IIE/RA CONTEST PROBLEMS 1CONTEST PROBLEM 1IIE/RA Contest ProblemsFirst Annual Contest: The SM SuperstoreYou have just been hired as a consultant by Sue Model of Sue’s Markets. Although Suehas been in the grocery business for many years with a large chain of small stores, shejust recently opened the first of a new type of store called The SM Superstore. The ideabehind this new concept is to provide a huge store with numerous types of brandsavailable and fast, friendly service. This first store is being used to test the layout andoperating 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 problemstaffing the checkout counters during peak times, which occur from 2 PM to 10 PM. Shehas received many customer complaints about the long lines in front of the checkoutcounters. She has 20 checkouts that she can use, but has not been able to develop anadequate staffing plan to eliminate the long waits. Your consulting firm has been asked todevelop an economical staffing plan that will meet Sue’s requirements.Prior to requesting your services, Sue hired a group of IE students from a localuniversity to collect and analyze data. Some of those data are summarized in thisdocument. Unfortunately, Sue is away on a well-deserved, one-month vacation in theSouth Pacific and cannot be reached. Furthermore, she indicated that she does not wanther store personnel to be bothered by a bunch of consultants asking dumb questions anddisrupting the store’s operation. Thus, no additional information is available, and Suewants 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 preferat most a 2- or 3-minute wait time, but are willing to wait as long as 10 or 12 minutes ifthe store is very busy. Customers with only a few items normally expect a shorter waitingtime. Customers did indicate that if they had to wait longer than 15 or 20 minutes, theymight go to another store the next time. In addition, if the number of customers exceeds4 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 studentshave provided average arrival rates at the checkout lines (in customers per hour) for eachhalf hour of the times under consideration. These rates are as follows:2 IIE/RA CONTEST PROBLEMS Time RateTime Rate2:00 – 2:30 952:30 – 3:00 1003:00 – 3:30 1203:30 – 4:00 1504:00 – 4:30 1604:30 – 5:00 1505:00 – 5:30 1605:30 – 6:00 1106:00 – 6:30 1056:30 – 7:00 957:00 – 7:30 1257:30 – 8:00 1508:00 – 8:30 1558:30 – 9:00 959:00 – 9:30 709:30 – 10:00 60 During the data collection phase, it was assumed that all days were identical so datawere only collected on Monday through Thursday. It now appears that the overall demandon Friday increases about 15%, and the weekend demand is very different. Thus, youshould only be concerned with the weekday staffing.Actual shopping time has a great degree of variability. Customers purchasing fewerthan 10 items generally average about 42 seconds per item, although it takes a minimumof 3 minutes just to travel through the store. Customers who purchase more items average about 34 seconds per item.The number of items per customer is quite variable, but appears to be consistent overtime. A large sample of items per customer was obtained from cash register receipts andcan be found in file IIE_SM_1.dat. The average checkout time per item is about 3seconds, but can vary as much as 25%. About 1.3% of the time a price check will beneeded on an item or a damaged item will need to be replaced. Although the store usesscanners for checkout, customers sometimes request that the price list at the item displaybe checked. The time for this activity is highly variable, but averages about 2.2 minutes.The form of payment depends on the number of items that a customer purchases. Forpurchases of 20 or fewer items, 45% of the customers pay cash, 30% pay by check, and25% pay with a credit card. For purchases of greater than 20 items, the values for thosecategories are 20%, 45%, and 35%, respectively. All payment transaction times appear tofollow a normal distribution, but vary by payment type. Cash payments average 0.95minute, with a standard deviation of 0.17. Check payments for customers with a checkcashing card average 1.45 minutes, with a standard deviation of 0.35. With no checkcashing card (27% of the time), the supervisor must approve the check, which requiresanother 0.95 minute, with a standard deviation of 0.15. Credit card payments average1.24 minutes, with a standard deviation of 0.21.Bagging times average about 1.25 seconds per item, but can vary as much as 20%.Customers have a greater preference, 63%, for plastic bags rather than paper. If a baggeris not available, the cashier will bag the groceries after payment is made. About 30% ofthe time the customer will help. The time does not appear to be dependent upon who isdoing the bagging. Baggers may be assigned to a single aisle, to multiple aisles, or maysimply move among all aisles as required.IIE/RA CONTEST PROBLEMS 3Sue’s employees for cashier and bagging activities are mostly part-time people. Cashiers are paid an average of $7.25 per hour, and baggers are paid an average of $5.50 perhour. There are several rules that must be followed in staffing with part-time employees.Any part-time person must be scheduled for a minimum of 3 hours and a maximum of 5hours. Cashiers are generally not asked to work as baggers, and baggers are not allowedto work as cashiers.Clearly, one can make all customers happy almost all the time by keeping all thecheckouts completely staffed all the time. However, the cost to implement this strategywould be prohibitive. Ideally, a staffing schedule would provide minimal waiting time ata minimum cost. Although Sue is expecting a single schedule, she did note at the lastmeeting that she expects demand to change over time. So, she might be interested in howand when to adjust her schedule as the demand changes.Sue is looking forward to receiving your recommendations.
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