An airline maintenance base wants to make a change in its overhaul operation. The present situation is that only one airplane can be repaired at a time, and the expected repair time is 36 hours, whereas the expected time between arrivals is 45 hours. This situation has led to frequent and prolonged delays in repairing incoming planes, even though the base operates continuously. The average cost of an idle plane to the airline is $3,000 per hour. It is estimated that each plane goes into the maintenance shop 5 times per year. It is believed that the input process for the base is essentially Poisson and that the probability distribution of repair times is Erlang, with shape parameter k = 2.
Alternative A is to provide a duplicate maintenance shop, so that two planes can be repaired simultaneously. The cost, amortized over 5 years, is $400,000 per year for each of the airline's airplanes. Alternative B is to replace the present maintenance equipment by the most efficient (and expensive) equipment available, thereby reducing the expected repair time to 18 hours. The cost, amortized over 5 years, is $550,000 per year for each airplane. Which alternative should the airline choose?