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Safari File Edit View History Bookmarks Window Help mathxl.com Do Homework- Michael Wynder Pearson's MyLab & Mastering-MGMT328.002 Spri.. PROD. AND OPERATIONS MGMT. - SPRING 2018 - MGMT 328.002 Homework: Homework #3 Score: 2 of 5 pts & Problem D.13 Save 12 of 13 (12 complete) N Score: 77.5%, 31 O Question Help Janson's Department Store in Stark, Ohio, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog t are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about 12 per hour. The clerk can take an order in an average of 3.0 minutes. Calls tend to follow a Poisson distribution, and service times tend to be negative exponential. The cost of the clerk is $12 per hour, but because of lost goodwill and sales, Janson's loses about $27 per hour of customer time spent waiting for the clerk to take an order a) The average time that catalog customers must wait before their calls are transferred to the order clerk 4.5 minutes (round your response to two decimal places). two b) The average number of callers waiting to place an order decimal places) 9 callers (round your response to The present total cost per hour (service cost + waiting cost)-sper hour (round your response to two decimal places) Enter your answer in the answer box and then click Check Answer Clear All Check Answer 28

Explanation / Answer

This is a M/M/1 queue system with following parameters

Arrival rate, ? = 12 per hour

Service rate, ? = 1 / service time in hours) = 1/(3/60) = 20 per hour

Cost of server (clerk), Cs = $ 12 per hour

Cost of customer waiting, Cw = $ 27 per hour

a) Average waiting time (Wq) = ?/(?*(?-?)) = 12/(20*(20-12)) = 0.075 hour = 4.50 minutes

b) Average number of callers waiting to place an order, Lq = Wq*? = 0.075*12 = 0.9 callers

The present total cost per hour = Cs + Cw*Lq = 12 + 27*0.9 = $ 36.30 per hour

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