PROBLEM : Loan Services at a Bank

Suppose that you are the general manager of a local bank that provides loan services to its customers. Currently, you have a dedicated area in the bank for loan services. In this loan area, there is one loan expert, who helps the customers with their loan requests. In the loan area, there are 2 waiting seats available for the customers waiting for a loan request. If the loan expert is busy and both of the waiting seats are occupied, a customer waits in a general standing area within the loan area. You are practically assuming that the general standing area can hold as many customers as possible. The figure below illustrates the loan area in the bank.

Note that a customer being helped by the loan expert sits on a separate chair by the loan expert's desk, i.e., the customer being helped does not sit on the waiting seats. Based on the past observations, you are estimating that the customers come to the bank with loan requests every 30 minutes on average, i.e., every 30 minutes, a customer walks into the loan area. Again, based on the past data, you observed that the loan expert can help a customer with his/her loan request within 15 minutes on average. Both the customer interarrival times and the service times are exponentially distributed.

As the general manager, you have standards about the customer service for any type of service you provide within your bank. Specifically, you have the following three standards for the loan service:

- Standard-1: On average, there should not be more than 1 person waiting for the loan expert.
- Standard-2: On average, at most 5% of the customers should wait standing in the general standing area for waiting.
- Standard-3: On average, at least half of the customers should complete their requests with the loan expert within 20 minutes after arriving at the loan area.

You want to see if the current loan service system is satisfying these standards.

a) Determine whether or not the standards 1, 2, and 3 are being satisfied currently. Show your calculations or how you reach to your answer (i.e., if a standard implies L<=3, you do not need to show your calculations because the excel template already calculates L; however if a standard implies some probability calculations, you need to determine that probability using the information in excel template if possible).

Suppose that the current loan service is not satisfying all or some of the standards; hence, you are thinking about taking possible actions that might improve other standards.

b) Without solving anything, state whether the following ideas are correct or wrong and briefly explain your reasoning. That is, do not assume any values and solve for the standards and state that the idea is correct or wrong based on the solution.

a. You want to reduce the average number of people waiting for the loan expert, either in the seats or in the standing area. To do so, you tell the loan expert to work more efficiently so that he can complete a customer's loan request in a shorter amount of time. Will this really reduce the average number of people waiting for the loan expert?

b. You are planning to give a promotion to customers who come to your bank for loan services. This promotion is expected to result in an increase in the customer arrival rate. Will this promotion decrease the average number of customers a loan expert can help with loan requests?

c. You are thinking to hire another loan expert with the same service rate that will also help customers in the same loan service area, i.e., the customers will wait for the next available loan expert. Will hiring the second loan expert decrease the average total time a customer spends in the bank for completing his/her loan request?

For some reason, you thought that the ideas you had are not directly helping for you to achieve your standards. Therefore, you decided to seek help from other managers in the bank and you got two suggestions:

- Facilities Manager suggested adding another waiting seat, right next to the second waiting seat, to the loan area.

- Human Resources Manager suggested replacing the current loan expert with a new one. The new loan expert can complete a customer's loan request within 12 minutes on average; and, the service time is still exponentially distributed.

You want to implement one or both of these suggestions.

c) If you decide to implement the Facilities Manager's suggestion, will the loan service satisfy standards 1, 2, and 3? Show your calculations if needed.

d) If you decide to implement the Human Resources Manager's suggestion, will the loan service satisfy standards 1, 2, and 3? Show your calculations if needed.