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 $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

Here the resttiction is given as the produced items to be used in thier current month or upto next month only

Case 1:

In this scenarion we produce the demand for month 1 and month 2 in Month 1 itself and requirement of Month 3 in Month 2

Price of producion=$9 (Moth 1&2) , $12 (Month 3)

Set up cost=$250

Holding cost=$2.50

	Month 1	Month 2	Month 3
Demand	200	300	300
Production	200+300 =500	300	0
Cost	250 + 500*9+2.50 *300 =$5500	250 + 300*9+2.50 *300 =$3700	0

Total cost = 5500 +3700 =$9200

Here in Month 1 Holding costs For items produced for Month 2 is added Similarly For month 2 Holding costs for items produced for Month 3 is Included.

Case 2:

In this scenarion we produce the demand for month 1 in Month 1 itself and requirement of Month 2 & 3 in Month 2.

Price of producion=$9 (Moth 1&2) , $12 (Month 3)

Set up cost=$250

Holding cost=$2.50

	Month 1	Month 2	Month 3
Demand	200	300	300
Production	200	300+300=600	0
Cost	250 + 200*9 =$2050	250 + 600*9+2.50 *300 =$6400	0

Total cost = 2050 +6400 =$8450

Case 3:

In this scenario production will be done to meet the demand of their respective months.

Price of producion=$9 (Moth 1&2) , $12 (Month 3)

Set up cost=$250

Holding cost=$2.50

	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/-

Here we can see that case 2 is the most optimal production schedule with minimal cost.

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