The Schmedley Discount Department Store has approximately 300 customers shopping

Question

The Schmedley Discount Department Store has approximately 300 customers shopping in its store be¬tween 9 a.m. and 5 P.M. on Saturdays. In deciding how many cash registers to keep open each Satur¬day, Schmedley’s manager considers two factors: customer waiting time (and the associated waiting cost) and the service costs of employing additional checkout clerks. Checkout clerks are paid an average of $8 per hour. When only one is on duty, the wait¬ing time per customer is about 10 minutes (or 1/6 hour); when two clerks are on duty, the average checkout time is 6 minutes per person; 4 minutes when three clerks are working; and 3 minutes when four clerks are on duty. Schmedley's management has conducted cus¬tomer satisfaction surveys and has been able to estimate that the store suffers approximately $10 in lost sales and goodwill for every hour of customer time spent waiting in checkout lines. Using the information provided, determine the optimal number of clerks to have on duty each Saturday to minimize the store's total expected cost.

Explanation / Answer

This posting contains two problems on Queuing:M/M/s model. First problem is that of determining optimal no of clerks by comparing waiting time and cost and the hourly salary of clerks. Second problem is also that of comparing no of Tellers in a bank and determining optimal no of tellers based on given costs and waiting times.

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