Supermarket cashier management, A supermarket is open 24
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Supermarket cashier management, A supermarket is open 24/7 and operates in 3 shifts: first shift from 8:00 A.M. to 4:00
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Supermarket cashier management, A supermarket is open 24/7 and operates in 3 shifts: first shift from 8:00 A.M. to 4:00 P.M., second shift from 4:00 P.M. to 12:00 A.M., and third shift from 12:00 A.M. to 8:00 A.M. Customers arrive according to a Poisson process with shift-dependent arrival rates, and their shopping times (excluding checkout) are iid but shift dependent. Consequently, the supermarket management assigns variable numbers of cashiers per shift. The arrival, shopping, and cashier parameters are displayed in the following table. After shopping, customers queue up in a single line for checkout. Checkout times of customers are iid, but shopping-time dependent as follows: Shift number Arrival Rate (customer per minute) Shopping Time Distribution (minutes) Number of Cashier 1 2 3 16.8 24 0.7 Unif.(5,15) Unif.(15,40) Unif.(1,5) 2 4 1 a customer's checkout time is 2 minutes plus a random fraction of its shopping time, where the fraction is iid triangular between 20% and 30%, with a most likely value of 25%. Finally, a customer is assigned to the shift during which it departs from the supermarket (note that a customer may arrive during one shift and depart during a subsequent one). a. Develop an Arena model of the supermarket, and simulate it for 30 days. b. Compute the average, variance, and squared coefficient of variation of customer waiting times for a cashier (excluding checkout processing times). c. What is the per-shift average sojourn time of customers in the supermarket? d. What are the overall instant and scheduled cashier utilizations?
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