Description
understand the concepts and methods of aggregate planning and formulate and solve capacity planning problem
Aggregate Planning
Learning Objectives: ?Understand the concepts and methods of aggregate planning ?Formulate and solve capacity planning problem
1
Demand Management
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Demand management is the interface between manufacturing planning and control and the marketplace. Activities include: ? Forecasting. ? Order Processing. ? Making delivery promises.
2
Operations Planning Overview
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Long-range planning
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Greater than one year planning horizon
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Intermediate-range planning
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Six to nine months
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Short-range planning
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One day to less than six months
3
The Planning Process
Long-range plans (over one year)
Research & Development New product plans Capital investment Facility location/expansion Top executives
Intermediate-range plans (3 to 18 months)
Sales planning Production planning and budgeting Setting employment, inventory, subcontracting levels Analyzing cooperating plans
Operations managers
Short-range plans (up to 3 months)
Operations managers, supervisors, foremen Responsibility Job assignments Ordering Job scheduling Dispatching Overtime Part-time help Planning tasks and horizon
Figure 13.1
4
Process Planning
Long Range
Strategic Capacity Planning
Medium Aggregate Planning Range Manufacturing Master Production Scheduling
Material Requirements Planning Order Scheduling
Services
Weekly Workforce & Customer Scheduling Daily Workforce & Customer Scheduling
Short Range
4
Hierarchical Production Planning
Decision Level Corporate Decision Process
Allocates production among plants
Forecasts needed
Annual demand by item and by region
Plant manager
Determines seasonal plan by product type
Monthly demand for 15 months by product type
Shop superintendent
Determines monthly item production schedules
Monthly demand for 5 months by item
5
Aggregate Planning
Marketplace and demand Product decisions Research and technology
Demand forecasts, orders
Process planning and capacity decisions Workforce Aggregate plan for production Raw materials available Inventory on hand
Master production schedule and MRP systems
External capacity (subcontractors)
Detailed work schedules
Figure 13.2
7
How should an aggregate plan fit with other plans?
Business or annual plan Production or staffing Plan (Aggregate Plan) MPS or workforce schedule
Figure 14.1
8
Aggregate Planning
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Goal: Specify the optimal combination of
?
? ?
production rate workforce level inventory on hand
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Product group or broad category (Aggregation)
Medium-Range: 6-18 months
?
6
Aggregate Plan
Aggregate Plan: A statement of a company’s production rates, workforce levels, and inventory holding based on estimates of customer requirements and capacity limitations
Service Industry
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Manufacturing Industry
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Staffing Plan Regarding staffs and labor related factors
Production Plan Regarding production rates and inventory
10
?
?
? ?
?
? ?
Aggregate Planning: Attempts to match the supply of and demand for a product or service by determining the appropriate quantities and timing of inputs, transformation, and outputs. Decisions made on production, staffing, inventory and backorder levels. Characteristics of aggregate planning: Considers a "planning horizon" from about 3 to 18 months, with periodic updating Looks at aggregate product demand, stated in common terms Looks at aggregate resource quantities, stated in common terms Possible to influence both supply and demand by adjusting production rates, workforce levels, inventory levels, etc., but facilities cannot be expanded.
11
Aggregate Production Planning (APP)
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Determines resource capacity to meet demand For intermediate time horizon, 6-12 months Not feasible to build new facility May be feasible to hire/lay off workers, overtime, or subcontract Adjusting capacity OR managing demand
? ? ?
?
12
Aggregate Plan – Managerial Inputs
Operations
Current machine capacities Plans for future capacities Workforce capacities Current staffing level
Distribution and marketing Customer needs Demand forecasts Competition behavior
Materials Supplier capabilities Storage capacity Materials availability
Aggregate plan
Accounting and finance Cost data Financial condition of firm
Engineering New products Product design changes Machine standards
Human resources Labor-market conditions Training capacity
13
Aggregate Plan – Outputs
Aggressive Alternatives Complementary Products Reactive Alternatives Size of Workforce and Workforce Adjustment
Aggregate plan
Competitive Pricing
Units or dollars Of Backlogs, backorders , or stockout
Inventory Levels
Production per month (in units or $)
Units or dollars subcontracted
14
Aggregate Planning Objectives
? ? ? ? ?
Minimize Costs/Maximize Profits
Maximize Customer Service Minimize Inventory Investment Minimize Changes in Production Rates Minimize Changes in Workforce Levels
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Maximize Utilization of Plant and Equipment
15
Aggregate Planning Determine the quantity and timing of production for the immediate future
? Objective is to minimize cost over the planning period by adjusting
? Production rates ? Labor levels ? Inventory levels ? Overtime work ? Subcontracting ? Other controllable variables
16
Aggregate Planning
Required for aggregate planning
? A logical overall unit for measuring sales and output ? A forecast of demand for intermediate planning period in these aggregate units
? A method for determining costs
? A model that combines forecasts and costs so that scheduling decisions can be made for the planning period
17
Aggregate Planning
? Combines appropriate resources into general terms
? Part of a larger production planning system
? Disaggregation breaks the plan down into greater detail ? Disaggregation results in a master production schedule
18
ABC Company
? ABC Co produces nearly 40% of the industrial paints consumed in the India
? Matches fluctuating demand by brand to plant, labor, and inventory capacity to achieve high facility utilization ? High facility utilization requires
? Meticulous cleaning between batches
? Effective maintenance ? Efficient employees ? Efficient facility scheduling
19
Aggregate Planning
Quarter 1 Feb 120,000
Jan 150,000
Mar 110,000 Quarter 2 May 130,000
Apr 100,000
Jun 150,000 Quarter 3 Aug 150,000
Jul 180,000
Sep 140,000
20
Aggregate Planning Strategies
1. Use inventories to absorb changes in demand 2. Accommodate changes by varying workforce size 3. Use part-timers, overtime, or idle time to absorb changes 4. Use subcontractors and maintain a stable workforce 5. Change prices or other factors to influence demand
21
Capacity Options ? Changing inventory levels
? Increase inventory in low demand periods to meet high demand in the future ? Increases costs associated with storage, insurance, handling, obsolescence, and capital investment ? Shortages can mean lost sales due to long lead times and poor customer service
22
Capacity Options ? Varying workforce size by hiring or layoffs
? Match production rate to demand
? Training and separation costs for hiring and laying off workers
? New workers may have lower productivity
? Laying off workers may lower morale and productivity
23
Capacity Options ? Varying production rate through overtime or idle time
? Allows constant workforce
? May be difficult to meet large increases in demand
? Overtime can be costly and may drive down productivity
? Absorbing idle time may be difficult
24
Capacity Options ? Subcontracting
? Temporary measure during periods of peak demand ? May be costly ? Assuring quality and timely delivery may be difficult ? Exposes your customers to a possible competitor
25
Capacity Options ? Using part-time workers
? Useful for filling unskilled or low skilled positions, especially in services
26
Demand Options ? Influencing demand
? Use advertising or promotion to increase demand in low periods ? Attempt to shift demand to slow periods
? May not be sufficient to balance demand and capacity
27
Demand Options ? Back ordering during highdemand periods
? Requires customers to wait for an order without loss of goodwill or the order ? Most effective when there are few if any substitutes for the product or service
? Often results in lost sales
28
Demand Options ? Counterseasonal product and service mixing
? Develop a product mix of counterseasonal items
? May lead to products or services outside the company’s areas of expertise
29
Aggregate Planning Options
Option Changing inventory levels Advantages Changes in human resources are gradual or none; no abrupt production changes Disadvantages Inventory holding cost may increase. Shortages may result in lost sales. Some Comments Applies mainly to production, not service, operations
Varying workforce size by hiring or layoffs
Avoids the costs of other alternatives
Hiring, layoff, and training costs may be significant
Used where size of labor pool is large
Table 13.1
30
Aggregate Planning Options
Option Varying production rates through overtime or idle time Advantages Matches seasonal fluctuations without hiring/ training costs Disadvantages Overtime premiums; tired workers; may not meet demand Some Comments Allows flexibility within the aggregate plan
Subcontracting
Permits flexibility and smoothing of the firm’s output
Loss of quality control; reduced profits; loss of future business
Applies mainly in production settings
Table 13.1
31
Aggregate Planning Options
Option Using part-time workers Advantages Is less costly and more flexible than full-time workers Disadvantages High turnover/ training costs; quality suffers; scheduling difficult Some Comments Good for unskilled jobs in areas with large temporary labor pools
Influencing demand
Tries to use excess capacity. Discounts draw new customers.
