Donna Shader, the Winter Park Hotel manager, is considering restructuring the front desk to reach an optimum staff efficiency and guest service level. At present, the hotel has four clerks on duty, each with a separate waiting line, during the peak check-in time of 3:00 PM to 5:00 PM Observation of inter-arrival time during this time show that an average inter-arrival time is 1.5 minute (although there is no upward limit on the number that could arrive at any given time). An average of 12 customers can be served per hour for the front-desk clerk to register each guest. Assuming that inter-arrival times and service times are exponential.

Ms. Shader is considering a new plan for improving quest service by reducing the length of time the quest spends waiting in line. The new plan is to implement a single-line system. All guests could form a single waiting line to be served by whichever of four clerks became available. This option would require sufficient lobby space for what could be a substantial queue.

The clerk is paid $25 per hour, but because of lost goodwill and sales, Winter Park Hotel's losses about $ 10 per hour of customer time spent waiting for the clerk to register each guest.

Hint: Example

If 210 guests arrive per hour and there are three three-desk clerks, then

1. Under the current system: arriving rate of each service person is 210/3 = 70.
2. Under New System: Arriving rate is 210 per hour

Problem:

A. Determine Po and the average amount of time (W: Minutes) that a guest spends checking in.

I. Current Plan: Po= W=

II. New Plan: Po= W=

B. What is the total cost? (Hint: TC= LqCw+SCs)

Current Plan=

New Plan =

C. What is your reccomendation? Why?

Please show work, thank you!