Project 12.2  Friendly Bank Services

question 49

Essay

Project 12.2  Friendly Bank Services
Friendly Bank has various branches throughout the city. Ronnie Fare is a branch manager. Ronnie has always been very customer focused. Her branch is relatively small; three counter tellers and two drive-through tellers. Her drive-through support appears more than adequate. Her concern is with the in-branch service. She is concerned with the level of service being provided and whether or not each of her three tellers are of equal proficiency.
When a customer comes in for service, they wait in a single line and move to the first available teller. Once serviced, the customer leaves the bank. Six weeks ago, Ronnie enlisted a small company to conduct time studies of the bank processes. The data was collected over a four-week period. This extended collection period helped overcome bias in the data collection due to observation activities. The final set of data just arrived in the mail and Ronnie is ready to conduct some desk-top analysis of the data to answer her own questions about her branch.
The data pertinent to her concerns are:
Customer inter-arrivals: Uniformly distributed between 1 and 3 minutes. Average of 250 arrivals per day.

In-bank teller performance (service time):
Teller 1: Normally distributed, mean 5 minutes, standard deviation 1.2 minutes
Teller 2: Normally distributed, mean 3 minutes, standard deviation 1.1 minutes
Teller 3: Normally distributed, mean 4.2 minutes, standard deviation 1.5 minute:
(The minimum service time observed was 30 seconds despite the distribution fit)
At first glance, it appears there is no difference between the tellers. However, Ronnie wants to simulate the bank process to provide estimates on the following pieces of information:
Customer Information:
Average wait time per customer.
Average time in bank per customer.
Percentage of time the customer does not wait
Percentage of time the customer waits less than a minute
How often, if at all the entire work day experiences no waiting lines

Teller Performance Information:
Average utilization per day.
Average number of customers seen per day. Build a simulation model to help answer Ronnie Fare's questions. Use 250 arrivals per day. Provide appropriate statistical information in your answer.

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Definitions:

Deadweight Losses

Economic inefficiencies that occur when the allocation of resources is not optimal, resulting from distortions in the market such as taxes, subsidies, or monopolies.

Perfect Price Discrimination

A pricing strategy where a seller charges the maximum possible price for each unit consumed that each buyer is willing to pay, thus capturing the entire consumer surplus as profit.

Total Revenue

The total income received by a firm from its sales of goods or services before any costs or expenses are deducted.

Arbitrage

The practice of buying and selling a commodity or financial instrument in different markets to profit from differing prices for the same asset.