Q51472 Michigan manufacturing produces a product that has a 6-month demand cycle, as shown in Table 1. Each unit requires 10 worker-hours to produce, at a labour cost of Rs. 6 per hour regular rate (or Rs. 9 per hour overtime). The total cost per unit is estimated at Rs. 200, but units can be subcontracted at a cost of Rs. 208 per unit. There are currently 20 workers employed in the subject department, and hiring and training costs for additional workers are Rs. 300 per person, whereas layoff costs are Rs. 400 per person. Company policy is to retain a safety stock equal to 20 per cent of the monthly forecast, and each month's safety stock becomes the beginning inventory for the next month. There are currently 50 units in stock carried at a cost of Rs. 2 per unit-month. Unit shortage, or stockouts, has been assigned a cost of Rs. 20 per unit month.

	January	February	March	April	May	June
Forecast demand	300	500	400	100	200	300
Workdays	22	19	21	21	22	20
Work hr at 8 per day	176	152	168	168	176	160

Table No. 1

Three aggregate plans are proposed.

Plan 1: Vary work force size to accommodate demand.

Plan 2: Maintain constant work force of 20, and use overtime and idle time to meet demand.

Plan 3: Maintain constant work force of 20, and build inventory or incur Stockout cost. The firm must begin January with the 50-unit inventory on hand.

Compare the costs of the three plans in table form.

Solution:

: We must first determine what the production requirements are, as adjusted to include a safety stock of 20 per cent of next month’s forecast. Beginning with a January inventory of 50, each subsequent month’s inventory reflects the difference between the forecast demand and the production requirement of the previous month. See Table 2. The costs of the three plans are shown in Tables 3, 4, and 5.

	Forecast demand	Cumulative demand	Safety stock @20 per cent forecast	Beginning inventory	Production requirement (fest. + SS – beg. inv.)
January	300	300	60	50	300 + 60 – 50 = 310
February	500	800	100	60	500 + 100 – 60 = 540
March	400	1,200	80	100	400 + 80 – 100 = 380
April	100	1,300	20	80	100 + 20 – 80 = 40
May	200	1,500	40	20	200 + 40 – 20 = 220
June	300	1,800	60	40	300 + 60 – 40 = 320

Table No. 2

January	February	March	April	May	June	Total
1. Production required	310	540	380	40	220	320
2. Production hours Required (1 × 10)	3,100	5,400	3,800	400	2,200	3,200
3. Hours available per Worker at 8/day	176	152	168	168	176	160
4. Number of workers Required (2/3)	18	36	23	3	13	20
5. Number of workers Hired		18			10	7
6. Hiring cost (S × Rs. 300)		Rs. 5,400		Rs. 3,000	Rs. 2,100	Rs. 10,500
7. Number of workers Laid off	2		13	20
8. Layoff cost (7 × Rs. 400)	Rs. 800		Rs. 5,200	Rs. 8,000		Rs. 14,000

Table No. 3 Plan 1(Vary Work-force Size)

21 8 image 1351 — **Table No. 4** Plan 2 (Use Overtime and Idle Time)

*Incremental cost of OT = overtime cost – regular time cost = Rs. 9 – Rs. 6 = Rs. 3.

21 8 image 1352 — **Table 5 Plan 3 (Use Inventory and Stockout Based on Constant 20-Worker Force)**

Note that plan 3 assumes that a Stockout cost is incurred if safety stock is not maintained at prescribed levels of 20 per cent of forecast. The firm is in effect managing the safety-stock level to yield a specific degree of protection by absorbing the cost of carrying the safety stock as a policy decision.

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