Uncertainty in demand. Hard to match demand to supply exactly.
Creates marketing ideas. Overbooking used in some businesses.
Table 13.1
32
Aggregate Planning Options
Option Back ordering during highdemand periods Advantages May avoid overtime. Keeps capacity constant. Disadvantages Customer must be willing to wait, but goodwill is lost. Some Comments Allows flexibility within the aggregate plan
Counterseasonal product and service mixing
Fully utilizes resources; allows stable workforce
May require skills or equipment outside the firm’s areas of expertise
Risky finding products or services with opposite demand patterns
Table 13.1
33
Methods for Aggregate Planning
? A mixed strategy may be the best way to achieve minimum costs
? There are many possible mixed strategies
? Finding the optimal plan is not always possible
34
Mixing Options to Develop a Plan ? Chase strategy
? Match output rates to demand forecast for each period ? Vary workforce levels or vary production rate
? Favored by many service organizations
35
Mixing Options to Develop a Plan ? Level strategy
? Daily production is uniform ? Use inventory or idle time as buffer ? Stable production leads to better quality and productivity
? Some combination of capacity options, a mixed strategy, might be the best solution
36
Graphical and Charting Methods ? Popular techniques ? Easy to understand and use
? Trial-and-error approaches that do not guarantee an optimal solution
? Require only limited computations
37
Graphical and Charting Methods
1. Determine the demand for each period 2. Determine the capacity for regular time, overtime, and subcontracting each period 3. Find labor costs, hiring and layoff costs, and inventory holding costs 4. Consider company policy on workers and stock levels 5. Develop alternative plans and examine their total costs
38
Planning Example 1
Month Jan Expected Demand 900 Production Days 22 Demand Per Day (computed) 41
Feb
Mar
700
800
18
21
39
38
Apr
May
1,200
1,500
21
22
57
68
June
1,100
6,200
20
124
55
Table 13.2
Total expected demand Average requirement = Number of production days 6,200 = = 50 units per day 124
39
Planning Example 1
Production rate per working day Forecast demand
70 – 60 – 50 – 40 – 30 –
Level production using average monthly forecast demand
0 –
Jan
?
Feb
?
Mar
?
Apr
?
May
?
June
?
= Month
= Number of working days
40
22
Figure 13.3
18
21
21
22
20
Planning Example 1
Cost Information
Inventory carrying cost Subcontracting cost per unit Average pay rate Overtime pay rate Labor-hours to produce a unit Cost of increasing daily production rate (hiring and training) Cost of decreasing daily production rate (layoffs)
$ 5 per unit per month
$10 per unit $ 5 per hour ($40 per day) $ 7 per hour (above 8 hours per day) 1.6 hours per unit $300 per unit $600 per unit
Table 13.3
41
Planning Example 1
Cost Information Production at Month 50 Units per Day Inventory carry cost Jan 1,100 Subcontracting cost per unit
Average pay rate Overtime pay rate
Demand Forecast 900 700 800
Monthly Inventory Ending Change Inventory $ 5 per unit per month +200 $10 per unit +250 200 650 100 0 1,850 +200 400 $ 5 per hour ($40 per day)
$ 7 per hour (above 8 hours per day) -150 500 1.6 hours per unit
Feb
900 1,050
Mar
Apr
1,050
1,200
1,500
Labor-hours to produce a unit May 1,100
-400 -100
Cost of increasing daily production rate (hiring June 1,000 1,100 and training) Cost of decreasing daily production rate (layoffs)
$300 per unit $600 per unit
Total units of inventory carried over from one month to the next = 1,850 units Table 13.3 Workforce required to produce 50 units per day = 10 workers
42
Planning Example 1
Costs Cost Information Production at Month 50 Units per Day Inventory carry cost Inventory carrying Jan 1,100 Subcontracting cost per unit Feb Regular-time labor 900 Average pay rate Mar 1,050
Overtime pay rate
Monthly Calculations Demand Inventory Ending Forecast $ 5 per units carried x $5 per Change Inventory $9,250 (= 1,850 unit per month 900 unit) per unit $10 +200 200 700 (= $ 5 workers ($40 per day) x +200 400 49,600 10 per hour x $40 per day 800 124 days) +250 650
$ 7 per hour (above 8 hours per day) -150 500 1.6 hours per unit
Apr 1,050 1,200 Other costs (overtime, hiring, layoffs, Labor-hours to produce a unit May 1,100 1,500 subcontracting) 0 Cost of increasing daily production rate (hiring June 1,000 1,100 Total cost $58,850
and training) Cost of decreasing daily production rate (layoffs)
-400 -100
100 0
$300 per unit $600 per unit
1,850
Total units of inventory carried over from one month to the next = 1,850 units Table 13.3 Workforce required to produce 50 units per day = 10 workers
43
Planning Example 1
7,000 –
6,000 – Cumulative demand units 5,000 – 4,000 – 3,000 – Reduction of inventory Cumulative level production using average monthly forecast requirements
2,000 –
1,000 – – Jan Feb Mar
Cumulative forecast requirements
Excess inventory
Apr May June
44
Figure 13.4
Planning Example 2
Month Jan Expected Demand 900 Production Days 22 Demand Per Day (computed) 41
Feb
Mar
700
800
18
21
39
38
Apr
May
1,200
1,500
21
22
57
68
June
1,100
6,200
20
124
55
Table 13.2
Minimum requirement = 38 units per day
45
Planning Example 2
Production rate per working day Forecast demand
70 – 60 – 50 – 40 – 30 –
Level production using lowest monthly forecast demand
0 –
Jan
?
Feb
?
Mar
?
Apr
?
May
?
June
?
= Month
= Number of working days
46
22
18
21
21
22
20
Planning Example 2
Cost Information
Inventory carrying cost Subcontracting cost per unit Average pay rate Overtime pay rate Labor-hours to produce a unit Cost of increasing daily production rate (hiring and training) Cost of decreasing daily production rate (layoffs)
$ 5 per unit per month
$10 per unit $ 5 per hour ($40 per day) $ 7 per hour (above 8 hours per day) 1.6 hours per unit $300 per unit $600 per unit
Table 13.3
47
Planning Example 2
Cost Information
Inventory carry cost
$ 5 per unit per month
In-house production = 38 units per day $10 per unit x $ 5 per hour ($40 per day) 124 days Average pay rate $ 7 per units = 4,712 hour Overtime pay rate
Subcontracting cost per unit (above 8 hours per day) 1.6 hours Subcontract units = 6,200 - per unit 4,712 Cost of increasing daily production rate (hiring $300 per unit = 1,488 units and training) Labor-hours to produce a unit Cost of decreasing daily production rate (layoffs) $600 per unit
Table 13.3
48
Planning Example 2
Cost Information
Inventory carry cost
$ 5 per unit per month
In-house production = 38 units per day $10 per unit x $ 5 per hour ($40 per day) 124 days Average pay rate $ 7 per units = 4,712 hour Overtime pay rate
Subcontracting cost per unit (above 8 hours per day) 1.6 hours Subcontract units = Calculationsper unit 6,200 - 4,712 Cost of increasing daily production rate (hiring (= $300workers x $40 per day Regular-time labor $37,696 7.6 per unit = 1,488 units and training) x 124 days) Labor-hours to produce a unit Costs Cost of decreasing daily production rate (layoffs) $600 per unit
Subcontracting
14,880
(= 1,488 units x $10 per unit)
Table 13.3 Total cost
$52,576
49
Planning Example 3
Month Jan Expected Demand 900 Production Days 22 Demand Per Day (computed) 41
Feb
Mar
700
800
18
21
39
38
Apr
May
1,200
1,500
21
22
57
68
June
1,100
6,200
20
124
55
Table 13.2
Production = Expected Demand
50
Planning Example 3
Production rate per working day
70 – 60 – 50 – 40 – 30 –
Forecast demand and monthly production
0 –
Jan
?
