4.3 Repairs of MTA buses The metropolitan transit authority of a region wishes
to establish a crew of auto mechanics that will be responsible for repairing the
authority's buses. The crew is stationed at a single location. Bus breakdowns occur
randomly (Poisson process) at a mean rate of one per hour. The time required to fix a bus
has a negative exponential distribution (regardless of crew size). The expected repair
time required by a one-worker crew would be 2 hours.
The cost per hour for each member of a repair
crew is $10.00. The cost that is attributable to not having a bus in use (i.e., a bus
standing at the bus repair shop) is estimated to be $40.00 per hour. (Both men and buses
are on 8-hour days.)
Assume that the mean service rate of the repair
crew is proportional to its size. What should the crew size be in order to minimize the
expected total cost of this operation per hour? Repeat this question but with the mean
service rate proportional to the square root of the crew size.