# Question: M M Sprout a catalog mail order retailer has one

M. M. Sprout, a catalog mail order retailer, has one customer service representative (CSR) to take orders at an 800 telephone number. If the CSR is busy, the next caller is put on hold. For simplicity, assume that any number of incoming calls can be put on hold and that nobody hangs up in frustration over a long wait. Suppose that, on average, one call comes in every 4 minutes and that it takes the CSR an average of 3 minutes to take an order. Both interarrival and activity times are exponentially distributed. The CSR is paid \$ 20 per hour, and the telephone company charges \$ 5 per hour for the 800 line. The company estimates that each minute a customer is kept on hold costs it \$ 2 in customer dissatisfaction and loss of future business. a. Estimate the following:
• The proportion of time that the CSR will be busy
• The average time that a customer will be on hold
• The average number of customers on line
• The total hourly cost of service and waiting
b. More realistically, suppose that M. M. Sprout has four telephone lines. At most, therefore, three callers can be kept on hold. Assume, too, that any caller who gets a busy signal because all four lines are occupied simply hangs up and calls a competitor. M. M. Sprout’s average loss, in terms of current and potential future business, is \$ 100 per frustrated caller. Estimate the total cost of the following:
• Providing service
• Waiting
• Average hourly loss incurred because customers cannot get through
c. Suppose that M. M. Sprout is considering adding another line in order to reduce the amount of lost business. If the installation cost is negligible, can the addition of one line be justified on economic grounds? How would it affect customer waiting time?
d. In addition to adding another line, suppose M. M. Sprout wants to hire one more CSR to reduce waiting time. Should the firm hire another CSR?

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