Feb
?
Mar
?
Apr
?
May
?
June
?
= Month
= Number of working days
51
22
18
21
21
22
20
Planning Example 3
Cost Information
Inventory carrying cost Subcontracting cost per unit Average pay rate Overtime pay rate Labor-hours to produce a unit Cost of increasing daily production rate (hiring and training) Cost of decreasing daily production rate (layoffs)
$ 5 per unit per month
$10 per unit $ 5 per hour ($40 per day) $ 7 per hour (above 8 hours per day) 1.6 hours per unit $300 per unit $600 per unit
Table 13.3
52
Planning Example 3
Cost Information
Month Jan Forecast (units) 900 700
Inventory carrying cost
Daily Prod Rate 41 39
Basic Production Cost (demand x 1.6 hrs/unit x $5/hr) $ 7,200 5,600
Extra Cost of Increasing Production (hiring cost) $ 5 — —
Extra Cost of Decreasing Production (layoff per unitcost) month Total Cost per — $ 7,200
Subcontracting cost per unit Average pay rate
Mar 800 Overtime pay rate Feb
$10 per unit
(= 2 $600) $ 5 per hourx($40 per day)6,800 $600 $ 7 per hour 7,000 (= 1 x $600) (above 8 hours per day)
$1,200
38
6,400
—
Apr 1,200 57 Labor-hours to produce a unit
9,600
$5,700 1.6 (= 19 x $300)
hours per unit —
15,300
Cost of increasing daily production rate (hiring $3,300 $300 per unit May 1,500 68 12,000 — (= 11 x $300) and training) Cost of decreasing daily production rate (layoffs) — June 1,100 55 8,800
$49,600 $9,000
15,300
$600 per unit $7,800
$9,600
(= 13 x $600)
16,600 $68,200
Table 13.3
53
Comparison of Three Plans
Cost Inventory carrying Regular labor Overtime labor
Hiring Layoffs Subcontracting Total cost
Plan 1 $ 9,250 49,600 0
0 0 0 $58,850
Plan 2 $ 0 $
Plan 3 0
37,696 0
0 0 0 $52,576
49,600 0
9,000 9,600 0 $68,200
Plan 2 is the lowest cost option
Table 13.5 54
Mathematical Approaches
? Useful for generating strategies
? Transportation Method of Linear Programming
? Produces an optimal plan
? Management Coefficients Model
? Model built around manager’s experience and performance
? Other Models
? Linear Decision Rule ? Simulation
55
Transportation Method
Sales Period Mar Apr May 800 1,000 750 700 50 150 100 per tire per tire per tire per tire 700 50 150 tires 700 50 130
Demand Capacity: Regular Overtime Subcontracting Beginning inventory Costs Regular time Overtime Subcontracting Carrying $40 $50 $70 $2
Table 13.6
56
Transportation Example
Important points
1. Carrying costs are $2/tire/month. If goods are made in one period and held over to the next, holding costs are incurred 2. Supply must equal demand, so a dummy column called “unused capacity” is added 3. Because back ordering is not viable in this example, cells that might be used to satisfy earlier demand are not available
57
Transportation Example
Important points
4. Quantities in each column designate the levels of inventory needed to meet demand requirements
5. In general, production should be allocated to the lowest cost cell available without exceeding unused capacity in the row or demand in the column
58
Transportation Example
Table 13.7
59
Management Coefficients Model
? Builds a model based on manager’s experience and performance ? A regression model is constructed to define the relationships between decision variables
? Objective is to remove inconsistencies in decision making
60
Other Models
Linear Decision Rule
? Minimizes costs using quadratic cost curves ? Operates over a particular time period
Simulation
? Uses a search procedure to try different combinations of variables ? Develops feasible but not necessarily optimal solutions
61
Summary of Aggregate Planning Methods
Techniques Graphical/charting methods Solution Approaches Trial and error Important Aspects Simple to understand and easy to use. Many solutions; one chosen may not be optimal. LP software available; permits sensitivity analysis and new constraints; linear functions may not be realistic Simple, easy to implement; tries to mimic manager’s decision process; uses regression
Transportation method of linear programming
Optimization
Management coefficients model
Heuristic
Table 13.8
62
Law Firm Example
(1) Category of Legal Business Trial work Legal research Corporate law Real estate law Criminal law Total hours Lawyers needed (2) Best Case (hours) 1,800 4,500 8,000 1,700 3,500 19,500 39 (3) Likely Case (hours) 1,500 4,000 7,000 1,500 3,000 17,000 34 (4) Worst Case (hours) 1,200 3,500 6,500 1,300 2,500 15,000 30 (5) Maximum Demand in People 3.6 9.0 16.0 3.4 7.0 (6) Number of Qualified Personnel 4 32 15 6 12
Table 13.9
63
Yield Management
Allocating resources to customers at prices that will maximize yield or revenue
1. Service or product can be sold in advance of consumption 2. Demand fluctuates 3. Capacity is relatively fixed 4. Demand can be segmented 5. Variable costs are low and fixed costs are high
64
Yield Management Example
Room sales
100
Demand Curve Potential customers exist who are willing to pay more than the $15 variable cost of the room
Passed-up contribution
50
Some customers who paid $150 were actually willing to pay more for the room
$ margin = (Price) x (50 rooms) = ($150 - $15) x (50) = $6,750 $15 Variable cost of room
Money left on the table $150 Price charged for room Price
Figure 13.5 65
Yield Management Example
Room sales
100
Demand Curve
Total $ margin = (1st price) x 30 rooms + (2nd price) x 30 rooms = ($100 - $15) x 30 + ($200 - $15) x 30 = $2,550 + $5,550 = $8,100
60
30
$15 Variable cost of room
$100 Price 1 for room
$200 Price 2 for room
Price
Figure 13.6 66
Yield Management Matrix
Price
Tend to be fixed Predictable Quadrant 1: Movies Stadiums/arenas Convention centers Hotel meeting space Quadrant 3: Restaurants Golf courses Internet service providers Tend to be variable Quadrant 2: Hotels Airlines Rental cars Cruise lines Quadrant 4: Continuing care hospitals
Duration of use
Unpredictable
Figure 13.7
67
Making Yield Management Work 1. Multiple pricing structures must be feasible and appear logical to the customer 2. Forecasts of the use and duration of use 3. Changes in demand
68
Aggregate Planning Example
ABC Co, a small manufacturing company (200 employees), produces umbrellas. The company, founded in 1991 produces the following three product lines: 1) the Executive Line, 2) the Durable Line and 3) the Compact line shown in the following figure.
