 2009 CORNELL uNIVERsItY DOI: 10.1177/1938965509336064 Volume 50, Issue 3 314-324 Room-Risk Management at Sunquest Vacations by CHRIs K. ANDERsON and XIAOQINg XIE This article outlines some of the basic complexities Summary that originate with the acquisition of hotel rooms for Tour operators face a considerable risk when they a reseller of bundled vacations. A tour operator typi- cally acquires or contracts for service capacity, bun- contract far in advance for hotel rooms that they will dles the services (air, hotel, food and beverage, and then resell. These “at-risk” rooms are typically sold excursions), then markets and sells to consumers. as part of packages for multiple-day stays (often one The article focuses on the short-term aspects of week), which means that when customers purchase room-risk management for the tour operator, specifi- packages, sufficient rooms must be available for the cally how to manage blocks of take-or-pay contracted entire package period. Room availability is also sub- rooms. The room-risk management problem is for- ject to stayovers from packages sold for previous mulated as a math program with the objective of dates. The room-risk challenge can be modeled, with minimizing wasted rooms. While the exposition a goal of minimizing unusable rooms under contract. focuses on a particular reseller of packaged vaca- The specific example of Sunquest Vacations, pre- tions, the method is applicable to any firm acquiring sented here, shows a reduction of 25 percent in spoil- capacity on take-or-pay contracts and reselling this age. The tour operator’s room availability can be capacity as bundled vacations. augmented by additional rooms purchased on the Keywords: t our operators; revenue manage m - spot market. Although the operator is not financially ent; bundled package sales; Sunquest liable for those rooms, they are subject to prior sale Tours and are more expensive to use than the base supply of 314 Cornell Hospitality Quarterly August 2009 ROOM-RIsK MANAgEMENt At suNQuEst VACAtIONs HOtEL FINANCE at-risk rooms. The model is expanded to fully financially responsible for this room show the influence of adding the nonrisk block regardless of whatever packages it rooms to inventory, again with the goal of might sell. It might, for example, contract for minimizing spoilage of the contracted, at- a block of one hundred rooms per night for risk inventory. This shows an additional the months of December and January. By reduction of 2 percent in spoilage. contrast, nonrisk rooms are available for purchase by the tour operator at a contracted Introduction rate, but the tour operator has no financial Sunquest Vacations, Canada’s number obligation for these rooms, with the ability to one travel provider, is a wholly owned sub- resell the room (and food and beverage) at sidiary of MyTravel Group PLC, which is some contracted rate. Despite the label we headquartered in the United Kingdom. gave them, nonrisk rooms are not without Sunquest has been voted by the public as the risk entirely, as the tour operator receives no winner of the Consumer’s Choice Award for guarantee on availability. The rooms are not Excellence four years in a row. More than blocked, and they are subject to prior sale. half a million vacationers travel with The hotelier (probably also revenue manag- Sunquest each year to destinations such as ing and closing out deeply discounted rates) Mexico, the Caribbean, Central America, the can issue a stop sell, removing all room United Kingdom, and Ireland, departing availability for a given arrival period. The from fifteen Canadian locations. In the midst random elements in the supply resulting of this good news, Sunquest, like all tour from hotel stop sells is generally not an issue operators, faces a challenging operational except for a few extremely busy periods environment as it deals with variable supply (e.g., the week between December 25 and and demand in a highly competitive land- January 2 and spring break periods). scape. The typical tour operator owns little The tour operator’s glossy brochure or no capacity in the final product it sells. advertising all of its vacation locations and Sunquest does own some aircraft capacity associated hotels—including prices that that is operated for it under an operating are effectively rack rates—is published agreement, and it contracts for additional and sent to travel agents well in advance of seats with several charter airlines. Some tour the vacation season. To stimulate book- operators may choose to contract all their ings, the tour operator offers discounted airline capacity, while others may own all prices and promotions. From the consum- their flight capacity. er’s standpoint, prices typically decline In addition to providing sufficient airline with time, but the availability of desirable capacity, the tour operator must also ensure hotels, room styles, or views likewise that it has sufficient hotel-room