Donna Shader, manager of the Winter Park Hotel, is considering how to restructur

Question

Donna Shader, manager of the Winter Park 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 3:00 P.M. to 5:00 P.M. Observation of arrivals during this time show that an average of 90 guests arrive each hour (although there is no upward limit on the number that could enter at any given time). It takes an average of 3 minutes for the front desk clerk to register each guest. Ms. Shader is considering three plans for improving quest service by reducing the length of time quest 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. 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 noncorporate guests would choose any of the remaining four lines The second plan is to implement a single-line system. All guests could from a single waiting line to be served by whichever of 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 clerks is the basis of the third proposal. This ATM would provide approximately the same service rate as would a clerk. Given that initial use of this technology might be minimal, Shader estimated that 20% of customers, primarily frequent guest, would be willing to use the machines. (This might be a conservative estimate if the guests perceive direct benefits from using the ATM, as bank customers do. Citibank reports that some 80% of its Manhattan customer uses its ATMs.) Ms Shader would set up a single queue for customers who prefer human check-in clerks, and the four clerks would serve in addition to ATM

Explanation / Answer

Current data:

90 guests 5 desks=90/5=18

it takes 3 minutes for processing each customer so, 60/3=20

1/(20-18)=0.5hr i.e., 60min*0.5=30 minutes

Th average amount of time that a guest spends checking in the current mode is 30 minutes.

Plan 1:

30% of the guests will be preregistered so

30%of 90=27 guests

these take only 2 minutes therefore 60/2=30 guests

The average wait time would be 1/(30-27)=0.33hr or 19.8 minutes  

remaining guests are 60, these go into 4lines; 60/4=15 guests per hour.

The averageprocessing time for them is 3.4 minutes or 0.057 or 17.54 per hour.

The average wait time is 1/(17.54-15)=0.393 hr or 23.62minutes

The mean time for all guests will be 0.3(19.8 minutes)+0.7(23.62)=22.474 minutes

similarly you can arrive at the other wait times...

hint: proposal 2 is better than any other alternative

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