Question

A firm need to produce the following number of units during the next three months; month 1, 200 units; month 2, 300 units; month 3, 300 units. For each unit produced during months 1 and 2, a $13 variable cost is incurred; for each unit produced during month 3, a $12 variable cost is incurred. The inventory cost is $0.5 for each unit in stock at the end of a month. The cost of setting up for production during a month is $300. Units made during a month may be used to meet demand for that month or next month only. Assume that production during each month must be a multiple of 100. Given that the initial inventory level is 0 units, use dynamic programming to determine an optimal production schedule

Answer 1

Case 1 :

Given

Set up cost for every month =$300

In this scenarion we just produce the required demand in their corresponidng months.

	Month 1	Month 2	Month 3
Demand	200	300	300
Production	200	300	300
Cost	300 + 200*13 =$2900/-	300 + 300*13 =$4200/-	300 + 300*12 =$3900/-

Total cost = 2900+4200+3900 = $11,000/-

Case 2:

Holding cost = $0.5

In this case as the production cost is $1 less in Month 2 we produce the demand of Month 3 in Month 2 itself .

	Month 1	Month 2	Month 3
Demand	200	300	300
Production	200	300+300 =600	0
Cost	300 + 200*13 =$2900/-	300 + 600*13+0.5*300 =$8250/-	0

Total cost = 2900+8250 =$11,150/-

We can see that Case 1 is more profitable. That by doing producition as per the individula month requirements is more beneficial than producition of demands of month 2 and 3 in Month 2 itself.

Hence the optimal production schedule is case 1.

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