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:
Period: 1 2 3 4 5 6 7 8 9 Total
Forecast : 190 230 260 280 210 170 160 260 180 1,940
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.
Prepare an aggregate plan that uses overtime ($9 per unit, maximum output 25 units per period) and inventory variation. The primary objective in this problem is to minimize backlogs to the extent possible without having any inventory remaining at the end of Period 9. The ending inventory in period 9 should be zero, and the limit on backlogs is 60 units per period. Note that Total output = Total regular output + Overtime quantity. Compute the total cost of your plan. Assume 20 full-time workers. (Omit the "$" sign in your response.)
Total cost: $ ______
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