# Question

The Southern Railroad Company has been subcontracting for the painting of its railroad cars as needed. However, management has decided that the company can save money by doing this work itself. A decision now needs to be made to choose between two alternative ways of doing this.

Alternative 1 is to provide two paint shops, where painting is done by hand (one car at a time in each shop), for a total hourly cost of $70. The painting time for a car would be 6 hours. Alternative 2 is to provide one spray shop involving an hourly cost of $100. In this case, the painting time for a car (again done one at a time) would be 3 hours. For both alternatives, the cars arrive according to a Poisson process with a mean rate of 1 every 5 hours.

The cost of idle time per car is $100 per hour.

(a) Use Fig. 17.8 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 hour for these alternatives.

Alternative 1 is to provide two paint shops, where painting is done by hand (one car at a time in each shop), for a total hourly cost of $70. The painting time for a car would be 6 hours. Alternative 2 is to provide one spray shop involving an hourly cost of $100. In this case, the painting time for a car (again done one at a time) would be 3 hours. For both alternatives, the cars arrive according to a Poisson process with a mean rate of 1 every 5 hours.

The cost of idle time per car is $100 per hour.

(a) Use Fig. 17.8 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 hour for these alternatives.

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