First Local Bank would like to improve customer service at its drive-in facility by reducing waiting and
Question:
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 is 15 cars per hour. All arriving cars line up in front of a window and are served on a first-come, first-served basis. Each transaction requires on average 3 minutes to complete. Assume that the arrival of cars follows a Poisson process, and that the transaction times are exponentially distributed.
The bank now has one window that serves the drive-in customers. It costs $20 an hour to staff this window. The customer relations (CR) manager estimates that the cost (loss of goodwill and future business, etc.) due to a customer's waiting in the queue has a linear form, i.e., the bank incurs a cost of 10 dollars per hour per customer in queue. On the other hand, as soon as a customer goes into service, the bank does not incur any goodwill loss.
Question: Comparing to the two separate lines layout, what is the difference, if any, in the utilization of the service windows when using the single line layout? Explain the difference (or indifference) with intuition.