Question

A manager is going to purchase new processing equipment and must decide on the number of spare parts to order with the new equipment. The spares cost $170 each, and any unused spares will have an expected salvage value of $40 each. The probability of usage can be described by this distribution:

Number	0	1	2	3
Probability	.05	.40	.20	.35

If a part fails and a spare is not available, 2 days will be needed to obtain a replacement and install it. The cost for idle equipment is $550 per day. What quantity of spares should be ordered?

a. Use the ratio method. (Round your answer to 2 decimal places.)

Service level is  , so we need to order  Spares.
  
b. Use the tabular method.

Answer 1

Cost of Stock out Cs = 550*2 = 1100

Cost of Excess Inventory Ce= 170 - 40 = 130

Service Level = Cs/(Cs+Ce)

Service Level = 1100/(1100+130)

Service Level = 0.8943

Below is the probability table -

Number	Probability	Cumulative Probability
0	0.05	0.05
1	0.4	0.45
2	0.2	0.65
3	0.35	1

0.8943 lies between, 0.65 and 1, Hence

Number of Spare = 3

2)

Tabular Method -

Below is the calculation performed as per tabular method -

	Demand = 0	Demand = 1	Demand = 2	Demand = 3
Stocking Level	0.05	0.4	0.2	0.35	Expected Cost
0	0	440	440	1155	2035
1	6.5	0	220	770	996.5
2	13	52	0	385	450
3	19.5	104	26	0	149.5

Cost is lowest with 3 spare parts, hence 3 spare parts should be ordered.