A manager is attempting to put together an aggregate plan for the coming nine mo
ID: 452146 • Letter: A
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 $7 per unit. Inventory carrying cost is $5 per unit per period, and backlog cost is $19 per unit per period.
Suppose another option is to use part-time workers to assist during seasonal peaks. The cost per unit, including hiring and training, is $11. The output rate is 10 units per worker per period for all workers. A maximum of 10 part-time workers can be used, and the same number of part-time workers must be used in all periods that have part-time workers. The ending inventory in period 9 should be 10 units. The limit on backlogs is 20 units per period. Try to make up backlogs as soon as possible. Compute the total cost for this plan. Assume 20 full-time workers. (Omit the "$" sign in your response.)
Explanation / Answer
Period 1 2 3 4 5 6 7 8 9 Total Option 1 Opening balance / Back log 10 (20) (80) (160) (170) (140) (100) (160) -820 Forecast 190 230 260 280 210 170 160 260 180 1,940 Number of full time employees 20 20 20 20 20 20 20 20 20 180 Production by FTE 200 200 200 200 200 200 200 200 200 1,800 Closing balance 10 (20) (80) (160) (170) (140) (100) (160) (140) -960 Cost of production (Employee) 1,400 1,400 1,400 1,400 1,400 1,400 1,400 1,400 1,400 12,600 Carrying cost 50 50 Backlog Cost 380 1,520 3,040 3,230 2,660 1,900 3,040 2,660 18,430 Total Cost 1,450 1,780 2,920 4,440 4,630 4,060 3,300 4,440 4,060 31,080 Period 1 2 3 4 5 6 7 8 9 Total Option 1 Opening balance / Back log 30 20 (20) (80) (70) (20) 40 - -100 Forecast 190 230 260 280 210 170 160 260 180 1,940 Number of full time employees 20 20 20 20 20 20 20 20 20 180 Production by FTE 200 200 200 200 200 200 200 200 200 1,800 Part time workers 2 2 2 2 2 2 2 2 2 18 Production by Part time workers 20 20 20 20 20 20 20 20 20 180 Closing balance 30 20 (20) (80) (70) (20) 40 - 40 -60 Cost of production (Employee) 1,400 1,400 1,400 1,400 1,400 1,400 1,400 1,400 1,400 12,600 Cost of part time employees 22 22 22 22 22 22 22 22 22 198 Carrying cost 150 150 Backlog Cost 380 380 1,520 1,330 380 760 - 760 5,510 Total Cost 1,572 1,802 1,802 2,942 2,752 1,802 2,182 1,422 2,182 18,458
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