Executive Line
Compact Line Durable Line
8
Units
Examples of Capacity Adjustment to Meet Demand
Demand
Time
1.
Producing at a constant rate and using inventory to absorb
fluctuations in demand Hiring and firing workers to match demand Maintaining resources for high demand levels
2. 3.
4.
5. 6. 7.
Increase or decrease working hours (overtime and undertime) Subcontracting work to other firms Using part-time workers Providing the service or product at a later time period (backordering)
70
Planning Strategies
?
Chase Strategies
?
PURE STRATEGIES
?
?
Match demand during the planning horizon by either Vary workforce or vary output rate
Level Strategies
?
?
Maintain a constant workforce level or constant output rate during the planning horizon Constant workforce or constant output rate
?
Mixed Strategies
?
Combined several strategies
71
Pure Strategy
Level Production
Demand
Chase Demand
Demand Production Units
Production
Units
Time
Time
What are pros / cons of these strategies?
72
TABLE 14.1
PLANNING STRATEGIES FOR AGGREGATE PLANS Possible Alternatives during Slack Season
Layoffs Layoffs, undertime, vacations No layoffs, building anticipation inventory, undertime, vacations Layoffs, building anticipation inventory, undertime, vacations
Strategy
1. Chase #1: vary workforce level to match demand 2. Chase #2: vary output rate to match demand 3. Level #1: constant workforce level
Possible Alternatives during Peak Season
Hiring Hiring, overtime, subcontracting No hiring, depleting anticipation inventory, overtime, subcontracting, backorders, stockouts Hiring, depleting anticipation inventory, overtime, subcontracting, backorders, stockouts
73
4. Level #2: constant output rate
Aggregate Planning Costs
? ? ?
?
?
Regular-Time Costs Overtime Costs Hiring and Layoff Costs Inventory Holding Costs Backorder and Stockout Costs
74
?
?
Aggregate Planning Methods: Intuitive Methods Intuitive methods use management intuition, experience, and rules-of-thumb, frequently accompanied by graphical and/or spreadsheet analysis.
? ?
Advantage:
?
Disadvantage:
?
easy to use and explain many solutions are possible, most of which are not optimal
75
Ex 1 Candy Company
Given the following costs and quarterly sales forecasts of a candy company, compare the two strategies: Strategy 1: Level production with constant workforce level Strategy 2: Chase production by varying workforce level
Quarter
Spring Summer Fall Winter
Sale Forecast (LB)
80,000 50,000 120,000 150,000
? ? ?
Hiring cost Firing cost Inventory carrying cost
Production rate per employee ? Beginning workforce
?
$100 per worker $500 per worker $0.50 per pound per quarter 1000 pounds per quarter 100 workers
76
Transportation Method
?
Alternatives
Quarter
Quarter 1
0
2
h
3
2h
4
3h
Unused Total Capacity Capacity
4h
Beginning inventory Regular time
I0
r r+h r+2h r+3h u
R1
c c+h c+2h c+3h 0
?
?
A method of LP Gather all cost info into one matrix Try to obtain the lowest cost alternative
1
Overtime s r+b s+h r s+2h r+h s+3h r+2h 0
O1 S1
u
Subcontract Regular time 2 Overtime
R2
c+b c c+h c+2h 0
O2
s+b s s+h s+2h 0
Subcontract Regular time 3 Overtime
S2
r+2b r+b r r+h u
R3
c+2b c+b c c+h 0
O3
s+2b r+3b s+b r+2b s r+b s+h r 0
Subcontract Regular time 4 Overtime
S3
u
R4
c+3b c+2b c+b c 0
O4
s+3b s+2b s+b s 0
Subcontract
77
S4
Requirements
D1
D2
D3
D4 + I4
U
Notations
It = inventory at the end of period t (I0 = beginning inventory) h = holding cost per unit per period, r = regular production cost per unit, o = overtime cost per unit, u = undertime cost per unit s = subcontracting cost per unit, b = backordering cost per unit per period Rt = regular-time capacity in period t Ot = overtime capacity in period t St = subcontracting capacity in period t Dt = forecasted demand for period t U = total unused capacities
78
Tableau Method
?
Step 1: Put all capacities from the total capacity column into the unused capacity column. Next, put unit costs in each of the small boxes Step 2: In column 1 (period 1), allocate as much production as you can to the cell with the lowest cost but do not exceed the unused capacity in that row or the demand in that column. Step 3: Subtract your allocation from the unused capacity for the row. This quantity must never be negative.
?
?
79
Tableau Method
?
(Cont’d)
Step 4: If there is still some demand left, repeat step 2, allocating as much production as possible to the cell with the next-to-lowest cost. Repeat until the demand is satisfied. Step 5: Repeat steps 2 through 4 for periods 2 and beyond. Take each column separately before proceeding to the next. Be sure to check all cells with unused capacity for the cell with the lowest cost in a column.
?
80
Ex 2: Transportation Method
Given the following costs and quarterly sales forecasts, use the transportation method to design a production plan. What is the total cost of the plan?
Quarter 1 2 3 4
Sale Forecast (unit) 50,000 150,000 200,000 52,000
Inventory carrying cost = $3 per unit per quarter Production/worker = 1000 units/quarter Regular workforce = 50 workers Overtime capacity = 50,000 units Subcontracting capacity = 40,000 units Regular production cost = $50/unit Overtime production cost = $75/unit Subcontracting cost = $85/unit
81
Linear Programming Model (LP)
? ? ? ?
Pure/Mixed Strategy: not guarantee optimal solution LP: can get optimal solution LP: Excel, LINGO, CPLEX, … LP Formulation**
? ?
Objective function Constraints
Ex 2: Formulate LP model for Ex 1 Candy Company and Ex 2
82
? ?
? ?
Production Plan (manufacturing aggregate plan): A managerial statement of the period-by-period (timephased) production rates, work-force levels, and inventory investment, given customer requirements and capacity limitations. Staffing Plan (service aggregate plan): A managerial statement of the period-by-period staff sizes and labour-related capacities, given customer requirements and capacity limitations.
83
? ? ? ? ? ? ? ?
Objectives of Aggregate Planning Objective of aggregate planning frequently is to minimize total cost over the planning horizon. Other objectives should be considered: maximize customer service minimize inventory investment minimize changes in workforce levels minimize changes in production rates maximize utilization of plant and equipment
84
?
?
? ? ?
?
? ?
Aggregate Planning Strategies Active strategy: Attempts to handle fluctuations in demand by focusing on demand management Use pricing strategies and/or advertising and promotion Develop counter-cyclical products Request customers to backorder or advance-order Do not meet demand
85
?
?
? ? ? ? ? ? ? ? ?
Passive strategy (reactive strategy): Attempts to handle fluctuations in demand by focusing on supply and capacity management Vary size work force size by hiring or layoffs Vary utilization of labour and equipment through overtime or idle time Build or draw from inventory Subcontract production Negotiate cooperative arrangements with other firms Allow backlogs, back orders, and/or stockouts Mixed strategy: Combines elements of both an active strategy and a passive (reactive) strategy Firms will usually use some combination of the two
86
?
Basic Approaches
?
? ? ? ? ? ? ?
Chase approach
capacities (workforce levels, production schedules, output rates, etc.) are adjusted to match demand requirements over the planning horizon. Advantages: anticipation inventory is not required, and investment in inventory is low labour utilization is kept high Disadvantages: expense of adjusting output rates and/or workforce levels alienation of workforce Capacities (workforce levels, production schedules, output rates, etc.) are kept constant over the planning horizon. Advantages: stable output rates and workforce levels Disadvantages: greater inventory investment is required increased overtime and idle time resource utilizations vary over time
?
