Question:

Sharp Discounts Wholesale Club has two service desks 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 216 seconds per customer following the exponential service distribution.

a)  How many customers, on average, are waiting in line in front of each service desk?

b)  How much total time does a customer spend at the service desk either waiting for help or receiving help?

c)  Looking at only one of the service desks, what is the probability that there are at least three customers waiting in line when the next individual arrives at this service desk?

d) 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 216 seconds per customer. 

• How many customers, on average, are waiting in line?
• How much total time does a customer spend at the service desk?

e)  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.

f)  Suppose that it is no longer required that the clerks be paid the same under either operation.  The clerks under the consolidated operation are each paid $30 per hour and the estimated cost to Sharp for time a customer is at the service desk either waiting or being helped is $1 per minute.  What is the maximum hourly rate that each of the clerks can be paid under the 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.