A Queueing and Facility Design Case by
Production and Operations Management: An Applied Modern Approach |
This case is intended to be the basis for a business analysis and
class discussion rather than to illustrate either effective or
ineffective handling of a business situation. Companies and
characters are fictitious and are not intended to represent actual
companies or people.
Copyright 1997 by Joseph Martinich. All rights reserved. No part
of this publication may be reproduced, stored in a retrieval system,
or transmitted in any form or by any means without the permission of
Joseph Martinich or the distributor, John Wiley & Sons, 605 Third
Ave., New York, NY 10158. Printed in the U.S.A. |
The BackgroundCurrent OperationsLunchtime is the busiest period for the cafeteria, and in a typical day the cafeteria will serve 3500-5000 customers for lunch (ranging from purchase of a beverage to a complete meal). The lunch period runs from 11:00 a.m. to 2:00 p.m., with the heaviest volume occurring between 11:30 a.m. and 1 p.m.. (Table 1 gives the average customer volume for each half-hour period during a ten-day period, along with the average number of customers in line.) During most of this period the cafeteria uses all ten of its check-out stations. Each station is staffed by a cashier who has an electronic cash register, a scale (for weighing foods priced by the ounce, such as salads), a meal-card scanner (students who purchase a food contract are issued a card that can be scanned and the charges deducted from the account without having to use cash), and a long metal track upon which four or five food trays can be placed by waiting customers. Even with all ten check-out stations operating, during peak periods, there are often as many as 25 people in each check-out line and customers can wait more than 10 minutes in line. This waiting creates considerable complaining because hot food becomes cold, cold drinks become warm, and students and faculty have a limited amount of time between classes for lunch. As with most restaurants, it is not cost-effective to use only full-time workers, because the customer demand varies so much during the course of a day. Therefore the cafeteria manager typically uses three full-time cashiers and several part-time cashiers during the course of the day. (There are usually 12-15 part-time cashiers (who are students) on the payroll. Typically seven part-time cashiers are scheduled during lunch and two during dinner. The extra part-time workers are available as replacements when other cashiers have vacations, days off, or are sick.) Two of the full-time cashiers work from 7:00 a.m. to 3:30 p.m. with a half-hour lunch break from 11:00-11:30 a.m., so they can return to their work stations during the peak of the lunch period. The third full-time cashier works from 10:30 a.m. until 7 p.m. with a half-hour lunch break from 2:30-3 p.m. The part-time cashiers all work three hour shifts. The manager establishes a weekly schedule for the part-time workers, taking into account the number of hours each one wants to work each week, their class schedules, requests for days off, and special circumstances that might suggest a larger or smaller number of customers on given days (e.g., during finals week demand patterns change). The manager tries to stagger the starting times for the part-time workers so that during the 11:30 a.m. - 1 p.m. period all ten cashiers are on duty, and during other times fewer than ten are scheduled to match the somewhat lower customer demand. For example, the following schedule for part-time cashiers is typical: |
# of Workers |
Scheduled Shift |
| 10 a.m. - 1 p.m. |
| 10:30 a.m. - 1:30 p.m. |
| 11 a.m. - 2 p.m. |
| 11:30 a.m. - 2:30 p.m. |
With this schedule the number of cashiers working (not counting those on meal-break) during each half-hour period is |
Period | # Working |
10 - 10:30 a.m. |
|
10:30 - 11 a.m. |
|
11 - 11:30 a.m. |
|
11:30 - 12 noon |
|
12 - 12:30 p.m. |
|
12:30 - 1 p.m. |
|
1 - 1:30 p.m. |
|
1:30 - 2 p.m. |
|
2 - 2:30 p.m. |
|
2:30 - 3 p.m. |
|
This schedule allows there to be some extra cashiers available during the hour before and after the lunch period, when demand is too great for the full-time cashiers alone, but is not at a peak level. The ProblemThe manager of the cafeteria is concerned that as the University population continues to grow, the waiting lines and waiting times will get even longer and service will degrade further. The University has scheduled construction of a new Student Union Building that will have greater capacity, but because of the time required to secure funding and perform construction, the building will not be open for 3-4 years. Until then short-term solutions are needed. Several solutions have been recommended by the Student Government Association: (1) Knock down a wall and expand the food service and check-out area into the eating area (which is also in short supply), so as to add three more check-out stations; (2) require all purchases to be made using meal-cards because data that was collected indicated that the average meal-card purchase took 19 seconds while the average cash transaction took 27 seconds; (3) have an express beverage line, so that people who just want to buy a beverage don't have to wait in line so long. The manager of the cafeteria was very receptive to these suggestions, and agreed to investigate the feasibility, benefits, and costs of each. |
Period | Avg. Customer | Avg. Number of |
10 - 10:30 |
|
|
10:30 -11 |
|
|
11 - 11:30 |
|
|
11:30 - 12 |
|
|
12 - 12:30 |
|
|
12:30 - 1 |
|
|
1 - 1:30 |
|
|
1:30 - 2 |
|
|
2 - 2:30 |
|
|
2:30 - 3 |
|
|
* Each cash register records the clock time at which a transaction is completed. The number of customers in each period is the number of customer transactions completed during that half hour. It is not the number of customers who entered the cafeteria or joined a check-out queue during that period. ** This is the total number of customers in all the check-out lines at the beginning of the half-hour period, including those being served by the cashiers. It is not the number in each check-out line. Discussion Questions
Part Two: Additional Data and QuestionsSuppose the cafeteria manager had some students study the check-out operation and collect data on the check-out process. The students studied the operation from 10 a.m. until 3 p.m. every day for 5 days. Table 2 is part of a time-study chart that describes the activities of one cashier for a typical period. |
Activity Description | Time Spent (sec) |
Observe Customer Tray |
|
Receive Cash/Give Change |
|
Wait for Customer to Leave/ |
|
Observe Customer Tray |
|
Receive Cash/Give Change |
|
Wait for Customer to Leave/ |
|
Observe Customer Tray |
|
Scan Meal Card |
|
Wait for Customer to Leave/ |
|
Weigh Customer's Salad |
|
Observe Customer Tray |
|
Scan Meal Card |
|
Wait for Customer to Leave/ |
|
Observe Customer Tray |
|
Answer customer questions |
|
Receive Cash/Give Change |
|
Wait for Customer to Leave/ |
|
Observe Customer Tray |
|
Scan Meal Card |
|
Wait for Customer to Leave/ |
|
Find worker to refill soda machine |
|
Observe Customer Tray |
|
Receive Cash/Give Change |
|
Wait for Customer to Leave/ |
|
Discussion Questions
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Copyright 1997, John Wiley & Sons, Inc.