Wendys opens a drive through with one cashier and one food preparer. Customers w

Question

Wendys opens a drive through with one cashier and one food preparer. Customers will first enter the "place order" line to meet the cashier and then enter the "pick up" line to get the food from the food preparer. Currently, the cashier can take an order in exactly 4 minutes and the food preparer can prepare an order in exactly 3 minutes. During an hour, 12 customers arrive on average. The inter-arrival times are exponentially distributed.

a) What is the average length of the "place order line"? What is the average length of the "pick up line"?

b) What is the average number of customers in the drive through area?

c) The manager feels that the cashier has slowed down the process and send him to a strict training class. After the class, the cashier can take an order in exactly 2 minutes. What is the capacity of the system now?

d) After the training, what is the average length of the "place order" line?

Explanation / Answer

It takes the cashier 4 minutes to serve one customer, and the cashier can serve 15 customers /hour. 12 = = 0.8 15 S = 1, Ca = 1, Cs = 0 2 ( s +1) C a2 + C s2 = 1.6 customers Nl = 1- 2 Since a customer can enter the "pick-up" line only after finishing the "place order" line and it always takes longer to place an order, no customers will wait in the "pick-up" line. ============================================================================================================================================================================================ b. What is the average number of customers in the drive through area? On average, we have 1.6 customers wait to take the order, 12/15=0.8 customers are with the cashier, and 12/(60/3)=0.6 customers are with the food preparer. In total, we have on average 3 customers in the restaurant. ============================================================================================================================================================================================ c. The manager feels that the cashier has slowed down the process and send him to a strict training class. After the class, the cashier can take an order in exactly 2 minutes. What is capacity of the system now? It takes the cashier 2 minutes to serve one customer, and the cashier can serve 30 customers /hour. It takes the food preparer 3 minutes to serve one customer, and the food preparer can serve 20 customers /hour. We see the bottleneck shifting and the new capacity of the system is 20 customers per hour. ============================================================================================================================================================================================ d. After the training, what is the average length of the "place order" line? It takes the cashier 2 minutes to serve one customer, and the cashier can serve 30 customers /hour. 12 = 0.4 = 30 S = 1, Ca = 1, Cs = 0 2( s +1) C a2 + C s2 = 0.133 customers Nl = 1- 2 e

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