, the lead-time costs reduce. Therefore ( 10 ) Now, ( 11 )
?p * ?p * ?C I ?p * ?C L ={ x } +{ x }, ?PC ?C I ?PC ?C L ?PC ?C L <0 ?PC
since p* will be affected by PC via CI and CL. To understand what happens to p* in this process, let us look at Graph 2.
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Graph 2 The thicker lines pertain to lower level of product customization and the dotted lines pertain to higher level of product customization. As explained by (9) and (10) in the previous page, higher PC leads to higher CI and therefore the curve shifts upwards to the right of the thicker line. Similarly, higher PC results in lower CL and therefore the curve shifts downward to the right. This means that when the curve CI shifts to the right, p* shifts to the right as well. That is, ( 12 )
?p * >0 ?C I
C CT CL CTa CLa
CIa
CI 0 p* p* * p
Intuitively, this means that with higher inventory holding costs, the cost-optimizing level of postponement is higher, since higher level of postponement offers greater savings in CI. Similarly, when the curve CL shifts to the right (meaning a reduction in CL), p* shifts to the right too. That is, lower the lead-time costs, higher is the level of postponement that optimizes total costs. This implies, ( 13 )
?p * <0 ?C L
Intuitively, this means that with lower lead-time costs, the opportunity to reduce total costs further by increasing postponement level exists and this warrants an increase in postponement level to reach the optimum. These two curves, CIa and CLa add up to give the curve CTa (all three dotted curves). The curve CTa is to the right of the curve CT, implying a shift of the optimal level of p* to the right, that is higher, at p**. This means that with increased product customization, the optimal level of postponement is higher. This can be proved mathematically as well. In (11), we have two expressions on the right-hand side, as follows:
?p * ?C I ?p * ?C L ?p * ={ x } +{ x } ?C I ?PC ?C L ?PC ?PC (A) (B)
From (9) and (12), expression (A) is positive. From (10) and (13), (B) is positive. Therefore,
?p * ?C I ?p * ?C L ?p * ={ x } +{ x }>0 ?C I ?PC ?C L ?PC ?PC
This concludes the proposition #2 that increased customization (PC) warrants higher p*.
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Reference
Shah, Janat & Balram Avittathur. 1999. Improving Supply Chain Performance Through Postponement Strategy, Management Review, IIM-B, June. pp. 5-13 Waller, Matthew A., Pratibha A.Dabholkar and Julie J. Gentry, 2000. Postponement, product Customization and market-oriented Supply Chain Management, Journal of Business Logistics, Vol. 21, No. 2. pp 133-159. Zinn, Walter and Donald J. Bowersox, 1988. Planning Physical Distribution with the Principle of Postponement, Journal of Business Logistics, Vol. 9, No. 2. pp. 117-135.
Recommended Readings Bucklin, Louis P. 1965. Postponement, Speculation and the Structures of Distribution Channels, Journal of Marketing Research, February. pp. 26 - 31 Feitzinger, Edward and Hau L. Lee. 1997. Mass Customization at Hewlett-Packard: The Power of Postponement, Harvard Business Review, Jan-Feb. pp. 116 - 121 Lee, Hau L. and Corey Billington. 1993. Material Management in Decentralized Supply Chain, Operations Research, Vol. 41, No. 5, Sep-Oct. pp. 835 - 847 Simchi-Levi, David, Philip Kaminsky and Edith Simchi-Levi. 2000. Designing and Managing the Supply Chain, McGraw Hill. pp 167-195.
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APPENDIX A I. TO FIND THE REORDER POINT & LEADTIME BUFFER FOR DESKTOP-A UNDER POSTPONEMENT CONDITION Given Demand follows normal distribution. Mean Demand Std. Deviation Lead-time = 1000 units per period = 400 units = 3 periods Figure a
Service Expectations = 98 % Since lead-time is 3 periods, we need to carry stocks to manage three periods, with buffer. This means,
x
= 3000
2%
s = 400 ?3 = 693.
