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 $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           $

Answer 1

Below is the aggregate plan based on details given in the problem.

20 full time employees will produce 20*10=200 units per period - this is fixed production per period

Since demand is higher between period 2 till period 5 we will produce overtime max production of 25 units each period and 5 units in period 6 so that backlog is minimum

Period	1	2	3	4	5	6	7	8	9	Total
Forecast	190	230	260	280	210	170	160	260	180	1940
Full time employee production	200	200	200	200	200	200	200	200	200	1800
Overtime Production	25	25	25	25	25	5	0	0	0	130
Beginning Inventory	0	35	30	0	0	0	0	40	0	105
Ending Inventory	200+25-190=35	200+25+35-230=30	0	0	0	170+35-200-5=0	200-160=40		200-180-20=0	105
Backlog	0		260-200+25+30=5	280+5-200-25=60	210+60-210-25=35	0		260-200-40=20		120

Total cost is $13,695

	Units	Cost
Forecast	1940
Full time employee production	1800	1800*6=10800
Overtime Production	130	130*9=1170
Beginning Inventory	105	105*5=525
Ending Inventory	105
Backlog	120	120*10=1200
TOTAL COST		$                   13,695

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