Question

A warehouse has to meet the demand for a product shown below. Each unit of stock remaining at the end of a month has a notional holding cost of 20. If there are shortages, 20 % of orders are lost with a cost of 200 a unit, and the rest are met by late deliveries with a cost of 50 a unit. A production department sends the product to the warehouse. Designed capacity of this department is 400 units a month, but utilization seldom exceeds 80 %. Every time the production rate is changed it costs 15 000.

How would you set about designing an aggregate plan for the product?

Month Aggregate demand 310 280 260 300 360 250 160 100

In preparing your answers you can use a spreadsheet software.

Answer 1

Maximum Production

400*80%

320 units

Shortage Cost (In case of even One Unit Shortage)

1	2	3	4	5	6	7	8
24800	22400	20800	24000	28800	20000	12800	8000

Month 1 Shortage cost : 310*20%*200# + 310*80%*50# = 24800

#Provided in question

In the First Month the Shortage Cost Comes around Rs. 24,800/- So definitely we cannot afford have a shortage. The Max. Production in QTY is 320 Units. For 310 units demand in the first month if we produce 320 units it will increase our holding cost. so in month 1 we produce 310 Units.

Production Plan for 8 months

Month	1	2	3	4	5	6	7	8
Production	310	310	310	310	310	310	80	80
excess units	0	30	80	90	40	100	20	0

Month 2 Holding cost : 30*20# = 600

#Provided in question

Holding cost for Above

1	2	3	4	5	6	7	8
0	600	1600	1800	800	2000	400	0

cost on Change in production rate

1	2	3	4	5	6	7	8
0	0	0	0	0	0	15000	0

Total Cost = 22,200

upto month 6 the same production pattern of 310 units can be maintained and if we change the production rate in between it will cost us Rs.15000/- . So out of 8 months, production rate has been changed for only one month to minimize the cost and to equalize demand and supply. Production rate is changed on month 7 because changing it in earlier months and producing remaining demand equally over the remaining months gives rise to shortage cost and if we plan to reduce shortage cost by changing the production rate again it will cost another 15,000/-. Therefore production rate is changed on month 7 and remaining demand has been produced equally over remaining months.

Result:

Production pattern

Month	1	2	3	4	5	6	7	8
Production	310	310	310	310	310	310	80	80

Total Cost 22,200/-