By using the normal distribution table Z = 2.05 3000 for 98% confidence level, we find that X = 4421 z=2.05, as shown in Figure-a. Solving the equation for X, we get the value X = 4421 units. This is the reorder point for the firm and the Lead-time + buffer stock is 1421 units. This is sketched in the Figure-b. Figure b Now, we can set on to Quantity (Units) find out the cost of inventory holding for this company for the Reorder point 4421 product A. This is done by taking the average stock and multiplying the inventory carrying 3000 cost. units We know that in a case where the buffer is 1421 Buffer + Lead-time stock and the order quantity is 1421 1161, the average inventory is given by 1421+(1161/2) = 2002. 0 Time Therefore, the inventory carrying cost for product A is Rs.12,91,290 per period. Now, we shall find the inventory carrying cost for product B. 14
II.
TO FIND THE REORDER POINT & LEADTIME BUFFER FOR DESKTOP-B UNDER POSTPONEMENT CONDITION Given Demand follows normal distribution. Mean Demand Std. Deviation Lead-time = 600 units per period = 300 units = 3 periods Figure c
Service Expectations = 98 % Since lead-time is 3 periods, we need to carry stocks to manage three periods, with buffer. This means,
x = 1800
s = 300 ?3 = 520.
By using the normal distribution table for 98% confidence level, we find Z = Z = 2.05 2.05, as shown in Figure-c. Solving 1800 the equation for X, we get the value X X = 2866 = 2866 units. This is the reorder point for the firm and the Lead-time + buffer stock is 1066 units. This is sketched in the Figure-d. Now, we can set on to find out the cost of inventory holding for this company for the product B. This is done by taking the Quantity (Units) Figure d average stock and multiplying the inventory carrying cost.
2866
Reorder point
2%
1800 units
We know that in a case where the buffer is 1066 and the order quantity is 910, the average inventory is given by 1066+(910/2) = 1521.
Buffer + Lead-time stock
1066
So, the inventory carrying cost for product B is Rs.9,58,230 per period.
Time
0
The total cost for A & B is Rs.22,50,150.
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APPENDIX B Using similar technique as in Appendix A, we can find that Buffer is 1775 and the reorder point is 6575 for C Buffer is 1421 and the reorder point is 4421for MP 1 Buffer is 1066 and the reorder point is 2866 for MP 2 We know from the given data that the total ordering cost for the RSP is Rs.8,70,000. We can apportion this amount among C, MP 1 and MP 2 either on the basis of the cost of these items ( 57%, 23 % and 21 %) or on the basis of the mean demand (50 %, 31 % and 19%). This is done because we have no historical data on the orders placed for these materials. I. Ordering costs are apportioned in the ratio of costs. This gives us the ordering costs as Components ordering cost MP 1 ordering cost MP 2 ordering cost QC QMP1 QMP2 = = = 1878 1491 1153 Rs. 4,95,900 Rs. 2,00,100 Rs. 1,82,700
On the basis of these, the EOQs are found to be
Average Inventory is calculated by the formula Buffer +(Q/2), which gives us Components 2714 MP1 MP2 2167 1643
The inventory carrying costs per period will be (2714 x 450 + 2167 x 180 + 1643 x 165) which works out to Rs. 18,82,455. The cost of inventory will be (2714 x 30000 + 2167 x 12000 + 1643 x 11000) which works out to Rs.12,54,97,000. II. Ordering costs are apportioned in the ratio of mean demand. This gives us the ordering costs as Components ordering cost MP 1 ordering cost MP 2 ordering cost QC = 1759 Rs. 4,35,000 Rs. 2,69,700 Rs. 1,56,600
On the basis of these, the EOQs are found to be
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QMP1 QMP2
= =
1731 1067
Average Inventory is calculated by the formula Buffer +(Q/2), which gives us Components 2655 MP1 MP2 2287 1600
The inventory carrying costs per period will be (2655 x 450 + 2287 x 180 + 1600 x 165) which works out to Rs. 18,70,410. The cost of inventory will be (2655 x 30000 + 2287 x 12000 + 1600 x 11000) which works out to Rs.12,46,94,000.
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