Aggregate planning involves determining resource capacity over an intermediate time horizon to meet product demand. It aims to establish a company-wide plan for allocating resources through various demand management strategies, including adjusting capacity, production levels, workforce, and inventory. Quantitative techniques like linear programming can help optimize solutions by minimizing costs associated with hiring, firing, production and inventory carrying under demand constraints.

2. Aggregate Planning Process

5. Level Production Demand Units Time Production

6. Chase Demand Demand Units Time Production

9. Pure Strategies Hiring cost = $100 per worker Firing cost = $500 per worker Regular production cost per pound = $2.00 Inventory carrying cost = $0.50 pound per quarter Production per employee = 1,000 pounds per quarter Beginning work force = 100 workers Example: QUARTER SALES FORECAST (LB) Spring 80,000 Summer 50,000 Fall 120,000 Winter 150,000

10. Level Production Strategy Level production = 100,000 pounds (50,000 + 120,000 + 150,000 + 80,000) 4 Spring 80,000 100,000 20,000 Summer 50,000 100,000 70,000 Fall 120,000 100,000 50,000 Winter 150,000 100,000 0 400,000 140,000 Cost of Level Production Strategy (400,000 X $2.00) + (140,00 X $.50) = $870,000 SALES PRODUCTION QUARTER FORECAST PLAN INVENTORY

11. Chase Demand Strategy Spring 80,000 80,000 80 0 20 Summer 50,000 50,000 50 0 30 Fall 120,000 120,000 120 70 0 Winter 150,000 150,000 150 30 0 100 50 SALES PRODUCTION WORKERS WORKERS WORKERS QUARTER FORECAST PLAN NEEDED HIRED FIRED Cost of Chase Demand Strategy (400,000 X $2.00) + (100 x $100) + (50 x $500) = $835,000

14. LP MODEL Minimize Z = $100 ( H 1 + H 2 + H 3 + H 4 ) + $500 ( F 1 + F 2 + F 3 + F 4 ) + $0.50 ( I 1 + I 2 + I 3 + I 4 ) Subject to P 1 - I 1 = 80,000 (1) Demand I 1 + P 2 - I 2 = 50,000 (2) constraints I 2 + P 3 - I 3 = 120,000 (3) I 3 + P 4 - I 4 = 150,000 (4) Production 1000 W 1 = P 1 (5) constraints 1000 W 2 = P 2 (6) 1000 W 3 = P 3 (7) 1000 W 4 = P 4 (8) 100 + H 1 - F 1 = W 1 (9) Work force W 1 + H 2 - F 2 = W 2 (10) constraints W 2 + H 3 - F 3 = W 3 (11) W 3 + H 4 - F 4 = W 4 (12)

15. Transportation Method 1 900 1000 100 500 2 1500 1200 150 500 3 1600 1300 200 500 4 3000 1300 200 500 Regular production cost per unit $20 Overtime production cost per unit $25 Subcontracting cost per unit $28 Inventory holding cost per unit per period $3 Beginning inventory 300 units EXPECTED REGULAR OVERTIME SUBCONTRACT QUARTER DEMAND CAPACITY CAPACITY CAPACITY

16. Transportation Tableau Unused PERIOD OF PRODUCTION 1 2 3 4 Capacity Capacity Beginning 0 3 6 9 Inventory 300 — — — 300 Regular 600 300 100 — 1000 Overtime 100 100 Subcontract 500 Regular 1200 — — 1200 Overtime 150 150 Subcontract 250 250 500 Regular 1300 — 1300 Overtime 200 — 200 Subcontract 500 500 Regular 1300 1300 Overtime 200 200 Subcontract 500 500 Demand 900 1500 1600 3000 250 1 2 3 4 PERIOD OF USE 20 23 26 29 25 28 31 34 28 31 34 37 20 23 26 25 28 31 28 31 34 20 23 25 28 28 31 20 25 28

17. Burruss’ Production Plan 1 900 1000 100 0 500 2 1500 1200 150 250 600 3 1600 1300 200 500 1000 4 3000 1300 200 500 0 Total 7000 4800 650 1250 2100 REGULAR SUB- ENDING PERIOD DEMAND PRODUCTION OVERTIME CONTRACT INVENTORY

19. Hierarchical Nature of Planning Items Product lines or families Individual products Components Manufacturing operations Resource Level Plants Individual machines Critical work centers Production Planning Capacity Planning Resource requirements plan Rough-cut capacity plan Capacity requirements plan Input/ output control Aggregate production plan Master production schedule Material requirements plan Shop floor schedule All work centers

21. ATP: Example

22. ATP: Example (cont.)

23. ATP: Example (cont.) ATP in April = (10+100) – 70 = 40 ATP in May = 100 – 110 = -10 ATP in June = 100 – 50 = 50 Take excess units from April = 30 = 0

24. Rule Based ATP Product Request Is the product available at this location? Is an alternative product available at an alternate location? Is an alternative product available at this location? Is this product available at a different location? Available-to-promise Allocate inventory Capable-to-promise date Is the customer willing to wait for the product? Available-to-promise Allocate inventory Revise master schedule Trigger production Lose sale Yes No Yes No Yes No Yes No Yes No

26. Yield Management

27. Yield Management (cont.)

28. Yield Management: Example Hotel should be overbooked by two rooms NO-SHOWS PROBABILITY P ( N < X ) 0 .15 .00 1 .25 .15 2 .30 .40 3 .30 .70 Optimal probability of no-shows P( n < x )  = = .517 C u C u + C o 75 75 + 70 .517