A) A large Midwestern railroad finds that it must steam clean its cars once a year. It is considering two alternatives for its steam-cleaning operation. Under alternative 1, the railroad would operate two steam-cleaning booths, operating in parallel at a total annual cost of $50,000. The service time distribution under this alternative is exponential with a mean of 5 hours per car. Under alternative 2, the railroad would operate one large steam-cleaning booth at a total cost of $100,000. However, the service time distribution under this alternative would be exponential with a mean of 3 hours per car. Under both alternatives, the railroad cars arrive according to a Poisson input process with an arrival rate of one car every 8 hours. The cost of an idle hour is thought to be $10 per hour. Assume that the steam-cleaning booths operate (8 hours per day) x (250 days per year) = 2000 hours per year. Which alternative should the railroad choose?
b) An auditor just revealed that as long as the cars are out of work, a loss of $500 per hour in revenue is incurred by the Railroad Company. Compute the economic advantage of the alternative recommended by you in part a) above over the other alternative.
Computations and equations provided.