availability, diminishes. This situation is similar to that because many of its packages are sold as all- of the cruise industry, where booking inclusive—covering the flight, room, food prices decline as the exterior cabins with and beverage, and airport transfers. Sunquest views are reserved, leaving small, interior uses two types of agreements for rooms, one cabins available for sale. in which the tour operator has full financial risk for the rooms and one in which there is Tour Operator Revenue no risk. In a full-risk agreement, the tour Management operator agrees to block a set number of Our focus in this article is on the man- rooms at a specified price for an agreed- agement of full-risk rooms, which falls upon arrival period. The tour operator is under Sunquest’s revenue-management August 2009 Cornell Hospitality Quarterly 315 HOtEL FINANCE ROOM-RIsK MANAgEMENt At suNQuEst VACAtIONs operation. Tour or bundled vacation pack- migration of tourism distribution to a less ages are a relatively new arena for the consolidated framework. Hoontrankul and direct application of revenue management Sahadev (2006) provide an excellent intro- (RM), and we have seen little published duction to the tour industry with a case research directed towards RM for tour study about MoreThailand.com. For a operators. Talluri and van Ryzin (2004) more general discussion of the tour indus- briefly mention tour as an area of RM try, see Cooper et al. (2005). The focus of application with some popular press dis- the model developed in the following sec- cussions of the JDS (formerly Manugistics) tions is on the optimal use of at-risk hotel RM rollout at Tui in Europe. The absence rooms, which the tour operator has already of published studies does not mean that purchased or contracted for on a take-or- tour operators are not active practitioners pay basis. Selling prices for the tour of RM concepts; in fact, they are assertive operator are competitively set in the mar- in the general application of RM funda- ketplace. So instead of addressing price, mentals. Most tour operators have teams the model is designed to reduce wasted of analysts responsible for markets who rooms or, stated differently, to minimize actively manage prices across a set of dis- the costs of the hotel rooms sold as part of tribution channels that continues to expand. packaged vacations. However, the industry has been slow to formalize the application of RM tools or systems. Room Risk at Sunquest Traditional RM focuses on inventory Vacations allocation decisions across demand seg- Exhibit 1 presents a snapshot of seven ments. The early approaches of Littlewood hotels (labeled A through G for our pur- (1972) and Belobaba (1989) were focused poses) during a fourteen-day window in on the allocation of capacity across a set of the winter of 2005-2006 for a particular product classes. Williamson and Belobaba Caribbean location. The table indicates (1988) discuss the use of optimization and total airline seats available as well as linear programming for the control of rooms required. The seats-available row inventory in complex settings like the net- indicates how many seats are empty on work of a large airline or a hotel trying to flights for all departure gateways for a manage rates across a set of different particular arrival location and arrival date. lengths of stay. Gallego and Phillips (2004) The seats-available number is variable as provide packaged holidays and bundling it aggregates all fifteen Canadian gateways as an example of how airlines can create serving the market in question, but depar- flexible products for the improved man- tures do not occur every day of the week, agement of their supply. Anderson and and some days see more departures than Marcus (2007) present a summary of rev- others. The rooms available in each of the enue management issues for the tour oper- seven properties also show variation owing ator and develop a two-period game to sales and nonuniform block allotments. theoretic model between the tour operator As these rooms (for these seven proper- and the hotel operator. Their efforts focus ties, among a list of others) are prepaid by on the optimal mix of risk versus nonrisk the tour operator, one of the operator’s rooms that the hotel should offer to the goals is to avoid issues like the results for tour operator. Buhalis and Licata (2002) property A, which shows twenty-nine provide an interesting discussion of the rooms one day and twenty-four the next, 316 Cornell Hospitality Quarterly August 2009 ROOM-RIsK MANAgEMENt At suNQuEst VACAtIONs HOtEL FINANCE Exhibit 1: sample Fourteen-Day Room and Flight Detail, Winter 2005-2006 total seats 218 101 14 0 96 84 203 235 169 67 0 283 197 305 available Beds 700 795 809 809 780 864 806 920 1,006 1,073 1,073 1,245 1,3631,514 required Rooms 350 398 405 405 390 432 403 460 503 537 537 623 682 757 required Property A 0 0 0 0 29 24 0 0 0 0 0 0 0 7 Property B 0 29 28 28 25 27 39 32 