An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 1

COUNTY BEVERAGE DRIVE-THRU
Country Beverage Drive-Thru, Inc., operates a chain of beverage supply stores in Northern Illinois. 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.
Country Beverage's new store will be located near a major shopping center. Based on experience at other locations, managements believes that during the peak late afternoon and evening hours, the time between arrivals follows an exponential probability distribution with a mean of six 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:
In case customer waiting times prove too long with just a single clerk, Country Beverage's management is considering two alternatives: add a second clerk to help with bagging, taking orders, and related tasks, or enlarge the drive-thru area so that two cars can be served at once (a two-channel system). With either of these options, two clerks will be needed. With the two-channel option, service times are expected to be the same for each channel.
With the second clerk helping with a single channel, service times will be reduced. The following probability distribution describes service times given that option:
Country Beverage's management would like you to develop a spreadsheet simulations model of the new system and use it to compare the operation of the system using the following three designs:
Management is especially concerned with how long customers have to wait for service. Research has shown that 30% of the customers will wait no longer than 6 minutes and that 90% will wait no longer than 10 minutes. As a guideline, management requires the average waiting time to be less than 1.5 minutes.
Managerial Report
Prepare a report that discusses the general development of the spreadsheet simulation model, and make any recommendations that you have regarding the best store desist, and S. King plan for County Beverage. One additional consideration is that the design allowing for a two-channel system will cost an additional $10,000 to build.
1. List the information the spreadsheet simulation model should generate so that a decision can be made on the store design and the desired number of clerks.
2. Run the simulation for 1000 customers for each alternative consider. You may want to consider making more than one run with each alternative. [Note: Values from an exponential probability distribution with mean µ can be generated in Excel using the following function: = - µ* LN(RAND()).]
3. Be sure to note the number of customers County Beverage is likely to lose due to long customer waiting times with each design alternative.