You are asked to perform a capacity analysis for a bank. The current resources of the bank are as follows:

Resources Number of Service Providers Processing Time $($min$)$

Drive$-$through $33$

Teller $510$

ATM $36$

Specialist $123$

In addition, the following information is presented to you on the operations of the bank.

$$ On average, $35\%$ of the customers use the drive$-$through lanes without leaving their cars.

Customers can perform tasks such as making a withdrawal, paying bills, or depositing a check via

the drive$-$through lanes. There are $3$ identical drive$-$through lanes currently operating and the

average processing time of a customer is $3$ minutes in each of these lanes.

$$ On average, $65\%$ of the customer walk into the bank, and $60\%$ of walk$-$in customer prefer talking

to a bank teller and the remaining $40\%$ prefer the ATM, which is located inside the store. There

are $5$ bank tellers and each of them services a customer in $10$ minutes on average. There are $3$

ATMs, and it takes $6$ minutes on average for a customer to complete service via ATM.

$$ After talking to a bank teller, $20\%$ of the customers are directed to a specialist because the bank

tellers cannot perform operations such as opening a new account or applying for a credit card.

There is $1$ specialist in the bank, and it takes an average of $23$ minutes for a specialist to complete

the service for a customer.

The above description of processes is provided as a diagram below for convenience. The number of

service providers per resource and processing time are given in each diagram block.

BUSI $403$ Problem Set B

Spring $2024$ Due: $1/30/2024$; $11$:$59$ PM

$2$

The manager of the bank is interested in the following questions:

Notes: Please provide final answers of customer arrival per hour with integer numbers. For example, if you

calculated $2\mathrm{.}45$ customers per hour, please write $2$ customers per hour; If you calculated $2\mathrm{.}52$ customers

per hour, please write $3$ customers per hour.

a$.$ What is the capacity of each resource in the bank $($drive$-$through lanes, tellers, ATM, and specialist$)$

in number of customer$-$arrivals per hour?

b$.$ What is the system capacity of the bank in number of customer$-$arrivals per hour? Identify the

bottleneck$($s$).$ What is the slack of each resource in total number of customer $-$arrivals per hour?

c$.$ If the bank can add $2$ additional units of resource at the current bottleneck step, what would be

the new system capacity and bottleneck$($s$)?$