Hotel room-inventory management: an overbooking model. (Hotel Management).

The gentle art of overbooking can be augmented with a carefully constructed computer model--but human expertise will always be necessary.

With their insistence that guests guarantee room reservations with a credit card, hotel operators have taken great strides to address the problems caused by no-shows, both for individual travelers and group-related guests. Moreover, some hotels are attempting to address the other end of the no-show problem, by imposing early departure penalties. Nevertheless, no-shows and early departures still cost hotels money. The credit-card guarantee compensates hotels for one night's stay in the case of a no-show, but the hotel still needs to make up for a revenue loss if that no-show guest had a multiple-night reservation.

Because of the prospect of no-shows and early departures, the hotel manager almost inevitably must engage in some level of overbooking to help ensure that those potentially unsold rooms are filled. As we all know, however, hoteliers who overbook will have to walk guests after the hotel is full. As we outline below, many researchers have investigated ways to untangle this Gordian knot of no-show guests, overbooked rooms, and walked guests. In this article we propose a model that we have developed to assist rooms managers in establishing an optimal level of overbooking. We show the model's derivation for readers who would like to see the mathematics, and provide a simple-to-use final formula for those who just want to plug in the numbers.

Survey Questionnaires and Results

We began by conducting a wide-ranging literature review. From that information we constructed a 44-question survey, which we sent to the rooms managers at six hotels that agreed to participate (some hotels that we contacted declined to participate because of confidentiality concerns). (1) Two to four weeks after the managers received the questionnaire, we interviewed each one at their hotel for approximately 90 minutes, and followed our interview with telephone inquiries to clarify issues. We subsequently interviewed managers at another six hotels by telephone, to minimize sampling errors on 20 crucial statistics, such as no-show and early departure rates, and the number of unexpected stayovers. Because of the sensitive nature of the answers (for example, the overbooking rate and walking protocol) all respondents requested strict confidentiality

Our model is based on the pertinent statistics summarized in Exhibit 1. In addition to those factors, the model includes the following factors. Most critically, the model will accept walk-ins only when there are unsold rooms. Additionally, luxury and handicap-accessible rooms are usually protected from overbooking, but vacant rooms in those classes can be used as upgrades in the case of an oversale. Furthermore, state laws give room priority to stayovers and holdovers (those who refuse to leave on schedule) over new arrivals. (2)

One other factor that affects room-reservation calculations is the growth of the MICE (meetings, incentives, conventions, and exhibitions) market. (3) While group reservations can constitute more than 50 percent of rooms sold in some large convention hotels, accepting a group's reservation involves another set of no-show and early departure issues, because conventioneers may arrive late, leave early or skip a meeting altogether (even if they planned to attend). Hoteliers have begun to shift groups' no-show risks to the groups themselves, with attrition provisions in the contracts. Groups can usually reduce a negotiated portion of their room blocks until 30 days before the arrival date, but for the final 30 days before arrival the number of room-nights in the contract is typically set in stone.

Our survey revealed that the booking profiles for individuals and groups are radically different. For individuals the total number of rooms booked increases as the day of arrival approaches, with the reservation rate peaking at seven to 14 days out, while bookings for groups decrease up to 30 days out, as we just explained in connection with attrition contracts. This convergence is illustrated in Exhibit 2.

Literature Review

In a celebrated article, Weatherford and Bodily came up with a comprehensive taxonomy of 14 elements (such as capacity) and their accompanying descriptors (for example, fixed or variable) related to what's called perishable-asset revenue management, or PARM. (4) They calculated that there are an astounding 124,416 possible combinations of elements and descriptors. It has been claimed that over 100 technical PARM-related papers have been published, none of which purport to address all aspects of perishable asset revenue management. (5) We present the major aspects of the salient articles in Exhibit 3 (overleaf).