29 30 30 31 32 36 Property C 5 18 15 15 7 7 5 9 9 14 14 27 27 31 Property D 0 0 0 0 7 2 11 10 0 4 4 1 5 0 Property E 25 22 21 21 20 20 18 20 28 29 29 27 23 25 Property F 0 0 0 0 1 0 0 0 0 0 0 0 0 6 Property g 0 2 3 3 2 2 2 1 1 1 1 2 2 3 Exhibit 2: forty-two days prior to arrival as well as typical Booking Pace and Profit Margins the margins during this period. The axis for sunquest has been scaled to 1 for confidentiality purposes, as the actual values are not as important as the shape of the curves. The lines (solid, dashed, or dotted) represent bookings (left scale); and the points repre- sented by diamonds, dots, and squares are margin (right scale). Demand builds quickly in the last few weeks while mar- gins decline quickly over this same period. The goal of the tour operator is to effi- ciently allocate this time-varying demand to its contracted hotels to maximize profit. Note: Graph shows three sample arrival days (labeled 3rd, In the short term, given a set of take-or- 10th, and 17th). pay contracts, Sunquest’s (potentially risk- averse) near-term goal is to sell or reserve surrounded by zero rooms on preceding prepaid (risk) rooms as quickly as possi- and successive days. As the typical guest ble. In the following sections, we develop package involves a seven-night stay at a a model to manage room risk, specifically single property, these two isolated blocks to minimize unusable rooms. We present of rooms are unusable. Instead, one might some numerical results using the tour prefer a pattern like that of Property E, operator’s actual data and benchmark these which shows similar numbers of results to methods that mimic those cur- rooms available for seven-day stretches rently in practice. (or longer). Exhibit 2 shows a graph of three sample Model Formulation arrival days (the 3rd, 10th, and 17th). The In the following section, we formulate graph shows the booking pattern over the the room-risk model as a mathematical August 2009 Cornell Hospitality Quarterly 317 HOtEL FINANCE ROOM-RIsK MANAgEMENt At suNQuEst VACAtIONs Exhibit 3: spoiled rooms (Xprepaid risk rooms that go i Nomenclature summary unsold) are Si − j=X− xj ,h and Xtotal selling i 6 iN i N total days in the selling season season spoilage is = Si − .i 1 j= − xj :i 6 Number of risk rooms on hand at One might assume that to minimize Si the ith night of this season rooms spoiled across the whole season, Number of nonrisk rooms on the whole season would need to be formu- NSi hand at the ith night of this sea- lated as one mathematical program—that son is, the objective of any model would be Number of total rooms on hand X h iN Xito minimize = Si − x . We ill-TS at the ith night of this season, ji 1 j= i− 6i TS = NS + S ustrate in Result I that this is not the case, i i i Number of rooms sold at the ith but rather the sequential application of a x night of the season for seven one-day myXopic formulation (that is, min-i nights in a row imize i Si − xj ) is equivalent to the j= i− 6 entire-season approach. For illustration purposes, we outline in Appendix A the program. For clarity of presentation, the one-day model with the development of nomenclature used is summarized in Result I. Exhibit 3. In the following formulation, we assume that the tour operator sells packages for a seven-night stay and that One-Day Rolling-Window Formulation each such stay is at a single property. We further assume that room allotments to the Our objective function is to minimize tour operator for both prepaid (risk) rooms the spoilage for day i by determining the and retail (nonrisk) rooms are fixed and number of packages to sell, xi, for arrival that demand exceeds the supply of risk day i, subject to the number of risk rooms rooms. While the model is developed for on hand on each day and stayovers from seven-night stays, the general framework the previous six days. of the model can extended to handle other The formulation for this model is, at the stay durations, whether three nights or ith day, fourteen nights. To address nonfixed inven- Xi Min Si − xj, (1) tory allotments, the model can simply be j= i− 6 repeatedly solved over the selling horizon subject to as inventory levels change. Given the goal of selling as many risk xj ≥ 0 (2) rooms as quickly as possible (or at least Xi remove the risk from the books as soon as Sl − xj ≥ 0, l= i, i+ 1, . . . , i+ 6: (3) possible), we formulate our model with j= l− 6 the objective of minimizing spoilage, or Here (1) is the spoiled rooms on day i unsellable risk rooms. For a tour operator (rooms available, minus stayovers minus selling week-long vacations, on any given day i’s allocation xi) and (3) makes sure that day, customer arrivals from the previous there are enough rooms over the next six six days will require a room-night on the days to accommodate any day i allocations. day in question. So the total number of To determine each day’s allocation, this rooms used on a given day, i, include the linear