Chapter 13 Capacity and Aggregate Planning

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

Adjusting Capacity to Meet Demand 1.Producing at a constant rate and using inventory to absorb fluctuations in demand (level production) 2.Hiring and firing workers to match demand (chase demand) 3.Maintaining resources for high demand levels 4.Increase or decrease working hours (overtime and undertime) 5.Subcontracting work to other firms 6.Using part-time workers 7.Providing the service or product at a later time period (backordering)

Strategy Details Level production - produce at constant rate & use inventory as needed to meet demand Level production - produce at constant rate & use inventory as needed to meet demand Chase demand - change workforce levels so that production matches demand Chase demand - change workforce levels so that production matches demand Maintaining resources for high demand levels - ensures high levels of customer service Maintaining resources for high demand levels - ensures high levels of customer service

Strategy Details Overtime & undertime - common when demand fluctuations are not extreme Overtime & undertime - common when demand fluctuations are not extreme Subcontracting - useful if supplier meets quality & time requirements Subcontracting - useful if supplier meets quality & time requirements Part-time workers - feasible for unskilled jobs or if labor pool exists Part-time workers - feasible for unskilled jobs or if labor pool exists Backordering - only works if customer is willing to wait for product/services Backordering - only works if customer is willing to wait for product/services

Level Production Production Demand Units Time

Chase Demand ProductionDemandUnits Time

APP Using Pure Strategies Hiring cost= $100 per worker Firing cost= $500 per worker Inventory carrying cost= $0.50 pound per quarter Production per employee= 1,000 pounds per quarter Beginning work force= 100 workers QUARTERSALES FORECAST (LB) Spring80,000 Summer50,000 Fall120,000 Winter150,000

APP Using Pure Strategies Hiring cost= $100 per worker Firing cost= $500 per worker Inventory carrying cost= $0.50 pound per quarter Production per employee= 1,000 pounds per quarter Beginning work force= 100 workers QUARTERSALES FORECAST (LB) Spring80,000 Summer50,000 Fall120,000 Winter150,000 Level production = 100,000 pounds (50, , , ,000) 4

Level Production Strategy Spring80,000100,00020,000 Summer50,000100,00070,000 Fall120,000100,00050,000 Winter150,000100, ,000140,000 Cost = 140,000 pounds x 0.50 per pound = $70,000 SALESPRODUCTION QUARTERFORECASTPLANINVENTORY

Spring80,00080, Summer50,00050, Fall120,000120, Winter150,000150, SALESPRODUCTIONWORKERSWORKERSWORKERS SALESPRODUCTIONWORKERSWORKERSWORKERS QUARTERFORECASTPLANNEEDEDHIREDFIRED Cost= (100 workers hired x $100) + (50 workers fired x $500) = $10, ,000 = $35,000 Chase Demand Strategy

APP by the Transportation Method 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 inventory300 units EXPECTEDREGULAROVERTIMESUBCONTRACT QUARTERDEMANDCAPACITYCAPACITYCAPACITY

The Transportation Tableau Unused PERIOD OF PRODUCTION1234CapacityCapacity Beginning0369 Inventory300 Regular 1000 Overtime 100 Subcontract500 Regular 1200 Overtime 150 Subcontract 500 Regular 1300 Overtime 200 Subcontract 500 Regular 1300 Overtime 200 Subcontract 500 Demand PERIOD OF USE

The Transportation Tableau Unused PERIOD OF PRODUCTION1234CapacityCapacity Beginning0369 Inventory300———300 Regular —1000 Overtime Subcontract Regular1200——1200 Overtime Subcontract Regular1300—1300 Overtime200—200 Subcontract Regular Overtime Subcontract Demand PERIOD OF USE

APP by Linear Programming where H t =# hired for period t F t =# fired for period t I t =inventory at end of period t P t =units produced in period t W t =workforce size for period t 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) DemandI 1 + P 2 - I 2 = 50,000(2) constraintsI 2 + P 3 - I 3 = 120,000(3) I 3 + P 4 - I 4 = 150,000(4) Production1000 W 1 = P 1 (5) constraints1000 W 2 = P 2 (6) 1000 W 3 = P 3 (7) 1000 W 4 = P 4 (8) H 1 - F 1 = W 1 (9) Work forceW 1 + H 2 - F 2 = W 2 (10) Work forceW 1 + H 2 - F 2 = W 2 (10) constraintsW 2 + H 3 - F 3 = W 3 (11) constraintsW 2 + H 3 - F 3 = W 3 (11) W 3 + H 4 - F 4 = W 4 (12) Decision Variables