Level Approach
? ? ? ? ? ? ?
87
doc_438772163.pptx
understand the concepts and methods of aggregate planning and formulate and solve capacity planning problem
Aggregate Planning
Learning Objectives: ?Understand the concepts and methods of aggregate planning ?Formulate and solve capacity planning problem
1
Demand Management
?
Demand management is the interface between manufacturing planning and control and the marketplace. Activities include: ? Forecasting. ? Order Processing. ? Making delivery promises.
2
Operations Planning Overview
?
Long-range planning
?
Greater than one year planning horizon
?
Intermediate-range planning
?
Six to nine months
?
Short-range planning
?
One day to less than six months
3
The Planning Process
Long-range plans (over one year)
Research & Development New product plans Capital investment Facility location/expansion Top executives
Intermediate-range plans (3 to 18 months)
Sales planning Production planning and budgeting Setting employment, inventory, subcontracting levels Analyzing cooperating plans
Operations managers
Short-range plans (up to 3 months)
Operations managers, supervisors, foremen Responsibility Job assignments Ordering Job scheduling Dispatching Overtime Part-time help Planning tasks and horizon
Figure 13.1
4
Process Planning
Long Range
Strategic Capacity Planning
Medium Aggregate Planning Range Manufacturing Master Production Scheduling
Material Requirements Planning Order Scheduling
Services
Weekly Workforce & Customer Scheduling Daily Workforce & Customer Scheduling
Short Range
4
Hierarchical Production Planning
Decision Level Corporate Decision Process
Allocates production among plants
Forecasts needed
Annual demand by item and by region
Plant manager
Determines seasonal plan by product type
Monthly demand for 15 months by product type
Shop superintendent
Determines monthly item production schedules
Monthly demand for 5 months by item
5
Aggregate Planning
Marketplace and demand Product decisions Research and technology
Demand forecasts, orders
Process planning and capacity decisions Workforce Aggregate plan for production Raw materials available Inventory on hand
Master production schedule and MRP systems
External capacity (subcontractors)
Detailed work schedules
Figure 13.2
7
How should an aggregate plan fit with other plans?
Business or annual plan Production or staffing Plan (Aggregate Plan) MPS or workforce schedule
Figure 14.1
8
Aggregate Planning
?
Goal: Specify the optimal combination of
?
? ?
production rate workforce level inventory on hand
?
Product group or broad category (Aggregation)
Medium-Range: 6-18 months
?
6
Aggregate Plan
Aggregate Plan: A statement of a company’s production rates, workforce levels, and inventory holding based on estimates of customer requirements and capacity limitations
Service Industry
? ?
Manufacturing Industry
? ?
Staffing Plan Regarding staffs and labor related factors
Production Plan Regarding production rates and inventory
10
?
?
? ?
?
? ?
Aggregate Planning: Attempts to match the supply of and demand for a product or service by determining the appropriate quantities and timing of inputs, transformation, and outputs. Decisions made on production, staffing, inventory and backorder levels. Characteristics of aggregate planning: Considers a "planning horizon" from about 3 to 18 months, with periodic updating Looks at aggregate product demand, stated in common terms Looks at aggregate resource quantities, stated in common terms Possible to influence both supply and demand by adjusting production rates, workforce levels, inventory levels, etc., but facilities cannot be expanded.
11
Aggregate Production Planning (APP)
?
Determines resource capacity to meet demand For intermediate time horizon, 6-12 months Not feasible to build new facility May be feasible to hire/lay off workers, overtime, or subcontract Adjusting capacity OR managing demand
? ? ?
?
12
Aggregate Plan – Managerial Inputs
Operations
Current machine capacities Plans for future capacities Workforce capacities Current staffing level
Distribution and marketing Customer needs Demand forecasts Competition behavior
Materials Supplier capabilities Storage capacity Materials availability
Aggregate plan
Accounting and finance Cost data Financial condition of firm
Engineering New products Product design changes Machine standards
Human resources Labor-market conditions Training capacity
13
Aggregate Plan – Outputs
Aggressive Alternatives Complementary Products Reactive Alternatives Size of Workforce and Workforce Adjustment
Aggregate plan
Competitive Pricing
Units or dollars Of Backlogs, backorders , or stockout
Inventory Levels
Production per month (in units or $)
Units or dollars subcontracted
14
Aggregate Planning Objectives
? ? ? ? ?
Minimize Costs/Maximize Profits
Maximize Customer Service Minimize Inventory Investment Minimize Changes in Production Rates Minimize Changes in Workforce Levels
?
Maximize Utilization of Plant and Equipment
15
Aggregate Planning Determine the quantity and timing of production for the immediate future
? Objective is to minimize cost over the planning period by adjusting
? Production rates ? Labor levels ? Inventory levels ? Overtime work ? Subcontracting ? Other controllable variables
16
Aggregate Planning
Required for aggregate planning
? A logical overall unit for measuring sales and output ? A forecast of demand for intermediate planning period in these aggregate units
? A method for determining costs
? A model that combines forecasts and costs so that scheduling decisions can be made for the planning period
17
Aggregate Planning
? Combines appropriate resources into general terms
? Part of a larger production planning system
? Disaggregation breaks the plan down into greater detail ? Disaggregation results in a master production schedule
18
ABC Company
? ABC Co produces nearly 40% of the industrial paints consumed in the India
? Matches fluctuating demand by brand to plant, labor, and inventory capacity to achieve high facility utilization ? High facility utilization requires
? Meticulous cleaning between batches
? Effective maintenance ? Efficient employees ? Efficient facility scheduling
19
Aggregate Planning
Quarter 1 Feb 120,000
Jan 150,000
Mar 110,000 Quarter 2 May 130,000
Apr 100,000
Jun 150,000 Quarter 3 Aug 150,000
Jul 180,000
Sep 140,000
20
Aggregate Planning Strategies
1. Use inventories to absorb changes in demand 2. Accommodate changes by varying workforce size 3. Use part-timers, overtime, or idle time to absorb changes 4. Use subcontractors and maintain a stable workforce 5. Change prices or other factors to influence demand
21
Capacity Options ? Changing inventory levels
? Increase inventory in low demand periods to meet high demand in the future ? Increases costs associated with storage, insurance, handling, obsolescence, and capital investment ? Shortages can mean lost sales due to long lead times and poor customer service
22
Capacity Options ? Varying workforce size by hiring or layoffs
? Match production rate to demand
? Training and separation costs for hiring and laying off workers
? New workers may have lower productivity
? Laying off workers may lower morale and productivity
23
Capacity Options ? Varying production rate through overtime or idle time
? Allows constant workforce
? May be difficult to meet large increases in demand
? Overtime can be costly and may drive down productivity
? Absorbing idle time may be difficult
24
Capacity Options ? Subcontracting
? Temporary measure during periods of peak demand ? May be costly ? Assuring quality and timely delivery may be difficult ? Exposes your customers to a possible competitor
25
Capacity Options ? Using part-time workers
? Useful for filling unskilled or low skilled positions, especially in services
26
Demand Options ? Influencing demand
? Use advertising or promotion to increase demand in low periods ? Attempt to shift demand to slow periods
? May not be sufficient to balance demand and capacity
27
Demand Options ? Back ordering during highdemand periods
? Requires customers to wait for an order without loss of goodwill or the order ? Most effective when there are few if any substitutes for the product or service
? Often results in lost sales
28
Demand Options ? Counterseasonal product and service mixing
? Develop a product mix of counterseasonal items
? May lead to products or services outside the company’s areas of expertise
29
Aggregate Planning Options
Option Changing inventory levels Advantages Changes in human resources are gradual or none; no abrupt production changes Disadvantages Inventory holding cost may increase. Shortages may result in lost sales. Some Comments Applies mainly to production, not service, operations
Varying workforce size by hiring or layoffs
Avoids the costs of other alternatives
Hiring, layoff, and training costs may be significant
Used where size of labor pool is large
Table 13.1
30
Aggregate Planning Options
Option Varying production rates through overtime or idle time Advantages Matches seasonal fluctuations without hiring/ training costs Disadvantages Overtime premiums; tired workers; may not meet demand Some Comments Allows flexibility within the aggregate plan
Subcontracting
Permits flexibility and smoothing of the firm’s output
Loss of quality control; reduced profits; loss of future business
Applies mainly in production settings
Table 13.1
31
Aggregate Planning Options
Option Using part-time workers Advantages Is less costly and more flexible than full-time workers Disadvantages High turnover/ training costs; quality suffers; scheduling difficult Some Comments Good for unskilled jobs in areas with large temporary labor pools
Influencing demand
Tries to use excess capacity. Discounts draw new customers.
