Q1. Sharp Discounts Wholesale Club consists of two service desks with one server at every desk. There is one desk at each entrance of store. Customers arrive at each service desk at an average of one each 6 minutes following a Poisson distribution. The average service time at every service desk is 216 seconds per customer following the exponential service distribution.
a) How many customers, on average, are waiting in the line in front of every service desk?
b) How much total time does a customer expend at the service desk either waiting for the help or receiving help?
c) Looking at just one of the service desks, determine the probability that there are at least four customers already waiting in line whenever the next individual arrives at service desk?
d) Sharp is now considering consolidating its two service desks to one location, staffed by two clerks. The clerks will carry on working at the similar individual speed of 216 seconds per customer.
- Determine the number of customers, on average, is waiting in line?
- How much total time does a customer spend at service desk?
e) Do you suppose the Sharp Discounts Wholesale Club must consolidate the service desks? Describe and your discussion should consider both the economics and the customer service features of this waiting line operation. There would be no additional cost for moving the two operations to one operation. The clerks would continue to be paid similar as they were paid at single desk operation.
f) Assume that it is no longer needed that the clerks be paid similar under either operation. The clerks beneath the consolidated operation are each paid $40 per hour and the estimated cost to Sharp for time a customer is at service desk either waiting or being helped is $1 per minute. Describe the maximum hourly rate that each of the clerks can be paid in the two service desk operation so that the total cost of operation is similar for either arrangement. Suppose that there is no cost for consolidating the service.