Question

Exercise 37 A store for spare parts estimates the cost of holding one unit of a replacement part in stock for a month to be $30. Any shortage of the part is estimated to cost $500 a unit a month. Over the past few months the following figures have been collected: Demand for the part 1 2 4 5 6 7 9 10 Percentage of 50 20 10 5 5 3 3 2 1 1 months What is the optimal stock level for the part? If the store currently holds 7 units of the part in stock, what is the implied shortage cost? Sol. a) 7 units b) $720 a unit a month a

Answer 1

Demand for the part	Percentage of the months	Cumulative percentage of the months
1	50%	50%
2	20%	70%
3	10%	80%
4	5%	85%
5	5%	90%
6	3%	93%
7	3%	96%
8	2%	98%
9	1%	99%
10	1%	100%

Service level = c c .

C_s = Cost of shortage = $ 500

C₀ = Cost of overage = Cost per unit - Salvage value per unit = $ 30 - $ 0

C₀ = $ 30

500 Service level = 200 120 = 0.9434 or 94.34%

94.34 % lies in between 93 % and 96 % , therefore for a service level of 94.34 %, the optimal stocking level = 7 units

Optimal stock level = 7 units

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To find the implied shortage cost, we consider a service level of 96%

0.96 = C, +30

0.96 C_s + 28.8 = C_s

C_s - 0.96 C_s = 28.8

0.04 C_s = 28.8

28.8 Cs 0.04

C_s = $ 720

Implied shortage cost = $ 720 a month