A manager is attempting to put together an aggregate plan for the coming nine mo

Question

A manager is attempting to put together an aggregate plan for the coming nine months. She has obtained a forecast of expected demand for the planning horizon. The plan must deal with highly seasonal demand; demand is relatively high in periods 3 and 4 and again in period 8, as can be seen from the following forecasts:

The department now has 20 full-time employees, each of whom can produce 10 units of output per period at a cost of $6 per unit. Inventory carrying cost is $5 per unit per period, and backlog cost is $10 per unit per period. The manager is considering a plan that would involve hiring two people to start working in period 1, one on a temporary basis who would work only through period 5. This would cost $500 in addition to unit production costs.

Prepare an aggregate plan that uses overtime ($9 per unit, maximum output 25 units per period) and inventory variation. Try to minimize backlogs. The ending inventory in period 9 should be zero, and the limit on backlogs is 60 units per period. Note that Total output = Total regular output + Overtime quantity. Compute the total cost of your plan. Assume 20 full-time workers. (Omit the "$" sign in your response.)

    Period 1 2 3 4 5 6 7 8 9 Total   Forecast 190 230 260 280 210 170 160 260 180 1,940

Explanation / Answer

Regular Output Period   Total   Forecast Output Cost Inventory Cost Backlog cost Additional Cost 1 190 210 1260 0 0 500 2 230 210 1260 200 400 500 3 260 210 1260 250 500 500 4 280 210 1260 350 700 500 5 210 210 1260 0 0 500 6 170 210 1260 0 0 0 7 160 210 1260 0 0 0 8 260 210 1260 0 0 0 9 180 210 1260 0 0 0 Total 1940 1890 11340 800 1600 2500 Total Cost= 16240 New Plan Period   Total   Forecast Output Backlog Overtime Cost Backlog Cost 1 190 210 0 0 1260 0 2 230 210 0 0 1260 0 3 260 210 50 20 1440 500 4 280 210 70 50 1710 700 5 210 210 0 50 1710 0 6 170 210 50 0 1260 500 7 160 210 50 0 1260 500 8 260 210 30 0 1260 300 9 180 210 0 0 0 0 Total 1940 1890 250 120 11160 2500 Total Cost 13660

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