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 30 per hour. All arriving cars line up in a single file and are served at one of four windows on a first- come/ first- served basis. Each teller currently requires an average of 6 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?