1. Aggregate Production Planning
(APP)

2. Aggregate Production Planning (APP)
Matches market demand to company resources
Plans production 6 months to 12 months in advance
Expresses demand, resources, and capacity in general terms
Develops a strategy for economically meeting demand
Establishes a companywide game plan for allocating resources

3. Inputs and Outputs to Aggregate Production Planning
Capacity
Constraints
Strategic
Objectives
Company
Policies
Demand
Forecasts
Financial
Constraints
Aggregate
Production
Planning
Size of
Workforce
Units or dollars
subcontracted,
backordered, or
lost
Production
per month
(in units or $)
Inventory
Levels

4. Strategies for Meeting Demand
1. Use inventory to absorb fluctuations in demand
(level production)
2. Hire and fire workers to match demand (chase demand)
3. Maintain resources for high demand levels
4. Increase or decrease working hours (over & undertime)
5. Subcontract work to other firms
6. Use part-time workers
7. Provide the service or product at a later time period (backordering)

5. Strategy Details
Level production - produce at constant rate & use inventory as needed to meet demand
Chase demand - change workforce levels so that production matches demand
Maintaining resources for high demand levels - ensures high levels of customer service
Overtime & undertime - common when demand fluctuations are not extreme

6. Strategy Details
Subcontracting - useful if supplier meets quality & time requirements
Part-time workers - feasible for unskilled jobs or if labor pool exists
Backordering - only works if customer is willing to wait for product/services

7. Level Production
Demand
Production
Units
Time

8. Chase Demand
Demand
Units
Production
Time

9. APP Example
The Bavarian Candy Company (BCC) makes a variety of candies in three factories worldwide. Its line of chocolate candies exhibits a highly seasonal pattern with peaks in winter months and valleys during the summer months. Given the costs and quarterly sales forecasts, determine whether a level production or chase demand production strategy would be more economically meet the demand for chocolate candies.

10. APP Using Pure Strategies
Quarter Sales Forecast (kg)
Spring 80,000
Summer 50,000
Fall 120,000
Winter 150,000
Hiring cost = $100 per worker
Firing cost = $500 per worker
Inventory carrying cost = $0.50 per kilogram per quarter
Production per employee = 1,000 kilograms per quarter
Beginning work force = 100 workers

11. Level Production Strategy
Sales Production
Quarter Forecast Plan Inventory
Spring 80, ,000 20,000
Summer 50, ,000 70,000
Fall 120, ,000 50,000
Winter 150, ,000 0
400, ,000
Cost = 140,000 kilograms x $0.50 per kilogram = $70,000

12. Chase Demand Strategy Sales Production Workers Workers Workers
Quarter Forecast Plan Needed Hired Fired
Spring 80,000 80,
Summer 50,000 50,
Fall 120, ,
Winter 150, ,
100 50
Cost = (100 workers hired x $100) + (50 workers fired x $500)
= $10, ,000 = $35,000

13. LP Formulation Define Ht = # hired for period t Ft = # fired for period t It = inventory at end of period t Pt = Production in period t Wt = Workforce in period t
Min Z = $100 (H1 + H2 + H3 + H4) + $500 (F1 + F2 + F3 + F4) + $0.50 (I1 + I2 + I3 + I4)

14. Subject to P1 - I1 = 80,000 (1) Demand
Min Z = $100 (H1 + H2 + H3 + H4) + $500 (F1 + F2 + F3 + F4)+ $0.50 (I1 + I2 + I3 + I4)
Subject to
P1 - I1 = 80,000 (1) Demand
I1 + P2 - I2 = 50,000 (2) constraints
I2 + P3 - I3 = 120,000 (3)
I3 + P4 - I4 = 150,000 (4)

15. P2 - 1,000 W2 = 0 (6) constraints P3 - 1,000 W3 = 0 (7)
Min Z = $100 (H1 + H2 + H3 + H4) + $500 (F1 + F2 + F3 + F4)+ $0.50 (I1 + I2 + I3 + I4) Subject to P1 - I1 = 80,000 (1) Demand I1 + P2 - I2 = 50,000 (2) constraints I2 + P3 - I3 = 120,000 (3) I3 + P4 - I4 = 150,000 (4)
P1 - 1,000 W1 = 0 (5) Production
P2 - 1,000 W2 = 0 (6) constraints
P3 - 1,000 W3 = 0 (7)
P4 - 1,000 W4 = 0 (8)

