# Problem

Pages: 6 (1848 words) Published: December 11, 2012
The SM Superstore

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...