Community Bank is planning to improve customer service at its drive-in facility by reducing waiting and transaction times. Observations of the existing single-teller window reveal that customers arrive according to a Poisson process at an average rate of 10 per hour, and that they are given first-come first-served service with an average transaction time of 5 minutes. Transaction times are exponentially distributed. The cost of keeping a customer waiting in queue is represented as a $5-per-hour loss of goodwill.
The bank is considering the following two improvement options.
(A) The bank can lease high-speed information-retrieval and communication equipment that would cost $20 an hour. The new equipment would reduce the average transaction time by one minute. Assume that the transaction times are still exponentially distributed with the leased equipment.
(B) The other option is to add another teller and to install four remote stations with pneumatic tubes running from the stations to the tellers, who are located in a glassed-in building. The hourly cost of a teller is $10. (The teller is paid regardless whether he/she is idle or not. Ignore the cost for installing the pneumatic tubes, which are systems that propel cylindrical containers through a network of tubes by compressed air or by partial vacuum.)
Answer the following questions.
a) What is the per-hour goodwill loss under the status quo (before any improvement)?
b) Consider option (A). What is the cost savings per hour relative to the status quo?
c) Consider option (B). Assume that each teller is assigned to two stations exclusively, and that demand is divided equally among the stations (i.e., each station gets 25% of the demand), and that no customers can switch lines. What is the hourly cost savings now?
d) Still consider (B). But now both tellers work all the stations and the customer waiting the longest is served by the next available teller. What is the cost saving now?
e) What concept of queueing theory explains the difference between c) and d)? Overall, what solution do you recommend for the bank and why?