program would be sequentially run arrivals on that day plus Xstayovers from for each day of the season starting at the the previous six days, or i xj . The first day, with subsequent days using the j= i− 6 318 Cornell Hospitality Quarterly August 2009 ROOM-RIsK MANAgEMENt At suNQuEst VACAtIONs HOtEL FINANCE decisions from previous days as inputs to Xi determine stayovers. TSi − xj ≥ 0, i= 1, 2, . . . ,N , j= i− 6 The above formulation looks at risk rooms in isolation. To be more realistic, a where TSi is the daily sum of total rooms model should take into account the fact available, both risk and nonrisk. that the tour operator often has additional In the following section, we illustrate rooms available at a particular property on application of the above two formulations a spot or nonrisk basis (NSi). These non- to the seven hotel properties during the risk rooms have the potential to add to the winter 2005-2006 season. available supply of rooms such that more risk rooms can be utilized. This is true Numerical Example because consumers do not care (or even Using data available from Sunquest know) whether they are staying in a risk or Vacations for a representative winter desti- nonrisk room as long as they are getting nation, we outline the impacts of optimal their seven nights at the property. The fol- risk-room allocation. We use data from a lowing develops a nonlinear formulation 151-day selling horizon for a high-volume for the allocation of risk and nonrisk rooms destination for all seven properties that jointly. Sunquest engaged in take-or-pay contracts for room acquisition. As Exhibit 4 shows, Inclusion of Nonrisk Rooms these seven properties have different degrees of risk. Property A has more than The inclusion of nonrisk rooms as avail- 10,000 rooms committed to inventory, able rooms, while conceptually not that whereas property G has only 258. different, changes the formulation enough The numerical results are summarized that it is no longer linear, nor is the one- in Exhibit 4. The table includes three day myopic formulation optimal. Below model formulations as well as a set of we develop the mathematical program for benchmark spoilage results, as follows: minimizing spoilage across the entire sell- the one-day model using only risk-based ing season, using both at-risk and nonrisk rooms as available supply, a nonlinear ver- rooms. In Appendix B, Result II illustrates sion of this model using nonrisk rooms to that the single-day rolling-window formu- augment supply, and a model using non- lation is not necessarily globally optimal risk and risk rooms that models the whole as in the risk-room-only case. season simultaneously. This formulation is similar to the case As a benchmark to evaluate the impact of risk-only rooms, except that the total of the room-allocation approaches, current rooms on hand, labeled TSi, is now the practice is replicated (labeled “benchmark sum of risk rooms and nonrisk rooms for spoilage” in Exhibit 4). In an effort to pro- each property. X h  vXide a benchmi ark, we created a proxy for X h  ThXe total spoiliage becomes N − i= max Sii 1 currj=eni−t 6pxjr,a0ctice. Current practice has no N i max Si − i= 1 j= i− xj, 0 .6 scientific approach to the allocation of risk The whole season model, selling seven- rooms but, rather, attempts to sell risk day packages in this case is as follows: rooms as fast as possible as requests come " !# XN Xi in. For example, whenever a reservation is min max S . (4)i − xj, 0 , requested for seven nights at property A, i= 1 j= i− 6 subject to this request is fulfilled with risk rooms until risk rooms are depleted (or no sale- xi ≥ 0, i = 1, 2, . . . , N able combinations exist). To replicate this August 2009 Cornell Hospitality Quarterly 319 HOtEL FINANCE ROOM-RIsK MANAgEMENt At suNQuEst VACAtIONs Exhibit 4: sample Results for seven Representative Properties Properties A B C D E F G Risk supply 10,508 5,518 3,204 2,539 3,999 1,055 258 Model: spoilage % Risk only 8.3 8.5 5.0 22.5 3.2 20.4 7.8 Risk and Nonrisk 1.4 3.8 1.7 16.2 3.2 3.5 7.8 Risk and nonrisk season 0.0 0.0 0.0 8.1 1.9 2.8 3.1 model Benchmark spoilage 29.5 30.0 26.6 32.9 23.1 39.4 27.0 Exhibit 5: Nonrisk Room Availability and usage Properties A B C D E F G Risk supply 10,508 5,518 3,204 2,539 3,999 1,055 258 Risk sold 10,508 5,518 3,204 2,338 3,925 1,025 238 Nonrisk supply 9,402 4,034 2,505 1,052 183 1,578 30 Nonrisk used 2,862 2,546 1,409 581 150 872 30 approach, we randomly selected arrival availability and usage of nonrisk rooms in days and then minimized spoilage on that the allocation of the risk rooms for the sell- arrival day (using the risk-rooms-only for- ing season that we studied. The availability mulation), and we sampled arrival days of nonrisk rooms is variable for the seven without replacement until the entire sea- properties in question, but fortunately, with son of arrival days had been allocated. We the exception of property E, properties in