Input Data (Demand) Input Data (Costs etc.)
Month Demand Item Cost
January 1,000 Materials cost/unit 20.0
February 1,100 Inventory holding cost/unit/month 3.0
March 1,000 Marginal cost of stockout/unit/month
April 1,200 Hiring and training cost/worker 800.0
May 1,500 Layoff cost/worker 1,200.0
June 1,600 Labor hours required/unit 0.1667
July 1,600 Regular time cost/hour 20.0
August 900 Over time cost/hour 30.0
September 1,100 Marginal subcontracting cost/unit
October 800
November 1,400 Initial Workforce size 1250
December 1,700 Maximum overtime per worker per month 20
Starting inventory (‘000s) 50
Ending inventory (‘000s) 50
Temporary Pool 50
Aggregate Plan Decision Variables (demand, inventory, production in ’000s) Constraints
Ht Lt Tt Wt Ot It St Ct Pt
Period # Hired # Laid off # Temp # Workforce Overtime Inventory Stockout Subcontract Production Demand Inventory Overtime Production Workforce OT Production
0 0 0 1,250 0 50 0 0 0
1 – – – 1,250 – 0.0 0 0.0 950 1,000 0 25000 250000 0 0
2– – – 1,250 – 84.0 0 0.0 1,184 1,100 0 25000 16000 0 0
3 – – – 1,250 – 284.0 0 0.0 1,200 1,000 0 25000 0 0 0
450 – 50 1,250 26,000 488.0 0 0.0 1,404 1,200 0 0 0 0 156
5 – – 50 1,250 26,000 392.0 0 0.0 1,404 1,500 0 0 0 0 156
6– – 50 1,250 26,000 196.0 0 0.0 1,404 1,600 0 0 0 0 156
7 – – 50 1,250 26,000 0.0 0 0.0 1,404 1,600 0 0 0 0 156
8– 50 – 1,250 – 0.0 0 0.0 900 900 025000 300000 0 0
9 – – – 1,250 – 0.0 0 0.0 1,100 1,100 0 25000 100000 0 0
10 – – – 1,250 – 400.0 0 0.0 1,200 800 025000 0 0 0
11 50 – 50 1,250 16,333 346.0 0 0.0 1,346 1,400 0 9666.666667 0 0 98
12 – – 50 1,250 26,000 50.0 0 0.0 1,404 1,700 0 0 0 0 156
50
Costs
Period Hiring Lay off Temp Regular Time Overtime Inventory Stockout Subcontract Material
1 0 0 0 4,000,000 0 0 0 0 19,000,000
20 0 0 4,000,000 0 252,000 0 0 23,680,000
3 0 0 0 4,000,000 0 852,000 0 0 24,000,000
440,000 0 160,000 4,000,000 780,000 1,464,000 0 0 28,080,000
5 0 0 160,000 4,000,000 780,000 1,176,000 0 0 28,080,000
60 0 160,000 4,000,000 780,000 588,000 0 0 28,080,000
7 0 0 160,000 4,000,000 780,000 0 0 0 28,080,000
80 60,000 0 4,000,000 0 0 0 0 18,000,000
9 0 0 0 4,000,000 0 0 0 0 22,000,000
10 0 0 0 4,000,000 0 1,200,000 0 0 24,000,000
11 40,000 0 160,000 4,000,000 490,000 1,038,000 0 0 26,920,000
12 0 0 160,000 4,000,000 780,000 150,000 0 0 28,080,000
298,000,000
Total Cost =
358,210,000$
0.0
200.0
800.0
1000.0
1200.0
1400.0
1600.0
1800.0
1 2 3 4 5 6 7 8 9 10 11 12
Month
Production Plan for Year
Inventory
Total Production
Demand
Overtime Production