Case Problem 3
Company A operates a chain ofdrinks supply stores. Each store has a single server lane; cars enter at one end of the store and exit at the other end. Customers pick up drinks, beer, and snackswithout 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; 2 clerks take and fill orders, and a 3rd clerk serves as cashier and store supervisor. They are considering a revised store design in which computerized order-taking and payment are integrated with specialized warhousing equipment. Senior staffare hopeful this new design will permit operating each store with one clerk. To determine whether the new design is beneficial, theydecided to build a new store using the revised design.
The new store will be located near a major shopping centre. Based on experirence at other locations, they believe that during the peak late afternoon and evening hrs, the time between arrivals will follow an exponential probability distribution with a mean of six minutes. The peak hours are the most critical time peiriod; most of their profit is generated during these peak hours.
An extensive study of time required to fill orders with a single clerk led to the following probability distribution of service times:
| Service Time
(minutes) |
Probability |
| 2 | 0.24 |
| 3 | 0.20 |
| 4 | 0.15 |
| 5 | 0.14 |
| 6 | 0.12 |
| 7 | 0.08 |
| 8 | 0.05 |
| 9 | 0.02 |
| Total | 1.00 |
In case customer waiting times prove to be too long with just a single clerk, they are considering two design alternatives:
- 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
- Enlarging the drive-trough 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 a 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 |
| 1 | 0.20 |
| 2 | 0.35 |
| 3 | 0.30 |
| 4 | 0.10 |
| 5 | 0.05 |
| Total | 1.00 |
They would like you to develop a spreadsheet simulation model of the new system and use it to compare the operation of the system using the following three designs:
| Design | |
| A | Single-server system operated by one clerk |
| B | Single-server system operated by two clerks |
| C | Two-server system operated by two clerks |
They are concerned with how long customers have to wait for service. As a guideline, they require the average waiting timeto be less than1.5 minutes.
Prepare a draft, point form document that discusses the general development of the spreadsheet simulation model, and make at least 3 recommendations that you have regarding the best store design and staffing plan. One additional consideration is that the design allowing for a two-server system will cost an additional $10,000 to build.
- Construct a separate simulation model to evaluate the performance of each design alternative.
- Execute the simulation for 360 minutes (representing the peak hours of 4pm to 10pm). You may assume that the system begins empty at 4pm. You may want to make more than one run with each alternative. Record relevant summary statistics over the simulation runs and use this information to support your final recommendations.
Source:
Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D., Cochran, J.J., Fry, M.J., & Ohlmann, J.W. (2018). An introduction to management science: Quantitative approaches to decision making (15th ed.). Boston, MA: Cengage Learning.