In the context of the Weatherford and Bodily taxonomy, for our own model we confined ourselves to examining the problems of random individual demand, uncertain cancellations, no-shows leading to overbooking, and oversale of multiple grades of a discrete perishable asset of fixed capacity, with the possibility of upgrades as well as non-auction displacement procedures, and with continuous-time dynamic decision rules. We allow for group reservations, multiple-type rooms, and multiple-night reservations, as well as deal with the concomitant problems of early departures and holdovers. We also do away with the unrealistic assumption that all guests arrive at the same time, and we do not allow for hotels to unilaterally cancel reservations, which is simply not done. Furthermore, like Williams, we acknowledge that holdovers have priority, followed by guests with reservations, and walkins are to be accommodated only on a space-available basis. (6) Note that our model attempts to realistically reflect the existing ins titutional framework in the hospitality industry, and deals primarily with the goal of full occupancy, once optimal room rates have been set, accepting reasonable displacement risks.

Overbooking Model

Despite reservation guarantees and groups' attrition agreements, overbooking still has good reason to exist. Indeed, it has been demonstrated that even if the hotel is assured of payment and there are penalties for oversales, the property has an incentive to overbook (7) for the following reasons. First, Lambert, Lambert, and Cullen demonstrated that same-day reservations and walkins cannot overcome the loss of reservations from late cancellations and no-shows. (8) Second, credit cards guarantee only the first night of a multiple-night reservation. Similarly, early departure penalties do not always cover all unsold room-nights. Third, even if group contracts are subject to attrition provisions, the odium of collecting on the penalties often induces hotels to sell into group bookings rather than invoke penalties. Fourth, overbooking allows hotels to double dip by collecting the no-show penalty and then reselling the room (unless prohibited by a group's contract). Finally, ancillary hotel revenues depend on the level of occupancy (e.g., restaurant and bar, convention services, concessionaires, and parking). (9) In short, hotels overbook to ensure that the property is operating at full occupancy during peak periods. (10)

Our principal hypothesis is that it is possible for hotel managers to assign explicit values and costs to empty rooms, loss of customer goodwill due to walks, and other relevant variables. Managers can then determine the trade-offs among those factors for the purpose of establishing a target customer-service level, which is the percentage of times the hotel can accommodate all its guaranteed reservations during peak times (given that the hotel will be overbooking). By determining the distribution of no-shows and early departures, the hotel manager can then establish optimal overbooking levels (basically determining how often guests are likely to be walked).

Our model assumes that the overarching objectives of yield management have determined the optimal rates to charge at the right times, and once those rates are set, our objective is to sell as many rooms as possible to fill up capacity, within the constraints of the predetermined optimal customer-service level. Thus, we propose an optimal overbooking model, within the broader framework of an optimal yield-management strategy. (11)

As is the case with many other room-inventory-management models, ours is based on airline overbooking models--in this case, one that one of the authors (Rex Toh) developed for Singapore Airlines, which was a simple overbooking model for IATA-regulated full-fare economy-class seats on the Singapore-Jakarta route. That model was subsequently expanded to accommodate joint reservation control for full-fare and discounted economy-class seats on US. airlines, using inventory-depletion dynamic-decision rules to adjust for reservations and cancellations of the two types of fares. (12) In this article we adjust the expanded airline model to handle hotel overbooking and to manage new arrivals and stayovers. Upgrades are still possible (from standard to luxury rooms), and multiple-night stays are treated the same way as multi-sector flight bookings, but we deal with the complicating fact that unlike flying on an airline where a passenger cannot step out of a plane in midair or refuse to disembark when the flight is over , a hotel guest can leave early or extended his or her stay.

We model a hypothetical convention hotel with 950 rooms, of which 150 are in the overbooking-protected categories of luxury (or deluxe) or handicap-accessible rooms, while the remaining 800 are standard rooms that can be overbooked. The booking profile over time (shown in Exhibit 4) is typical of large center-city convention hotels. As the graph in Exhibit 2 shows, group bookings tend to be almost rectangular in nature with discrete drops as the day of arrival approaches (as permitted by most group-sales contracts), while individual bookings tend to assume a reverse-S shape with the rate of bookings rising to a peak at seven to 14 days out. Typically, about 80 percent of individual reservations are made within 30 days of arrival. (13) The previous year's reservation profile of 40 fully booked days (excluding extraordinary days such as Memorial Day, Labor Day, Thanksgiving, and Christmas) is shown in Exhibit 4. We made a conscientious attempt to ensure that the numbers and percentages shown in our hypothetical hotel are typical and reflect our survey results.

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