# Question

The car rental company, Try Harder, has been subcontracting for the maintenance of its cars in St. Louis. However, due to long delays in getting its cars back, the company has decided to open its own maintenance shop to do this work more quickly. This shop will operate 42 hours per week.

Alternative 1 is to hire two mechanics (at a cost of $1,500 per week each), so that two cars can be worked on at a time. The time required by a mechanic to service a car has an Erlang distribution, with a mean of 5 hours and a shape parameter of k = 8.

Alternative 2 is to hire just one mechanic (for $1,500 per week) but to provide some additional special equipment (at a capitalized cost of $1,250 per week) to speed up the work. In this case, the maintenance work on each car is done in two stages, where the time required for each stage has an Erlang distribution with the shape parameter k 4, where the mean is 2 hours for the first stage and 1 hour for the second stage.

For both alternatives, the cars arrive according to a Poisson process at a mean rate of 0.3 car per hour (during work hours).

The company estimates that its net lost revenue due to having its cars unavailable for rental is $150 per week per car.

(a) Use Fig. 17.10 to estimate L, Lq, W, and Wq for alternative 1.

(b) Find these same measures of performance for alternative 2.

(c) Determine and compare the expected total cost per week for these alternatives.

Alternative 1 is to hire two mechanics (at a cost of $1,500 per week each), so that two cars can be worked on at a time. The time required by a mechanic to service a car has an Erlang distribution, with a mean of 5 hours and a shape parameter of k = 8.

Alternative 2 is to hire just one mechanic (for $1,500 per week) but to provide some additional special equipment (at a capitalized cost of $1,250 per week) to speed up the work. In this case, the maintenance work on each car is done in two stages, where the time required for each stage has an Erlang distribution with the shape parameter k 4, where the mean is 2 hours for the first stage and 1 hour for the second stage.

For both alternatives, the cars arrive according to a Poisson process at a mean rate of 0.3 car per hour (during work hours).

The company estimates that its net lost revenue due to having its cars unavailable for rental is $150 per week per car.

(a) Use Fig. 17.10 to estimate L, Lq, W, and Wq for alternative 1.

(b) Find these same measures of performance for alternative 2.

(c) Determine and compare the expected total cost per week for these alternatives.

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