First Local Bank would like to improve customer service at its drive-in facility by reducing waiting and transaction times. On the basis of a pilot study, the bank’s process manager estimates the average rate of customer arrivals at 40 per hour. All arriving cars line up in a single file and are served at one of 4 windows on a first-come/first-served basis. Each teller currently requires an average of 5 minutes to complete a transaction. The bank is considering the possibility of leasing high-speed information-retrieval and communication equipment that would cost $30 per hour. The new equipment would, however, serve the entire facility and reduce each teller’s transaction-processing time to an average of 4 minutes per customer. Assume that interarrival and activity times are exponentially distributed.
a. If our manager estimates the cost of a customer’s waiting time in queue (in terms of future business lost to the competition) to be $20 per customer per hour, can she justify leasing the new equipment on an economic basis?
b. Although the waiting-cost figure of $20 per customer per hour appears questionable, a casual study of the competition indicates that a customer should be in and out of a drive-in facility within an average of 8 minutes (including waiting). If First Local wants to meet this standard, should it lease the new high-speed equipment?