Ty Webb, manager of the Philadelphia Hotel, is considering how to restructure the front desk to reach an optimum level of staff efficiency and guest service. At present, the hotel has five clerks on...

Ty Webb, manager of the Philadelphia Hotel, is considering how to

restructure the front desk to reach an optimum level of staff efficiency

and guest service. At present, the hotel has five clerks on duty, each

with a separate waiting line, during the peak check-in time of 3:00pm to

5:00pm. Observation of arrivals during this time shows that an average

of 90 guests arrive each hour according to a Poisson process (although

there is no upward limit on the number that could arrive at any given

time). It takes an average of 3 minutes for the front-desk clerk to

register each guest. The service times by the clerks are exponentially

distributed.Mr. Webb is considering three plans for improving

guest service by reducing the length of time guests spend waiting in

line. The first proposal would designate one employee as a quick-service

clerk for guests registering under corporate accounts, a market segment

that fills about 30% of all occupied rooms. Because corporate guests

are preregistered, their registration takes just 2 minutes on the

average and also follows an exponential distribution. With these guests

separated from the rest of the clientele, the average time for

registering a typical guest would climb to 3.4 minutes. Under plan 1,

non corporate guests would choose any of the remaining four lines.The

second plan is to implement a single-line system. All guests could form

a single waiting line to be served by whichever of the five clerks

became available. This option would require sufficient lobby space for

what could be a substantial queue.The use of an automatic teller

machine (ATM) for check-ins is the basis of the third proposal. This

ATM would provide approximately the same service performance as would a

clerk, however, the ATM’s service time would be a constant 3 minutes per

guest. Given that initial use of this technology might be minimal, Webb

estimated that 20% of customers, primarily frequent guests, would be

willing to use the machines. This might be a conservative estimate if

the guests perceive direct benefits from using the ATMs. Mr. Webb would

set up a single queue for customers who prefer human interaction at

check-in. This queue would be served by the five clerks, although Webb

is hopeful that the machine will allow a reduction to four.Determine

the average amount of time that a guest spends checking in. How would

this change under each of the stated options? Which option would you

recommend?