Input Data (Costs etc.)
Item Cost (‘000s)
Material cost/unit 500
Inventory holding cost/unit/month 50
Marginal cost of stockout/unit/month 100
Hiring and training cost/worker 400
Layoff cost/worker 800
Team labor hours required/ thousand units 8
Regular time cost/hour 4
Over time cost/hour 6
Maximum overtime per worker per month 10
Team size 10
Aggregate Plan Decision Variables (demand, inventory, production in ‘000s) Constraints
HtLtWtOtItStPt
Period # Teams Hired # Teams Laid off # Teams Overtime Inventory Stockout Production Demand Inventory Overtime Production Workforce
0 0 0 667 0 1,000 0
1 0 0 667 0.0 4592.5 0.0 11593 8,000 0 6670 1747.5 0
20 0 667 0.0 7932.5 0.0 13340 10,000 0 6670 0 0
3 0 0 667 0.0 10272.5 0.0 13340 11,000 0 6670 0 0
40 0 667 0.0 12612.5 0.0 13340 11,000 0 6670 0 0
5 0 0 667 0.0 14952.5 0.0 13340 11,000 0 6670 0 0
60 0 667 0.0 16292.5 0.0 13340 12,000 0 6670 0 0
7 0 0 667 0.0 16632.5 0.0 13340 13,000 0 6670 0 0
80 0 667 0.0 15972.5 0.0 13340 14,000 0 6670 0 0
9 0 0 667 0.0 14312.5 0.0 13340 15,000 0 6670 0 0
10 0 0 667 0.0 10652.5 0.0 13340 17,000 0 6670 0 0
11 0 0 667 6670.0 5826.3 0.0 14174 19,000 0 0 0 0
12 0 0 667 6670.0 1000.0 0.0 14174 19,000 0 0 0 0
160,000
Costs
Period Hiring Lay off Regular Time Overtime Inventory Stockout Material
1 0 0 4,268,800 0 229,625 0 5,796,250
20 0 4,268,800 0 396,625 0 6,670,000
3 0 0 4,268,800 0 513,625 0 6,670,000
40 0 4,268,800 0 630,625 0 6,670,000
5 0 0 4,268,800 0 747,625 0 6,670,000
60 0 4,268,800 0 814,625 0 6,670,000
7 0 0 4,268,800 0 831,625 0 6,670,000
80 0 4,268,800 0 798,625 0 6,670,000
9 0 0 4,268,800 0 715,625 0 6,670,000
10 0 0 4,268,800 0 532,625 0 6,670,000
11 0 0 4,268,800 400,200 291,313 0 7,086,875
12 0 0 4,268,800 400,200 50,000 0 7,086,875
Total 0 0 51,225,600 800,400 6,552,563 0 80,000,000
Total Cost =
138,578,563
The cost data is provided on worksheet Data. Use Data | Solver to obtain the optimal production plan.
This is the optimal production plan when hring/firing is not allowed.
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Inventory
Production
Demand
Aggregate Plan Decision Variables (demand, inventory, production in ‘000s) Constraints
HtLtWtOtItStPt
Period # Teams Hired # Teams Laid off # Teams Overtime Inventory Stockout Production Demand Inventory Overtime Production Workforce
0 0 0 667 0 1,000 0
1 0 167 500 0.0 3000.0 0.0 10000 8,000 0 5000 0 0
20 0 500 0.0 3000.0 0.0 10000 10,000 0 5000 0 0
3 0 0 500 0.0 2000.0 0.0 10000 11,000 0 5000 0 0
40 0 500 0.0 1000.0 0.0 10000 11,000 0 5000 0 0
5 0 0 500 0.0 0.0 0.0 10000 11,000 0 5000 0 0
6100 0600 0.0 0.0 0.0 12000 12,000 0 6000 0 0
7218 0818 0.0 3360.0 0.0 16360 13,000 0 8180 0 0
80 0 818 0.0 5720.0 0.0 16360 14,000 0 8180 0 0
9 0 0 818 0.0 7080.0 0.0 16360 15,000 0 8180 0 0
10 0 0 818 8030.0 7443.7 0.0 17364 17,000 0 150 0 0
11 0 0 818 8180.0 5826.3 0.0 17383 19,000 0 0 0 0
12 0151 667 6670.0 1000.0 0.0 14174 19,000 0 0 0 0
160,000
Costs
Period Hiring Lay off Regular Time Overtime Inventory Stockout Material
1 0 1,336,000 3,200,000 0 150,000 0 5,000,000
20 0 3,200,000 0 150,000 0 5,000,000
3 0 0 3,200,000 0 100,000 0 5,000,000
40 0 3,200,000 0 50,000 0 5,000,000
5 0 0 3,200,000 0 0 0 5,000,000
6400,000 0 3,840,000 0 0 0 6,000,000
7 872,000 0 5,235,200 0 168,000 0 8,180,000
80 0 5,235,200 0 286,000 0 8,180,000
9 0 0 5,235,200 0 354,000 0 8,180,000
10 0 0 5,235,200 481,800 372,187 0 8,681,875
11 0 0 5,235,200 490,800 291,313 0 8,691,250
12 0 1,208,000 4,268,800 400,200 50,000 0 7,086,875
Total 1,272,000 2,544,000 50,284,800 1,372,800 1,971,500 0 80,000,000
Total Cost =
137,445,100
The cost data is provided on worksheet Data. Use Data | Solver to obtain the optimal production plan.
The production plan is charted on the worksheet Plan Chart – Q2. This is the optimal production plan when hiring/firing is allowed.
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Inventory
Production
Demand