Input Data (Costs etc.)
Item Cost
Material cost/unit 20,000$
Inventory holding cost/unit/month 300$
Marginal cost of stockout/unit/month 2,000$
Hiring and training cost/worker 3,000$
Layoff cost/worker 5,000$
Labor hours required/unit 100
Regular time cost/hour 20$
Over time cost/hour 30$
Maximum overtime per worker per month 20
Aggregate Plan Decision Variables (demand, inventory, production in ‘000s) Constraints
HtLtWtOtItStPt
Period # Hired # Laid off # Workforce Overtime Inventory Stockout Production Demand Inventory Overtime Production Workforce
0 0 0 244 0250 0
1236 0480 400.0 422.0 0.0 772 600 09200 0 0
20 0 480 9600.0 436.0 0.0 864 850 0 0 0 0
3 0 0 480 9600.0 0.0 0.0 864 1,300 0 0 0 0
40 0 480 3160.0 0.0 0.4 800 800 06440 0 0
5 0 136 344 0.0 0.0 0.0 550 550 06880 0 0
60265 79 0.0 26.4 0.0 126 100 01580 0 0
7 0 0 79 0.0 52.8 0.0 126 100 01580 0 0
80 0 79 0.0 79.2 0.0 126 100 01580 0 0
9 0 0 79 0.0 105.6 0.0 126 100 01580 0 0
10 0 0 79 0.0 132.0 0.0 126 100 01580 0 0
11 0 0 79 0.0 158.4 0.0 126 100 01580 0 0
12 165 0244 120.0 250.0 0.0 392 300 04760 0 0
Costs
Period Hiring Lay off Regular Time Overtime Inventory Stockout Material
1 708,000 0 1,536,000 12,000 126,600 0 15,440,000
20 0 1,536,000 288,000 130,800 0 17,280,000
3 0 0 1,536,000 288,000 0 0 17,280,000
40 0 1,536,000 94,800 0 800 15,992,000
5 0 680,000 1,100,800 0 0 0 11,008,000
60 1,325,000 252,800 0 7,920 0 2,528,000
7 0 0 252,800 0 15,840 0 2,528,000
80 0 252,800 0 23,760 0 2,528,000
9 0 0 252,800 0 31,680 0 2,528,000
10 0 0 252,800 0 39,600 0 2,528,000
11 0 0 252,800 0 47,520 0 2,528,000
12 495,000 0 780,800 3,600 75,000 0 7,832,000
Total 1,203,000 2,005,000 9,542,400 686,400 498,720 800 100,000,000
Total Cost =
113,936,320$
The cost data is provided on worksheet Data. Use Data | Solver to obtain the optimal production plan for planters.
The production plan is charted on the worksheet Planter Plan Chart.
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Inventory
Production
Demand
Aggregate Plan Decision Variables (demand, inventory, production in ‘000s) Constraints
HtLtWtOtItStPt
Period # Hired # Laid off # Workforce Overtime Inventory Stockout Production Demand Inventory Overtime Production Workforce
0 0 0 100 050 0
1 0 0 100 0.0 110.0 0.0 160 100 02000 (0) 0
20 0 100 0.0 170.0 0.0 160 100 02000 – 0
3 0 0 100 0.0 230.0 0.0 160 100 02000 – 0
40 0 100 0.0 290.0 0.0 160 100 02000 – 0
5271 0371 0.0 783.6 0.0 594 100 07420 – 0
60 0 371 0.0 1177.2 0.0 594 200 07420 – 0
7 0 0 371 0.0 1270.8 0.0 594 500 07420 – 0
80 0 371 0.0 864.4 0.0 594 1,000 0 7420 – 0
9 0 0 371 7420.0 32.2 0.0 668 1,500 0 0 – 0
10 0 0 371 7420.0 0.0 0.0 668 700 0 0 – 0
11 096 275 0.0 0.0 10.0 440 450 05500 – 0
12 0175 100 0.0 50.0 0.0 160 100 02000 – 0
Costs
Period Hiring Lay off Regular Time Overtime Inventory Stockout Material
1 0 0 320,000 0 33,000 0 3,200,000
20 0 320,000 0 51,000 0 3,200,000
3 0 0 320,000 0 69,000 0 3,200,000
40 0 320,000 0 87,000 0 3,200,000
5 813,000 0 1,187,200 0 235,080 0 11,872,000
60 0 1,187,200 0 353,160 0 11,872,000
7 0 0 1,187,200 0 381,240 0 11,872,000
80 0 1,187,200 0 259,320 0 11,872,000
9 0 0 1,187,200 222,600 9,660 0 13,356,000
10 0 0 1,187,200 222,600 0 0 13,356,000
11 0 480,000 880,000 0 0 20,000 8,800,000
12 0 875,000 320,000 0 15,000 0 3,200,000
Total 813,000 1,355,000 9,603,200 445,200 1,493,460 20,000 99,000,000
Total Cost =
112,729,860$
The cost data is provided on worksheet Data. Use Data | Solver to obtain the optimal production plan for planters.
The production plan is charted on the worksheet Harvester Plan Chart.
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Inventory
Production
Demand
Aggregate Plan Decision Variables (demand, inventory, production in ‘000s) Constraints
HtLtWtOtItStPt
Period # Hired # Laid off # Workforce Overtime Inventory Stockout Production Demand Inventory Overtime Production Workforce
0 0 0 344 0300 0
1187 0531 0.0 449.6 0.0 850 700 010620 0 0
20 0 531 9500.0 444.2 0.0 945 950 01120 0 0
3 0 0 531 10620.0 0.0 0.0 956 1,400 0 0 0 0
40 0 531 5040.0 0.0 0.0 900 900 05580 0 0
5 0 0 531 0.0 199.6 0.0 850 650 010620 0 0
60 0 531 0.0 749.2 0.0 850 300 010620 0 0
7 0 0 531 0.0 998.8 0.0 850 600 010620 0 0
80 0 531 0.0 748.4 0.0 850 1,100 0 10620 0 0
9 0 0 531 200.0 0.0 0.0 852 1,600 0 10420 0 0
10 031 500 0.0 0.0 0.0 800 800 010000 0 0
11 063 437 0.0 149.2 0.0 699 550 08740 0 0
12 093 344 40.0 300.0 0.0 551 400 06840 0 0
Costs
Period Hiring Lay off Regular Time Overtime Inventory Stockout Material
1 561,000 0 1,699,200 0 134,880 0 16,992,000
20 0 1,699,200 285,000 133,260 0 18,892,000
3 0 0 1,699,200 318,600 0 0 19,116,000
40 0 1,699,200 151,200 0 0 18,000,000
5 0 0 1,699,200 0 59,880 0 16,992,000
60 0 1,699,200 0 224,760 0 16,992,000
7 0 0 1,699,200 0 299,640 0 16,992,000
80 0 1,699,200 0 224,520 0 16,992,000
9 0 0 1,699,200 6,000 0 0 17,032,000
10 0 155,000 1,600,000 0 0 0 16,000,000
11 0 315,000 1,398,400 0 44,760 0 13,984,000
12 0 465,000 1,100,800 1,200 90,000 0 11,016,000
Total 561,000 935,000 19,392,000 762,000 1,211,700 0 199,000,000
Total Cost =
221,861,700$
The cost data is provided on worksheet Data. Use Data | Solver to obtain the optimal production plan for planters.
The production plan is charted on the worksheet Harvester Plan Chart. We assume that the combined plant ends
December with 344 workers and 300 machines in inventory, which equals the numberof workers at the two
separate plants combined.
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Production
Demand