Scenario # 1: Without the bagger Customer Arrival Rate () Cashier Service Rate (
ID: 415321 • Letter: S
Question
Scenario # 1: Without the bagger Customer Arrival Rate () Cashier Service Rate () Avg. Customer Wait Time in Cashier Queue (W_q) Cost of Waiting Time per Hour for the Grocery Store Scenario # 2: With the bagger Customer Arrival Rate () Cashier Service Rate () Avg. Customer Wait Time in Cashier Queue (W_q) Cost of Waiting Time per Hour for the Grocery Store Cost of bagger Hire the bagger or not? A small grocery store has a single checkout line. On Saturdays, customers arrive at the checkout on an average of one every 8 minutes. The cashier takes an average of 6 minutes to process a single customer. We assume that the service time is randomly distributed, and the customers arrive randomly. The store's owner believes that the amount of time that a customer has to wait hurts his business; he estimates that waiting time costs him S20 per hour in lost business. In order to speed up service, the owner is considering hiring a teenager to bag the groceries at $6 per hour. With the addition of the bagger, the cashier will be able to process a customer in an average of 4.5 minutes. Should the bagger be hired?Explanation / Answer
Scenario 1:
Arrival rate (A) = 8 minutes = 60/8 per hour = 7.5
Service rate (S) = 6 minutes = 60/6 per hour = 10
Average waiting time = A/(S*(S-A)) = 7.5/(10*(10-7.5)) = 0.3 hours
Cost of waiting time = Average waiting time*waiting time cost = 3/10*20 = 6$
Scenario 2:
Arrival rate (A) = 8 minutes = 60/8 per hour = 7.5
Service rate (S) = 4.5 minutes = 60/4.5 per hour = 40/3
Average waiting time = A/(S*(S-A)) = 7.5/(40/3*(40/3-7.5)) = 0.9684 hours
Cost of waiting time = Average waiting time*waiting time cost = 0.9684*20 = 1.93 $
Cost of Bagger = 6$
Should not hire as the total cost waiting and of bagger is 1.93+6 = 7.93$ which is higher than total cost of waiting in scenario 1
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