Uncertainty in demand. Hard to match demand to supply exactly.
Creates marketing ideas. Overbooking used in some businesses.
Table 13.1
32
Aggregate Planning Options
Option Back ordering during highdemand periods Advantages May avoid overtime. Keeps capacity constant. Disadvantages Customer must be willing to wait, but goodwill is lost. Some Comments Allows flexibility within the aggregate plan
Counterseasonal product and service mixing
Fully utilizes resources; allows stable workforce
May require skills or equipment outside the firm’s areas of expertise
Risky finding products or services with opposite demand patterns
Table 13.1
33
Methods for Aggregate Planning
? A mixed strategy may be the best way to achieve minimum costs
? There are many possible mixed strategies
? Finding the optimal plan is not always possible
34
Mixing Options to Develop a Plan ? Chase strategy
? Match output rates to demand forecast for each period ? Vary workforce levels or vary production rate
? Favored by many service organizations
35
Mixing Options to Develop a Plan ? Level strategy
? Daily production is uniform ? Use inventory or idle time as buffer ? Stable production leads to better quality and productivity
? Some combination of capacity options, a mixed strategy, might be the best solution
36
Graphical and Charting Methods ? Popular techniques ? Easy to understand and use
? Trial-and-error approaches that do not guarantee an optimal solution
? Require only limited computations
37
Graphical and Charting Methods
1. Determine the demand for each period 2. Determine the capacity for regular time, overtime, and subcontracting each period 3. Find labor costs, hiring and layoff costs, and inventory holding costs 4. Consider company policy on workers and stock levels 5. Develop alternative plans and examine their total costs
38
Planning Example 1
Month Jan Expected Demand 900 Production Days 22 Demand Per Day (computed) 41
Feb
Mar
700
800
18
21
39
38
Apr
May
1,200
1,500
21
22
57
68
June
1,100
6,200
20
124
55
Table 13.2
Total expected demand Average requirement = Number of production days 6,200 = = 50 units per day 124
39
Planning Example 1
Production rate per working day Forecast demand
70 – 60 – 50 – 40 – 30 –
Level production using average monthly forecast demand
0 –
Jan
?
Feb
?
Mar
?
Apr
?
May
?
June
?
= Month
= Number of working days
40
22
Figure 13.3
18
21
21
22
20
Planning Example 1
Cost Information
Inventory carrying cost Subcontracting cost per unit Average pay rate Overtime pay rate Labor-hours to produce a unit Cost of increasing daily production rate (hiring and training) Cost of decreasing daily production rate (layoffs)
$ 5 per unit per month
$10 per unit $ 5 per hour ($40 per day) $ 7 per hour (above 8 hours per day) 1.6 hours per unit $300 per unit $600 per unit
Table 13.3
41
Planning Example 1
Cost Information Production at Month 50 Units per Day Inventory carry cost Jan 1,100 Subcontracting cost per unit
Average pay rate Overtime pay rate
Demand Forecast 900 700 800
Monthly Inventory Ending Change Inventory $ 5 per unit per month +200 $10 per unit +250 200 650 100 0 1,850 +200 400 $ 5 per hour ($40 per day)
$ 7 per hour (above 8 hours per day) -150 500 1.6 hours per unit
Feb
900 1,050
Mar
Apr
1,050
1,200
1,500
Labor-hours to produce a unit May 1,100
-400 -100
Cost of increasing daily production rate (hiring June 1,000 1,100 and training) Cost of decreasing daily production rate (layoffs)
$300 per unit $600 per unit
Total units of inventory carried over from one month to the next = 1,850 units Table 13.3 Workforce required to produce 50 units per day = 10 workers
42
Planning Example 1
Costs Cost Information Production at Month 50 Units per Day Inventory carry cost Inventory carrying Jan 1,100 Subcontracting cost per unit Feb Regular-time labor 900 Average pay rate Mar 1,050
Overtime pay rate
Monthly Calculations Demand Inventory Ending Forecast $ 5 per units carried x $5 per Change Inventory $9,250 (= 1,850 unit per month 900 unit) per unit $10 +200 200 700 (= $ 5 workers ($40 per day) x +200 400 49,600 10 per hour x $40 per day 800 124 days) +250 650
$ 7 per hour (above 8 hours per day) -150 500 1.6 hours per unit
Apr 1,050 1,200 Other costs (overtime, hiring, layoffs, Labor-hours to produce a unit May 1,100 1,500 subcontracting) 0 Cost of increasing daily production rate (hiring June 1,000 1,100 Total cost $58,850
and training) Cost of decreasing daily production rate (layoffs)
-400 -100
100 0
$300 per unit $600 per unit
1,850
Total units of inventory carried over from one month to the next = 1,850 units Table 13.3 Workforce required to produce 50 units per day = 10 workers
43
Planning Example 1
7,000 –
6,000 – Cumulative demand units 5,000 – 4,000 – 3,000 – Reduction of inventory Cumulative level production using average monthly forecast requirements
2,000 –
1,000 – – Jan Feb Mar
Cumulative forecast requirements
Excess inventory
Apr May June
44
Figure 13.4
Planning Example 2
Month Jan Expected Demand 900 Production Days 22 Demand Per Day (computed) 41
Feb
Mar
700
800
18
21
39
38
Apr
May
1,200
1,500
21
22
57
68
June
1,100
6,200
20
124
55
Table 13.2
Minimum requirement = 38 units per day
45
Planning Example 2
Production rate per working day Forecast demand
70 – 60 – 50 – 40 – 30 –
Level production using lowest monthly forecast demand
0 –
Jan
?
Feb
?
Mar
?
Apr
?
May
?
June
?
