2. A bank has one drive-up tel ler. The teller can serve at the rate of 10.5 ban

Question

2. 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

Queuing Theory Problem:

Let us consider the following notation:

Adding the second drive-up window will cost $18,000
Reduction in customers waiting time will increase the bank revenue by $2,400 annually.

Utilization of the service can be calculated as follows:
Utilization, p = l/m = 8/10.5 = 0.76 = 76%

Waiting time for the second teller machine being installed.

Waiting time , Wq = l/m(m-l) = 8/10.5(10.5-8) = 8/26.25 = 0.30 hours

When the second teller machine is installed, the serving capacity of the window increased. Hence, Arrival rate, l = 4 customers per hour

Waiting time can be calculated as Wq = 4/10.5(10.5-4) = 4/68.25 = 0.059 ~ 0.06 hours

By installing the second machine, the bank can reduce the waiting time for 8.5 minutes. If each minute gains a profit of $2,400, then the profit will be $20,400

Inference & Conclusion: Hence, if the second teller machine is installed, the bank will get a profit of $2,400 for the first year, as it costs $18,000 to install the teller machine. The bank should go for the installation of second teller machine, as it yields the profit of $20,400 in the upcoming years.

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