Question

1. Courtney Newell, manager of the Silver Park Hotel, is considering how to restructure the front desk to improve guest service during the peak check-in hours of 3:00 to 5:00 p.m.  At present, the hotel has 5 clerks on duty each with a separate waiting line.

Courtney is considering two plans for reducing the guest’s waiting time. The first proposal would be to implement a single waiting line in which guests would be served by whichever of the 5 clerks becomes available first.  Observations of arrivals during the peak check-in time show that a guest arrives on average every 40 seconds.  It takes an average of 3 minutes for the front-desk clerk to register each guest.

The second proposal would designate one employee as a “quick-service” clerk for guests registering under corporate accounts, a market segment that comprises about 30% of Silver Park’s guests.  Since these guests would be pre-registered, it would take an average of only 0.5 minutes for the front-desk clerk to register them.  Under this plan, the non-corporate guests would form a single line and proceed to the first available of the 4 remaining clerks.  The average time for registering a non-corporate guest is 3.4 minutes.

Which proposal should Courtney implement?  Provide appropriate quantitative evidence to support your recommendation.

Answer 1

Solution:

If the number of guests under corporate accounts are more than 128 out of 180( arrival of guests in every 40 seconds between 3 pm and 5 pm), the second plan is suggested. In all other circumstances the first plan is recommended.

The detailed analysis is given as under:

First Plan	Second Plan
No. of guest arrivals is every 40s in 2 hrs.(between 3pm. and 5 pm)=60*60/40 = 180 guests	No. of guest arrivals is = 180 guests
Average time spend by a clerk for registration is 3 minutes. So for 180 guest registration, the total time spend by 5 clerks together = 180*3/5=108/60=1.8 Hours.	One Clerk is designated as ‘quick service’ for corporate accounts to quick register in 0.5 minutes. So let ‘n’ as the total number of guests under corporate accounts Here the time taken = (n * 0.5) = 0.5n minutes Out of guests under corporate accounts, 30% of n belongs to Silver Park’s guests. The average waiting time for registering other guests by the 4 clerks is 3.4 minutes The time spend by these 4 clerks together is ((180-n)*3.4/4 ) minutes Total time taken = 0.5n + 153-0.85n=(153 - 0.35n)/60 = 2.55-0.00583n hours. Therefore if the number of guests under corporate guests is more than 128 out of 180 guest(all), the second plan is preferred.