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:

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 $9 per unit. Inventory carrying cost is $7 per unit per period, and backlog cost is $7 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 $12. The output rate is 10 units per worker per period for all workers. A maximum of 10 part-time workers can be used, and the same number of part-time workers must be used in all periods that have part-time workers. The ending inventory in period 9 should be 10 units. The limit on backlogs is 20 units per period. Try to make up backlogs as soon as possible. Compute the total cost for this plan. Assume 20 full-time workers. (Omit the "$" sign in your response.)

Answer 1

Regular production = 200 units per period.

Therefore, regular production could be used to meet the demand of 9 * 200 = 1,800 units.

So, the part-time workers to produce = Total Forecast + Ending Inventory Goal – Beginning Inventory – Total Regular Production = 1,940 + 10 - 0 - 1,800 = 150 units.

A part-time worker can produce 10 units per period. Therefore, we will need to hire 5 part-time workers. These 5 part-time workers will produce 50 units per month * 3 months = 150 units.

The cost of $7 is levied on Ending Inventory

Period	Forecast	Hire part-time	Ending Inventory	Average Inventory	Backlog	Regular Production	Part-time Production
			0
1	190		10	5	0	200	0
2	230	5	30	20	0	200	50
3	260	5	20	25	0	200	50
4	280	5	0	10	10	200	50
5	210		0	0	20	200	0
6	170		10	5	0	200	0
7	160		50	30	0	200	0
8	260		0	25	10	200	0
9	180		10	5	0	200	0
Total	1940	15	130	125	40	1800	150	Total cost
Cost/ unit			$7	-	$7	$9	$12	$19,190

The cost of $7 is levied on Average Inventory.

Period	Forecast	Hire part-time	Ending Inventory	Average Inventory	Backlog	Regular Production	Part-time Production
			0
1	190		10	5	0	200	0
2	230	5	30	20	0	200	50
3	260	5	20	25	0	200	50
4	280	5	0	10	10	200	50
5	210		0	0	20	200	0
6	170		10	5	0	200	0
7	160		50	30	0	200	0
8	260		0	25	10	200	0
9	180		10	5	0	200	0
Total	1940	15	130	125	40	1800	150	Total cost
Cost/ unit			-	$7	$7	$9	$12	$19,155