# Question

The maintenance base for Friendly Skies Airline has facilities for overhauling only one airplane engine at a time. Therefore, to return the airplanes to use as soon as possible, the policy has been to stagger the overhauling of the four engines of each airplane. In other words, only one engine is overhauled each time an airplane comes into the shop. Under this policy, airplanes have arrived according to a Poisson process at a mean rate of 1 per day. The time required for an engine overhaul (once work has begun) has an exponential distribution with a mean of 1/2 day.

A proposal has been made to change the policy so that all four engines are overhauled consecutively each time an airplane comes into the shop. Although this would quadruple the expected service time, each plane would need to come to the maintenance base only one-fourth as often.

Management now needs to decide whether to continue the status quo or adopt the proposal. The objective is to minimize the average amount of flying time lost by the entire fleet per day due to engine overhauls.

(a) Compare the two alternatives with respect to the average amount of flying time lost by an airplane each time it comes to the maintenance base.

(b) Compare the two alternatives with respect to the average number of airplanes losing flying time due to being at the maintenance base.

(c) Which of these two comparisons is the appropriate one for making management’s decision? Explain.

A proposal has been made to change the policy so that all four engines are overhauled consecutively each time an airplane comes into the shop. Although this would quadruple the expected service time, each plane would need to come to the maintenance base only one-fourth as often.

Management now needs to decide whether to continue the status quo or adopt the proposal. The objective is to minimize the average amount of flying time lost by the entire fleet per day due to engine overhauls.

(a) Compare the two alternatives with respect to the average amount of flying time lost by an airplane each time it comes to the maintenance base.

(b) Compare the two alternatives with respect to the average number of airplanes losing flying time due to being at the maintenance base.

(c) Which of these two comparisons is the appropriate one for making management’s decision? Explain.

## Answer to relevant Questions

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