Introduction

Donna Shader, manager of 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 PM to 5:00 PM. Observations of arrivals during this time showed that an average of 90 guest arrived each hour (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. Donna is considering three plans for improving guest service by reducing the length of time each guest spends waiting in line. The first proposal would designate one employee as a quick service clerk for guest registry under corporate accounts, a market segment that fills about 30% of all occupied rooms. Because corporate guest preregistered, the registration takes just 2 minutes.

With these guest separated from the rest of the clientele, the average time for registering a typical guest would climb to 3.4 minutes. Under plan one, noncorporate guest which use any of the remaining four lines. The second plan is to implement a single-line system. All guest could form a single waiting line to be served by whichever of the five clerks becomes available. This option would require sufficient lobby space for what could be a substantial queue. The third proposal involves using an automatic telomere teller machine (ATM) for check-ins. This ATM would provide approximately the same service rate as a clerk would.

Given that initial use of the technology might be minimal, Shader estimates estimated that 20% of customers, primarily frequent guest, would be willing to use the machines. (This might be a conservative estimate if the guest receive direct benefit from using the ATM, as bank customers do. Citibank reports that 95% of its Manhattan customers use ATMs.) Donna was set up a single queue for customers who prefer human check-in clerks. This would be served by the five clerks, although Donna is hopeful that the machine will allow a reduction to four.

Discussion Questions

1. Determine the average amount of time that a guest spends checking in. How would this change under each of the stated options? The current system utilizes five clerks with five individual lines. The average arrival rate for guests is 90 per hour for the five lines. It can be assumed that the arriving guests will split evenly among the five lines which will reduce the arrival rate for each line to 1/5th the overall arrival rate (Arrival time (λ) = 90/5 = 18 per hour). The provided average service rate is one guest every 3 minutes with equates to 20 guests per hour (Service rate (µ) = one every 3 minutes = 20 per hour). Inputting these data into QM for Windows with the number of servers set to 1 since the calculation is based on a single line provides the following results.

The results table shows that the average amount of time a guest spends checking in is 0.5 or 30 minutes. Donna wants to reduce this time so she developed three plans. The first plan involves separating the corporate guests into a single separate line since they check in faster than the standard guests. This plan assumes that 30% of the arriving guests (λ = 0.3*90 = 27 per hour) fall into the corporate category and that since the corporate guests are preregistered their check-in will only take 2 min. on average (µ = 60/2 = 30 per hour). Inputting these data into QM for Windows with the number of servers set to 1 since the calculation is based on a single corporate line provides the following results.

The results table shows that the average amount of time a guest spends checking in for the first plan is 0.33 or 20 minutes for the corporate guests. This plan would also spread standard guest arrivals among the remaining four lines (λ =63/4 = 15.75 per hour) and increase the average check-in time to 3.4 minutes (µ = 60/3.4 = 17.65 per hour). Inputting these data into QM for Windows with the number of servers set to 1 since the calculation is based on a single line provides the following results.

The results table shows that the average amount of time a guest spends checking in for the first plan is 0.53 or 31.58 minutes for the standard guests. The overall average check-in time for the first plan is 0.3(20) + 0.7(31.6) = 28.1 minutes.

The second plan to reduce the check-in time involves implementing a single-line system in which all arriving guests form a single queue and are served by the five clerks as they become available. The arrival rate (λ) for this plan is 90 guests per hour, the service rate (µ) is 20 guests per hour, and the number of servers is 5. Inputting these data into QM for Windows provides the following results.

The results table shows that the average amount of time a guest spends checking in for the first plan is 0.13 or 7.57 minutes. The third plan involves using an automated teller machine (ATM) for check-ins providing approximately the same service rate as a clerk (µ = 20 per hour). The estimate is that this ATM would serve about 20% of arriving customers while the remainder of the guests would form into a single queue and be served by the five clerks (eventually four hopefully). Using QM for Windows to solve the ATM queuing problem (λ = 0.2*90 = 18 per hour, µ = 20 per hour, servers = 1) provides the following results.

The results table shows that the average amount of time a guest spends checking in is 0.5 or 30 minutes when using the ATM. The remaining guests (λ = 0.8*90 = 72 per hour) all queue in a single line and are served by five servers at a service rate (µ) of 20 per hour. Inputting these data into QM for Windows provides the following results.

The results table shows that the average amount of time a guest spends checking in is 0.06 or 3.88 minutes when five clerks are available. The ATM and five clerk plan provides an average time of 0.2*30+0.8*3.88 = 9.1 min. Donna however hopes to reduce the number of clerks to four after adding the ATM so the number of servers should also be changed to four, providing the following results.

The results table shows that the average amount of time a guest spends checking in is 0.15 or 8.91 minutes when four clerks are available. The ATM and four clerk plan provides an average time of 0.2*30+0.8*8.91 = 13.1 min. 2. Which option do you recommend?

Based on the check-in times calculated for discussion questions 1 the best choice would be to implement the second plan that utilizes five clerks and a single queue since it provides the shortest check-in time. It is important however to note that as customers became familiar with the ATM more would chose that option possibly changing the dynamics of the problem. As the utilization of the ATM increases it may be prudent to revisit the problem and investigate the effects of multiple ATMs if they prove to be less expensive than clerks.

References

Hanna, M.E., Rneder, B., Stair, R. M., (2012). Quantitative Analysis for Management (11th Ed.). Upper Saddle River, NJ: Prentice Hall. N.A. (N. D.). Winter Park Hotel. In Hanna, M. E., Render, B., Stair, R. M., Quantitative Analysis for Management (11th Ed., p. 531). Upper Saddle River, NJ: Prentice Hall.

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