16. W2 - W1 - H2 + F2 = 0 (10) constraints W3 - W2 - H3 + F3 = 0 (11)
Min Z = $100 (H1 + H2 + H3 + H4) + $500 (F1 + F2 + F3 + F4)+ $0.50 (I1 + I2 + I3 + I4) Subject to P1 - I1 = 80,000 (1) Demand I1 + P2 - I2 = 50,000 (2) constraints I2 + P3 - I3 = 120,000 (3) I3 + P4 - I4 = 150,000 (4) P1 - 1,000 W1 = 0 (5) Production P2 - 1,000 W2 = 0 (6) constraints P3 - 1,000 W3 = 0 (7) P4 - 1,000 W4 = 0 (8)
W1 - H1 + F1 = 100 (9) Work force
W2 - W1 - H2 + F2 = 0 (10) constraints
W3 - W2 - H3 + F3 = 0 (11)
W4 - W3 - H4 + F4 = 0 (12)

17. Min Z = $100 (H1 + H2 + H3 + H4) + $500 (F1 + F2 + F3 + F4)+ $0
Min Z = $100 (H1 + H2 + H3 + H4) + $500 (F1 + F2 + F3 + F4)+ $0.50 (I1 + I2 + I3 + I4)
Subject to
P1 - I1 = 80,000 (1) Demand
I1 + P2 - I2 = 50,000 (2) constraints
I2 + P3 - I3 = 120,000 (3)
I3 + P4 - I4 = 150,000 (4)
P1 - 1,000 W1 = 0 (5) Production
P2 - 1,000 W2 = 0 (6) constraints
P3 - 1,000 W3 = 0 (7)
P4 - 1,000 W4 = 0 (8)
W1 - H1 + F1 = 100 (9) Work force
W2 - W1 - H2 + F2 = 0 (10) constraints
W3 - W2 - H3 + F3 = 0 (11)
W4 - W3 - H4 + F4 = 0 (12)

18. LP Solution:
Z = $32,000
H1= 0, F1= 20, I1= 0, P1=80000;
H2= 0, F2= 0, I2= 30000, P2=80000;
H3= 10, F3= 0, I3= 0, P3=90000;
H4= 60, F4= 0, I4= 0, P4=150000;

19. Summary: APP By Linear Programming
Min Z = $100 (H1 + H2 + H3 + H4) + $500 (F1 + F2 + F3 + F4)+ $0.50 (I1 + I2 + I3 + I4)
Subject to
P1 - I1 = 80,000 (1) Demand
I1 + P2 - I2 = 50,000 (2) constraints
I2 + P3 - I3 = 120,000 (3)
I3 + P4 - I4 = 150,000 (4)
P1 - 1,000 W1 = 0 (5) Production
P2 - 1,000 W2 = 0 (6) constraints
P3 - 1,000 W3 = 0 (7)
P4 - 1,000 W4 = 0 (8)
W1 - H1 + F1 = 100 (9) Work force
W2 - W1 - H2 + F2 = 0 (10) constraints
W3 - W2 - H3 + F3 = 0 (11)
W4 - W3 - H4 + F4 = 0 (12)
where
Ht = # hired for period t
Ft = # fired for period t
It = inventory at end
of period t
LP Solution:
Z = $32,000
H1= 0, F1= 20, I1= 0, P1=80000;
H2= 0, F2= 0, I2= 30000, P2=80000;
H3= 10, F3= 0, I3= 0, P3=90000;
H4= 60, F4= 0, I4= 0, P4=150000;

20. APP By The Transportation Method
Expected Regular Overtime Subcontract
Quarter Demand Capacity Capacity Capacity
Regular production cost per unit = $20
Overtime production cost per unit = $25
Subcontracting cost per unit = $28
Inventory carrying cost per unit per period = $3
Beginning inventory = 300 units

25. Production Plan Strategy Variable
Period Demand Reg Prodn Overtime Sub End Inv
Total

26. Regular Production Cost = (4,800 * $20)=$96,000
Overtime Production Cost = (650 * $25)= $16,250
Subcontracting Cost = (1,250 * $28) = $35,000
Inventory Cost = (2,100 * $3) = $ 6,300
The Total Cost of the Plan = $153,550

27. Linear Programming Formulation
Let:
Dt = units required in period t, (t = 1,…,T)
m = number of sources of product in any period
Pit = capacity, in units of product, of source i in period t, (i = 1,…,m)
Xit = planned quantity to be obtained from source i in period t
cit = variable cost per unit from source i in period t
ht = cost to store a unit from period t to period t+1
It = inventory level at the end of period t, after satisfying the requirement in period t

