Reference no: EM132275244

Sharp Discounts Wholesale Club has two service desks (call them A and B) with one server at each desk. There is one desk at each entrance of the store. Customers arrive at each service desk at an average of one every six minutes following a Poisson distribution. The average service time at each service desk is 4 minutes per customer following the exponential service distribution.

A) Sharp is now considering consolidating its two service desks into one location, staffed by two clerks. The clerks will continue to work at the same individual speed of 4 minutes per customer.

How many customers, on average, are waiting in line?

How much total time does a customer spend at the service desk?

B) Do you think the Sharp Discounts Wholesale Club should consolidate the service desks? Explain and your discussion must consider both the economics and the customer service aspects of this waiting line operation. There would be no extra cost for moving the two operations to one operation. The clerks would continue to be paid the same as they were paid at the single desk operation.   

C) Suppose that it is no longer required that the clerks be paid the same under either operation. Considering the consolidated operation and based on past work experience one clerk is paid $45 per hour and the second clerk is paid $35 per hour. The estimated cost to Sharp for time a customer is at the service desk either waiting or being helped is $0.50 per minute. For the two-service desk operation assuming that each clerk will be paid the same hourly rate, what is the maximum hourly rate that each of the clerks can be paid under this two service desk operation so that the total cost of the operation is the same for either arrangement? Assume that there is no cost for consolidating the service.