A manager is going to purchase new processing equipment and must decide on the n

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 $174 each, and any unused spares will have an expected salvage value of $44 each. The probability of usage can be described by this distribution:

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 $590 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.

Number 0 1 2 3 Probability .10 .50 .25 .15

Explanation / Answer

Cu = Cost of understocking = cost of idle equipment = $590 x 2 = $1180
Co = Cost of overstocking = Purchase cost - Salvage value = $174 - $44 = $130

(a)

Critical Ratio = Cu / (Co+Cu) = 1180/(1180+130) = 0.9008

Sevice level is thus 90.08%.

Since Q=3 crosses the service level, the optimal order quantity is 3

(b)

Cost table

Minimum expected cost happens to b at Q=3 which is the optimal order quantity.

Number 0 1 2 3 Probability .10 .50 .25 .15 Cumulative Probability .10 .60 .85 1.00

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