Question

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 $9 variable cost is incurred; for each unit produced during month 3, a $12 variable cost is incurred. The inventory cost is $2.50 for each unit in stock at the end of a month. The cost of setting up for production during a month is $250. 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

Given Information

Opening Inventory=0 units

Set up cost for Every Month= $250

Inventory Holding Cost =$2.5 per Unit

	Variable cost per unit	Production(Units)
Month 1	$9	200
Month 2	$9	300
Month 3	$12	300

Case 1

Given

Set up cost for every month =$250

In this Case we just produce the required demand in their corresponding months.

	Month 1	Month 2	Month 3
Demand	200	300	300
Production	200	300	300
Cost	250 + 200*$9 =$2050/-	250 + 300*$9 =$2950/-	250 + 300*$12 =$3850/-

Total cost = $2050+$2950+$3850 =$8850/-

Case 2:

Inventory Holding Cost =$2.5 per Unit

In this case as the production cost is $3 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	250 + 200*9 =$2050/-	250 + 600*9+2.5*300 =$6400/-	0

Total cost = $2050+$6400=$8450/-

Conclusion:

We can see that Production cost in Case 2 is less than Case 1.

Hence the optimal production schedule is Case 2

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