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 department 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

11

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

$10

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.

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 department 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 11 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 $10 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 = minutes (round your response to two decimal places). The total present cost per hour =$35.00 per hour (Response should be rounded to nearest 2nd decimal place) Janson's is considering adding a second clerk to take calls. This would chan the queuing mode to M/M/s After adding the second clerk, the average time that catalog customers must wait before their calls are transferred to the order clerk = minutes (Response should be rounded to nearest 2nd decimal place) After adding a second clerk to take calls and assuming that the store's cost would be the same $8 per hour. The total cost =$17.78 per hour (Response should be rounded to nearest 2nd decimal place) By hiring the second clerk, the total per hour cost change for Janson's =$ per hour (Response should be rounded to nearest 2nd decimal place) The number of customers served per hour ()=30 per hour (Response should be rounded to nearest 2nd decimal place) For M/M/1 queuing model, the relationship for finding the Average Time in the Queue is: Wq=() The average time that catalog customers must wait before their calls are transferred to the order clerk = minutes (Response should be rounded to nearest 2nd decimal place) For M/M/1 queuing model, the relationship for finding the Average Number in the Queue is: Lq=()2 The average number of callers waiting to place an order = callers (Response should be rounded to nearest 2nd decimal place) The per hour total cost = Service cost + Waiting cost Where waitina cost =# of arrivals per hour waitina cost per hour averaae