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The current aggregate demand requirements for a firm are shown below for the next six months:
| Month | May | June | July | Aug | Sept | Oct |
| Demand | 250 | 230 | 230 | 230 | 260 | 280 |
The firm always plans to meet all demand. The firm currently has 250 workers capable of producing 250 units in a month (1 unit/worker). The workforce can be increased (at a cost of $600 per worker) or decreased (at a cost of $1,200 per worker). Inventory holding cost is $150 per unit per month. The firm currently has 30 units of inventory on hand, and it would like to have 30 units available at the end of each month. Regular production cost is $3,650 per unit. Assume hiring and layoff/firing, if necessary, occur at the beginning of the month.
a.
What should the aggregate plan be if the inventory holding cost is to be minimized? (Leave no cells blank – be certain to enter “0” wherever required.)
b. What is the cost of this plan?
Expert Answer
a. Aggregate plan
In this case, steady production capacity and labor force are adjusted according to the need with a constant output rate through holding minimal inventories the balance requirements.
Given that the labor rate of 1 per unit and total demand of 1,480 units over the six months period, the plan has to be optimized for inventory.
Demand vs regular production is tabulated,
| Month | May | June | July | Aug | Sept | Oct | Totals |
| Demand | 250 | 230 | 230 | 230 | 260 | 280 | 1,480 |
| Production/labor | 1 | 1 | 1 | 1 | 1 | 1 | |
| Workforce level | 250 | 230 | 230 | 240 | 250 | 250 | |
| Total Production (#units) | 250 | 230 | 230 | 240 | 250 | 250 | 1,450 |
| Hiring (# Labor) | 0 | 0 | 0 | 10 | 10 | 0 | |
| Layoff (# Labor) | 0 | 50 | 0 | 0 | 0 | 0 | |
| Starting Inventory (units) | 30 | 30 | 30 | 30 | 40 | 30 | |
| Ending Inventory (units) | 30 | 30 | 30 | 40 | 30 | 0 | |
| Average Inventory (units) | 30 | 30 | 30 | 35 | 35 | 15 |
As you can notice the production level considering only regular hours are below the demand for some of the months. Hence inventory is required to meet the balance demand
b. Total cost of the plan
Total cost = Production costs + Hiring costs + Layoff costs + Inventory costs
The below table shows the cost estimates for each of the months,
| Month | May | June | July | Aug | Sept | Oct | Totals |
| Demand | 250 | 230 | 230 | 230 | 260 | 280 | 1,480 |
| Production/labor | 1 | 1 | 1 | 1 | 1 | 1 | |
| Workforce level | 250 | 230 | 230 | 240 | 250 | 250 | |
| Total Production (#units) | 250 | 230 | 230 | 240 | 250 | 250 | 1,450 |
| Regular production costs | 912,500 | 839,500 | 839,500 | 876,000 | 912,500 | 912,500 | 5,292,500 |
| Hiring (# Labor) | 0 | 0 | 0 | 10 | 10 | 0 | |
| Layoff (# Labor) | 0 | 50 | 0 | 0 | 0 | 0 | |
| Hiring costs | 0 | 0 | 0 | 6000 | 6000 | 0 | 6,000 |
| Layoff costs | 0 | 60000 | 0 | 0 | 0 | 0 | 60,000 |
| Starting Inventory (units) | 30 | 30 | 30 | 30 | 40 | 30 | 190 |
| Ending Inventory (units) | 30 | 30 | 30 | 40 | 30 | 0 | 160 |
| Average Inventory (units) | 30 | 30 | 30 | 35 | 35 | 15 | 175 |
| Inventory costs | 4500 | 4500 | 4500 | 5250 | 5250 | 2250 | 26,250 |
Total cost of the plan = 1450 * 3650 + 20 * 600 + 50 * 1200 + 175 * 150 = 5,292,500 + 6,000 + 60,000 + 26,250 = $5,384,750