= Month
= Number of working days
46
22
18
21
21
22
20
Planning Example 2
Cost Information
Inventory carrying cost Subcontracting cost per unit Average pay rate Overtime pay rate Labor-hours to produce a unit Cost of increasing daily production rate (hiring and training) Cost of decreasing daily production rate (layoffs)
$ 5 per unit per month
$10 per unit $ 5 per hour ($40 per day) $ 7 per hour (above 8 hours per day) 1.6 hours per unit $300 per unit $600 per unit
Table 13.3
47
Planning Example 2
Cost Information
Inventory carry cost
$ 5 per unit per month
In-house production = 38 units per day $10 per unit x $ 5 per hour ($40 per day) 124 days Average pay rate $ 7 per units = 4,712 hour Overtime pay rate
Subcontracting cost per unit (above 8 hours per day) 1.6 hours Subcontract units = 6,200 - per unit 4,712 Cost of increasing daily production rate (hiring $300 per unit = 1,488 units and training) Labor-hours to produce a unit Cost of decreasing daily production rate (layoffs) $600 per unit
Table 13.3
48
Planning Example 2
Cost Information
Inventory carry cost
$ 5 per unit per month
In-house production = 38 units per day $10 per unit x $ 5 per hour ($40 per day) 124 days Average pay rate $ 7 per units = 4,712 hour Overtime pay rate
Subcontracting cost per unit (above 8 hours per day) 1.6 hours Subcontract units = Calculationsper unit 6,200 - 4,712 Cost of increasing daily production rate (hiring (= $300workers x $40 per day Regular-time labor $37,696 7.6 per unit = 1,488 units and training) x 124 days) Labor-hours to produce a unit Costs Cost of decreasing daily production rate (layoffs) $600 per unit
Subcontracting
14,880
(= 1,488 units x $10 per unit)
Table 13.3 Total cost
$52,576
49
Planning Example 3
Month Jan Expected Demand 900 Production Days 22 Demand Per Day (computed) 41
Feb
Mar
700
800
18
21
39
38
Apr
May
1,200
1,500
21
22
57
68
June
1,100
6,200
20
124
55
Table 13.2
Production = Expected Demand
50
Planning Example 3
Production rate per working day
70 – 60 – 50 – 40 – 30 –
Forecast demand and monthly production
0 –
Jan
?
Feb
?
Mar
?
Apr
?
May
?
June
?
= Month
= Number of working days
51
22
18
21
21
22
20
Planning Example 3
Cost Information
Inventory carrying cost Subcontracting cost per unit Average pay rate Overtime pay rate Labor-hours to produce a unit Cost of increasing daily production rate (hiring and training) Cost of decreasing daily production rate (layoffs)
$ 5 per unit per month
$10 per unit $ 5 per hour ($40 per day) $ 7 per hour (above 8 hours per day) 1.6 hours per unit $300 per unit $600 per unit
Table 13.3
52
Planning Example 3
Cost Information
Month Jan Forecast (units) 900 700
Inventory carrying cost
Daily Prod Rate 41 39
Basic Production Cost (demand x 1.6 hrs/unit x $5/hr) $ 7,200 5,600
Extra Cost of Increasing Production (hiring cost) $ 5 — —
Extra Cost of Decreasing Production (layoff per unitcost) month Total Cost per — $ 7,200
Subcontracting cost per unit Average pay rate
Mar 800 Overtime pay rate Feb
$10 per unit
(= 2 $600) $ 5 per hourx($40 per day)6,800 $600 $ 7 per hour 7,000 (= 1 x $600) (above 8 hours per day)
$1,200
38
6,400
—
Apr 1,200 57 Labor-hours to produce a unit
9,600
$5,700 1.6 (= 19 x $300)
hours per unit —
15,300
Cost of increasing daily production rate (hiring $3,300 $300 per unit May 1,500 68 12,000 — (= 11 x $300) and training) Cost of decreasing daily production rate (layoffs) — June 1,100 55 8,800
$49,600 $9,000
15,300
$600 per unit $7,800
$9,600
(= 13 x $600)
16,600 $68,200
Table 13.3
53
Comparison of Three Plans
Cost Inventory carrying Regular labor Overtime labor
Hiring Layoffs Subcontracting Total cost
Plan 1 $ 9,250 49,600 0
0 0 0 $58,850
Plan 2 $ 0 $
Plan 3 0
37,696 0
0 0 0 $52,576
49,600 0
9,000 9,600 0 $68,200
Plan 2 is the lowest cost option
Table 13.5 54
Mathematical Approaches
? Useful for generating strategies
? Transportation Method of Linear Programming
? Produces an optimal plan
? Management Coefficients Model
? Model built around manager’s experience and performance
? Other Models
? Linear Decision Rule ? Simulation
55
Transportation Method
Sales Period Mar Apr May 800 1,000 750 700 50 150 100 per tire per tire per tire per tire 700 50 150 tires 700 50 130
Demand Capacity: Regular Overtime Subcontracting Beginning inventory Costs Regular time Overtime Subcontracting Carrying $40 $50 $70 $2
Table 13.6
56
Transportation Example
Important points
1. Carrying costs are $2/tire/month. If goods are made in one period and held over to the next, holding costs are incurred 2. Supply must equal demand, so a dummy column called “unused capacity” is added 3. Because back ordering is not viable in this example, cells that might be used to satisfy earlier demand are not available
57
Transportation Example
Important points
4. Quantities in each column designate the levels of inventory needed to meet demand requirements
5. In general, production should be allocated to the lowest cost cell available without exceeding unused capacity in the row or demand in the column
58
Transportation Example
Table 13.7
59
Management Coefficients Model
? Builds a model based on manager’s experience and performance ? A regression model is constructed to define the relationships between decision variables
? Objective is to remove inconsistencies in decision making
60
Other Models
Linear Decision Rule
? Minimizes costs using quadratic cost curves ? Operates over a particular time period
Simulation
? Uses a search procedure to try different combinations of variables ? Develops feasible but not necessarily optimal solutions
61
Summary of Aggregate Planning Methods
Techniques Graphical/charting methods Solution Approaches Trial and error Important Aspects Simple to understand and easy to use. Many solutions; one chosen may not be optimal. LP software available; permits sensitivity analysis and new constraints; linear functions may not be realistic Simple, easy to implement; tries to mimic manager’s decision process; uses regression
Transportation method of linear programming
Optimization
Management coefficients model
Heuristic
Table 13.8
62
Law Firm Example
(1) Category of Legal Business Trial work Legal research Corporate law Real estate law Criminal law Total hours Lawyers needed (2) Best Case (hours) 1,800 4,500 8,000 1,700 3,500 19,500 39 (3) Likely Case (hours) 1,500 4,000 7,000 1,500 3,000 17,000 34 (4) Worst Case (hours) 1,200 3,500 6,500 1,300 2,500 15,000 30 (5) Maximum Demand in People 3.6 9.0 16.0 3.4 7.0 (6) Number of Qualified Personnel 4 32 15 6 12
Table 13.9
63
Yield Management
Allocating resources to customers at prices that will maximize yield or revenue
1. Service or product can be sold in advance of consumption 2. Demand fluctuates 3. Capacity is relatively fixed 4. Demand can be segmented 5. Variable costs are low and fixed costs are high
64
Yield Management Example
Room sales
100
Demand Curve Potential customers exist who are willing to pay more than the $15 variable cost of the room
Passed-up contribution
50
Some customers who paid $150 were actually willing to pay more for the room
$ margin = (Price) x (50 rooms) = ($150 - $15) x (50) = $6,750 $15 Variable cost of room
Money left on the table $150 Price charged for room Price
Figure 13.5 65
Yield Management Example
Room sales
100
Demand Curve
Total $ margin = (1st price) x 30 rooms + (2nd price) x 30 rooms = ($100 - $15) x 30 + ($200 - $15) x 30 = $2,550 + $5,550 = $8,100
60
30
$15 Variable cost of room
$100 Price 1 for room
$200 Price 2 for room
Price
Figure 13.6 66
Yield Management Matrix
Price
Tend to be fixed Predictable Quadrant 1: Movies Stadiums/arenas Convention centers Hotel meeting space Quadrant 3: Restaurants Golf courses Internet service providers Tend to be variable Quadrant 2: Hotels Airlines Rental cars Cruise lines Quadrant 4: Continuing care hospitals
Duration of use
Unpredictable
Figure 13.7
67
Making Yield Management Work 1. Multiple pricing structures must be feasible and appear logical to the customer 2. Forecasts of the use and duration of use 3. Changes in demand
68
Aggregate Planning Example
ABC Co, a small manufacturing company (200 employees), produces umbrellas. The company, founded in 1991 produces the following three product lines: 1) the Executive Line, 2) the Durable Line and 3) the Compact line shown in the following figure.
