You have just been hired as a consultant by Sue Model of Sue’s Markets. Although Sue has been in the grocery business for many years with a large chain of small stores, she just recently opened the first of a new type of store called The SM Superstore. The idea behind this new concept is to provide a huge store with numerous types of brands available and fast, friendly service. This first store is being used to test the layout and operating procedures for a large chain of superstores that Sue expects to build. The first store has been open for six months, and Sue is still having a problem staffing the checkout counters during peak times, which occur from 2 PM to 10 PM. She has received many customer complaints about the long lines in front of the checkout counters. She has 20 checkouts that she can use, but has not been able to develop an adequate staffing plan to eliminate the long waits. Your consulting firm has been requested to develop an economical staffing plan that will meet Sue's requirements. Prior to requesting your services, Sue hired a group of IE students from a local university to collect and analyze data. Some of those data are summarized in this document. Unfortunately, Sue is away on a well-deserved, one-month vacation in the South Pacific and cannot be reached. Furthermore, she indicated that she does not want her store personnel to be bothered by a bunch of consultants asking dumb questions and disrupting the store's operation. Thus, no additional information is available, and Sue wants your report on her desk when she returns from vacation. After reading the report, she may decide to ask for additional work. An informal survey was conducted to determine what wait times customers expect — the time customers wait in line before reaching the cashier. Most customers would prefer at most a 2- or 3-minute wait time, but are willing to wait as long as 10 or 12 minutes if the store is very busy. Customers did indicate that if they had to wait more minutes, they might go to another store the next time. In addition, if the number of customers exceeds 4 or 5 per lane, the congestion starts to interrupt the other shoppers.
Although the customer arrival rate has a great degree of variability, the IE students have provided average arrival rates at the checkout lines (in customers per hour) for each half hour of the times under consideration. These rates are as follows: Time Rate Time Rate
2:00-2:30 95 6:00-6:30 105
2:30 - 3:00 100 6:30 - 7:00 95
3:00-3:30 120 7:00-7:30 125
3:30-4:00 150 7:30-8:00 150
4:00-4:30 160 8:00-8:30 155
4:30-5:00 150 8:30-9:00 95
5:00-5:30 160 9:00-9:30 70
5:30-6:00 110 9:30- 10:00 60
During the data collection phase, it was assumed that all days were identical. Actual shopping time has a great degree of variability. Customers generally average about 35 seconds per item, although it takes a minimum of 3 minutes just to travel through the store. The number of items per customer is quite variable, but appears to be consistent over time. Previous studies show that the number of articles per costumer follows an exponential distribution with a mean of 20. The average checkout time per item is about 3 seconds, but can vary as much as 25%. The form of payment depends on the number of items that a customer purchases. For purchases of 20 or fewer items, 45% of the customers pay cash, 30% pay by check, and 25% pay with a credit card. For purchases of greater than 20 items, the values for those categories are 20%, 45%, and 35%, respectively. All payment transaction times appear to follow a normal distribution, but vary by payment type. Cash payments average 0.95 minute, with a standard deviation of 0.17. Check payments average 1.45 minutes, with a standard deviation of 0.35. Credit card payments average 1.24 minutes, with a standard deviation of 0.21.
Bagging times average about 1.25 seconds per item, but can vary as much as 20%. If a bagger is not available, the...