29. Optimal Value (Z) = $153,550 XR1 XR2 XR3 XR4 XO1 XO2 XO3 XO4 XS1 XS2
= 1000
= 1200
= 1300
= 0
= 150
= 200
= 350
= 500

30. Strategies for Managing Demand
Shift demand into other periods
incentives, sales promotions, advertising campaigns
Offer product or services with counter-cyclical demand patterns
create demand for idle resources

31. Aggregate Planning for Services
1. Most services can’t be inventoried
2. Demand for services is difficult to predict
3. Capacity is also difficult to predict
4. Service capacity must be provided at the appropriate place and time
5. Labor is usually the most constraining resource for services

32. Services Example
The central terminal at the Deutsche Cargo receives airfreight from aircraft arriving from all over Europe and redistributes it to aircraft for shipment to all European destinations. The company guarantees overnight shipment of all parcels, so enough personnel must be available to process all cargo as it arrives. The company now has 24 employees working in the terminal. The forecasted demand for warehouse workers for the next 7 months is 24, 26, 30, 28, 28, 24, and 24. It costs $2,000 to hire and $3,500 to lay off each worker. If overtime is used to supply labor beyond the present work force, it will cost the equivalent of $2,600 more for each additional worker. Should the company use a level capacity with overtime or a matching demand plan for the next six month?
Linear decision rule (LDR)
payroll, staffing, over/undertime, inventory costs
Search decision rule (SDR)
find minimum cost combination of labor levels & production rates
Management coefficients model
uses regression analysis to improve consistency of planning 20

33. The Level Capacity with Overtime Plan

34. The Matching Demand Plan

35. The cost of the Level Capacity with Overtime = $ 41,600
The total cost of the Matching Demand plan = $12,000 + $21,000 = $33,000
Hence, since the cost of matching demand plan is less than the level capacity plan with overtime and would be the preferred plan

36. Aggregate Planning Example 1
A manufacturer produces a line of household products fabricated from sheet metal. To illustrate his production planning problem, suppose that he makes only four products and that his production system consists of five production centers: stamping, drilling, assembly, finishing (painting and printing), and packaging. For a given month, he must decide how much of each product to manufacture, and to aid in this decision, he has assembled the data shown in Tables 1 and 2. Furthermore, he knows that only 2000 square feet of the type of sheet metal used for products 2 and 4 will be available during the month. Product 2 requires 2.0 square feet per unit and product 4 uses 1.2 square feet per unit.

37. TABLE 1 Production Data for Example 1
PRODUCTION RATES IN HOURS PER UNIT
Production
DEPARTMENT PRODUCT 1 PRODUCT 2 PRODUCT 3 PRODUCT Hours
Available
Stamping
Drilling
Assembly
Finishing
Packaging

38. TABLE 2 Product Data for Example 1
NET SELLING VARIABLE SALES POTENTIAL
PRODUCT PRICE/UNIT COST/UNIT MINIMUM MAXIMUM
$ $

39. A Linear Program of Example 1:
Define xi be the number of units of Product i to be produced per month, i = 1, 2, 3, and 4.

40. Solution of Example 1 using LINGO Software Package (get a free copy of this package from the web site at
Objective value:
Variable Value Reduced Cost X X X X

41. Row Slack or Surplus Dual Price
PROFIT
STAMPING
DRILLING
ASSEMBLY
FINISHING
PACKAGING
SHEETMETAL
MINPROD
MAXPROD
MAXPROD
MINPROD
MAXPROD
MINPROD
MAXPROD

42. Ranges in which the basis is unchanged:
Objective Coefficient Ranges
Current Allowable Allowable
Variable Coefficient Increase Decrease
X INFINITY INFINITY
X INFINITY INFINITY
X INFINITY INFINITY
X INFINITY INFINITY

43. Righthand Side Ranges:
Row Current Allowable Allowable
RHS Increase Decrease
STAMPING INFINITY
DRILLING INFINITY
ASSEMBLY INFINITY
FINISHING INFINITY
PACKAGING INFINITY
SHEETMETAL INFINITY
MINPROD INFINITY
MAXPROD INFINITY
MAXPROD INFINITY
MINPROD INFINITY
MAXPROD INFINITY
MINPROD INFINITY
MAXPROD INFINITY