Executive Line
Compact Line Durable Line
8
Units
Examples of Capacity Adjustment to Meet Demand
Demand
Time
1.
Producing at a constant rate and using inventory to absorb
fluctuations in demand Hiring and firing workers to match demand Maintaining resources for high demand levels
2. 3.
4.
5. 6. 7.
Increase or decrease working hours (overtime and undertime) Subcontracting work to other firms Using part-time workers Providing the service or product at a later time period (backordering)
70
Planning Strategies
?
Chase Strategies
?
PURE STRATEGIES
?
?
Match demand during the planning horizon by either Vary workforce or vary output rate
Level Strategies
?
?
Maintain a constant workforce level or constant output rate during the planning horizon Constant workforce or constant output rate
?
Mixed Strategies
?
Combined several strategies
71
Pure Strategy
Level Production
Demand
Chase Demand
Demand Production Units
Production
Units
Time
Time
What are pros / cons of these strategies?
72
TABLE 14.1
PLANNING STRATEGIES FOR AGGREGATE PLANS Possible Alternatives during Slack Season
Layoffs Layoffs, undertime, vacations No layoffs, building anticipation inventory, undertime, vacations Layoffs, building anticipation inventory, undertime, vacations
Strategy
1. Chase #1: vary workforce level to match demand 2. Chase #2: vary output rate to match demand 3. Level #1: constant workforce level
Possible Alternatives during Peak Season
Hiring Hiring, overtime, subcontracting No hiring, depleting anticipation inventory, overtime, subcontracting, backorders, stockouts Hiring, depleting anticipation inventory, overtime, subcontracting, backorders, stockouts
73
4. Level #2: constant output rate
Aggregate Planning Costs
? ? ?
?
?
Regular-Time Costs Overtime Costs Hiring and Layoff Costs Inventory Holding Costs Backorder and Stockout Costs
74
?
?
Aggregate Planning Methods: Intuitive Methods Intuitive methods use management intuition, experience, and rules-of-thumb, frequently accompanied by graphical and/or spreadsheet analysis.
? ?
Advantage:
?
Disadvantage:
?
easy to use and explain many solutions are possible, most of which are not optimal
75
Ex 1 Candy Company
Given the following costs and quarterly sales forecasts of a candy company, compare the two strategies: Strategy 1: Level production with constant workforce level Strategy 2: Chase production by varying workforce level
Quarter
Spring Summer Fall Winter
Sale Forecast (LB)
80,000 50,000 120,000 150,000
? ? ?
Hiring cost Firing cost Inventory carrying cost
Production rate per employee ? Beginning workforce
?
$100 per worker $500 per worker $0.50 per pound per quarter 1000 pounds per quarter 100 workers
76
Transportation Method
?
Alternatives
Quarter
Quarter 1
0
2
h
3
2h
4
3h
Unused Total Capacity Capacity
4h
Beginning inventory Regular time
I0
r r+h r+2h r+3h u
R1
c c+h c+2h c+3h 0
?
?
A method of LP Gather all cost info into one matrix Try to obtain the lowest cost alternative
1
Overtime s r+b s+h r s+2h r+h s+3h r+2h 0
O1 S1
u
Subcontract Regular time 2 Overtime
R2
c+b c c+h c+2h 0
O2
s+b s s+h s+2h 0
Subcontract Regular time 3 Overtime
S2
r+2b r+b r r+h u
R3
c+2b c+b c c+h 0
O3
s+2b r+3b s+b r+2b s r+b s+h r 0
Subcontract Regular time 4 Overtime
S3
u
R4
c+3b c+2b c+b c 0
O4
s+3b s+2b s+b s 0
Subcontract
77
S4
Requirements
D1
D2
D3
D4 + I4
U
Notations
It = inventory at the end of period t (I0 = beginning inventory) h = holding cost per unit per period, r = regular production cost per unit, o = overtime cost per unit, u = undertime cost per unit s = subcontracting cost per unit, b = backordering cost per unit per period Rt = regular-time capacity in period t Ot = overtime capacity in period t St = subcontracting capacity in period t Dt = forecasted demand for period t U = total unused capacities
78
Tableau Method
?
Step 1: Put all capacities from the total capacity column into the unused capacity column. Next, put unit costs in each of the small boxes Step 2: In column 1 (period 1), allocate as much production as you can to the cell with the lowest cost but do not exceed the unused capacity in that row or the demand in that column. Step 3: Subtract your allocation from the unused capacity for the row. This quantity must never be negative.
?
?
79
Tableau Method
?
(Cont’d)
Step 4: If there is still some demand left, repeat step 2, allocating as much production as possible to the cell with the next-to-lowest cost. Repeat until the demand is satisfied. Step 5: Repeat steps 2 through 4 for periods 2 and beyond. Take each column separately before proceeding to the next. Be sure to check all cells with unused capacity for the cell with the lowest cost in a column.
?
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Ex 2: Transportation Method
Given the following costs and quarterly sales forecasts, use the transportation method to design a production plan. What is the total cost of the plan?
Quarter 1 2 3 4
Sale Forecast (unit) 50,000 150,000 200,000 52,000
Inventory carrying cost = $3 per unit per quarter Production/worker = 1000 units/quarter Regular workforce = 50 workers Overtime capacity = 50,000 units Subcontracting capacity = 40,000 units Regular production cost = $50/unit Overtime production cost = $75/unit Subcontracting cost = $85/unit
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Linear Programming Model (LP)
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Pure/Mixed Strategy: not guarantee optimal solution LP: can get optimal solution LP: Excel, LINGO, CPLEX, … LP Formulation**
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Objective function Constraints
Ex 2: Formulate LP model for Ex 1 Candy Company and Ex 2
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Production Plan (manufacturing aggregate plan): A managerial statement of the period-by-period (timephased) production rates, work-force levels, and inventory investment, given customer requirements and capacity limitations. Staffing Plan (service aggregate plan): A managerial statement of the period-by-period staff sizes and labour-related capacities, given customer requirements and capacity limitations.
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Objectives of Aggregate Planning Objective of aggregate planning frequently is to minimize total cost over the planning horizon. Other objectives should be considered: maximize customer service minimize inventory investment minimize changes in workforce levels minimize changes in production rates maximize utilization of plant and equipment
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Aggregate Planning Strategies Active strategy: Attempts to handle fluctuations in demand by focusing on demand management Use pricing strategies and/or advertising and promotion Develop counter-cyclical products Request customers to backorder or advance-order Do not meet demand
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Passive strategy (reactive strategy): Attempts to handle fluctuations in demand by focusing on supply and capacity management Vary size work force size by hiring or layoffs Vary utilization of labour and equipment through overtime or idle time Build or draw from inventory Subcontract production Negotiate cooperative arrangements with other firms Allow backlogs, back orders, and/or stockouts Mixed strategy: Combines elements of both an active strategy and a passive (reactive) strategy Firms will usually use some combination of the two
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Basic Approaches
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Chase approach
capacities (workforce levels, production schedules, output rates, etc.) are adjusted to match demand requirements over the planning horizon. Advantages: anticipation inventory is not required, and investment in inventory is low labour utilization is kept high Disadvantages: expense of adjusting output rates and/or workforce levels alienation of workforce Capacities (workforce levels, production schedules, output rates, etc.) are kept constant over the planning horizon. Advantages: stable output rates and workforce levels Disadvantages: greater inventory investment is required increased overtime and idle time resource utilizations vary over time
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Level Approach
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