Chapter $12,$ Case Problem $3.$ County Beverage Drive$-$Thru

County Beverage Drive$-$Thru, Inc., operates a chain of beverage supply stores in northern Ohio. Each store has a single service lane; cars enter at one end of the store and exit at the other end. Customers pick up soft drinks, beer, snacks, and party supplies without getting out of their cars. When a new customer arrives at the store, the customer waits until the preceding customer$$s order is complete and then drives into the store for service.

Typically, three employees operate each store during peak periods; two clerks take and fill orders, and a third clerk serves as cashier and store supervisor. County Beverage is considering a revised store design in which computerized order$-$taking and payment are integrated with specialized warehousing equipment. Management hopes that the new design will permit operating each store with one clerk. To determine whether the new design is beneficial, management decided to build a new store using the revised design.

County Beverage$$s new store will be located near a major shopping center. Based on experience at other locations, management believes that during the peak late afternoon and evening hours, the time between arrivals will follow an exponential probability distribution with a mean of five and one half minutes. These peak hours are the most critical time period for the company; most of their profit is generated during these peak hours.

An extensive study of times required to fill orders with a single clerk led to the following probability distribution of service times:

Service Time $($minutes$)$ Probability

$20\mathrm{.}28$

$30\mathrm{.}20$

$40\mathrm{.}15$

$50\mathrm{.}14$

$60\mathrm{.}10$

$70\mathrm{.}07$

$80\mathrm{.}04$

$90\mathrm{.}02$

Total $1\mathrm{.}00$

In case customer waiting times prove to be too long with just a single clerk, County Beverage$$s management is considering two design alternatives: $(1)$ adding a second clerk to assist the first clerk with bagging, taking orders, and related tasks $($still serving one car at a time as a single$-$server system$),$ or

$(2)$ enlarging the drive$-$through area so that two cars can be served at once $($operating as a two$-$server system$).$ With the two$-$server option, service times are expected to be the same for each server. With the second clerk teaming with the first clerk in the single server design, service times will be reduced and would be given by the probability distribution in the following table:

Service Time $($minutes$)$ Probability

$10\mathrm{.}22$

$20\mathrm{.}34$

$30\mathrm{.}29$

$40\mathrm{.}10$

$50\mathrm{.}05$

Total $1\mathrm{.}00$

County Beverage$$s management would like you to develop a simulation model of the new system and use it to compare the operation of the system using the following three designs:

A $-$ Single$-$server system operated by one clerk

B $-$ Single$-$server system operated by two clerks

C $-$ Two$-$server system operated by two clerks

Management is especially concerned with how long customers have to wait for service. As a guideline, management requires the average waiting time to be less than $1\mathrm{.}5$ minutes.

Managerial Report

Prepare a report that discusses the general development of the simulation model, and make any recommendations that you have regarding the best store design and staffing plan for County Beverage. One additional consideration is that the design allowing for a two$-$server system will cost an additional $$10,000$ to build.

a$)$ Construct a separate simulation model to evaluate the performance of each design alternative.

b$)$ Execute the simulation for $360$ minutes $($representing the peak hours of $4$ p$.$m$.$ to $10$ p$.$m$.).$ You may assume that the system begins empty at $4$ p$.$m$.$ You will want to make several runs with each alternative. Record relevant summary statistics over the simulation runs and use this information to support your final recommendation.