A bank has one drive-up teller. The teller can serve at the rate of 10.5 bank cu

Question

A bank has one drive-up teller. The teller can serve at the rate of 10.5 bank customers in an hour. Customers arrive at the drive-up window on an average every 7.5 minutes. The bank is currently analyzing the possibility of adding a second drive-up window at an annual cost of $18,000. It is assumed that arriving cars would be equally divided between both windows. It is estimated that each minute’s reduction in customer waiting time would increase the bank’s revenue by $2,400 annually. What will be net change in the bank’s revenue? Should the second drive-up window be installed?

Note: Do hand calculations to answer this question. Show all details of your answer.

Explanation / Answer

One drive-up teller

Arrival rate, = 60/7.5 = 8 customers per hour

Service rate, = 10.5 customers per hour

Average waiting time, Lq = //(-) = 0.3048 hours =18.29 minutes

Two drive-up tellers

For each of the queues,

Arrival rate, = 8/2 = 4 customers per hour

Service rate, = 10.5 customers per hour

Average waiting time, Lq = //(-) = 0.0586 hours =3.52 minutes

Increase in Bank's revenue = Minutes of waiting time reduced * 2400 = (18.29 - 3.52)*2400 = $ 35,448

Net benefit = Increase in revenue - cost of adding second drive-up window = 35448 - 18000 = 17,448

The benefit is more than the cost of adding the second drive-up window.

Therefore the second drive-up window should be installed.

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