performed ten replications, resulting in the which Sunquest has large risk positions averages presented in Exhibit 4. As one also have considerable spot or nonrisk can see, considerable spoilage results from availability. We emphasize that nonrisk the nonsystematic allocation of risk rooms room availability is subject to prior sale as today’s decisions are increasingly lim- and continually changes, resulting in the ited by past decisions when these deci- probable need to repeatedly solve the math- sions are made nonsequentially. ematical program over time as (nonrisk) As shown in Exhibit 4, the inclusion of inventory becomes depleted. nonrisk rooms into the allocation of risk For illustration purposes, Exhibit 6 rooms greatly reduces spoilage. While the shows a sample set of available rooms, availability of nonrisk rooms is not within allocations, and the resulting spoilage for a the control of the tour operator (as other twenty-one-day window from property E, firms and the hotel itself are free to sell these with the tour operator selling seven-night rooms as well), as long as nonrisk room packages. The Rooms row in Exhibit 6 availability approaches that of risk rooms, contains the number of available risk rooms then the uncertainty in supply of nonrisk for each of the twenty-one days. The rooms should not significantly alter spoil- Optimal sales row, the decisions made by age. Exhibit 5 summarizes this prin ciple for the model, contains the optimal sales to the seven properties evaluated, showing the occur on each of these twenty-one days, 320 Cornell Hospitality Quarterly August 2009 ROOM-RIsK MANAgEMENt At suNQuEst VACAtIONs HOtEL FINANCE Exhibit 6: sample spoilage Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Rooms 23 22 19 22 22 24 24 30 25 22 21 21 20 20 18 20 28 29 29 27 23 Optimal 19 0 0 3 0 2 0 17 0 0 2 0 1 0 15 2 6 0 0 0 0 sales spoilage 4 3 0 0 0 0 0 8 3 0 0 0 0 0 0 0 2 5 5 4 0 with Spoilage representing rooms that can- allocation of risk rooms and provides a not be sold. On day 1 only nineteen pack- concomitant reduction in wasted rooms by ages can be sold, because day 3 only has a further 2 percent. The complication relat- nineteen rooms available, restricting sales ing to the nonrisk rooms is that their avail- of seven-day packages. This results in ability is not within the tour operator’s spoilage of four rooms on day 1 and three control. As rooms are sold through other rooms on day 2. An additional three pack- channels, the mathematical model relating ages can be sold on day 4, resulting in no to those rooms must be repeatedly solved spoilage until day 8, when only seventeen with new data as the nonrisk inventory additional packages can be sold, even becomes depleted. The lack of control on though there are thirty rooms available on nonrisk rooms owing to uncertain demand day 17. As on day 1, day 17 sales are lim- serves as a limitation of the model formu- ited by the rooms available on each of the lation, but the reapplication of the devel- next six days, complicated by the number oped model similar to the reapplication of of stayovers from earlier days. This means traditional revenue management models spoilage of eight rooms on day 8, calcu- (Talluri and van Ryzin, 2004) should limit lated as thirty rooms minus seventeen sales the negative effects of this uncertainty. As minus five stayovers (from days 4 and 6). the tour operator reduces its spoiled rooms (assuming demand is constant, sales would Conclusion probably increase as spoilage reduction This article has presented a brief intro- reduces room cost, making the firm more duction into aspects of the revenue man- price competitive), it directly increases its agement considerations of a tour operator. profit, particularly since it can restrict its Specifically, we examined the allocation purchases of nonrisk rooms on the spot or of prepaid rooms, which we call risk retail market. rooms, with the objective of using as many of these rooms as possible (to minimize spoilage). We demonstrated that if an Appendix A operator wishes to focus only on the risk rooms, a relatively straightforward model Result I—Equivalence of One- can be repetitively applied, resulting in Day and Seasonwide significant improvements in room utiliza- tion. Our calculation showed a reduction Formulations in spoiled rooms exceeding 25 percent. The inclusion of rooms that are acquired total spoilage of a one-day rolling- on a nonrisk basis adds flexibility to the window model is equal to that of the August 2009 Cornell Hospitality Quarterly 321 HOtEL FINANCE ROOM-RIsK MANAgEMENt At suNQuEst VACAtIONs whole-season model. Consider a simple xi, i = 1, 2 are the same with the objec- example of a one-day rolling-window tive function minimizing total spoilage model for a three-day window, selling for the entire three day window. Assume two-night hotel stays. the two decisions that x*, x*1 2 are the optimal solXution for  xi, I = 1, 2 are the number of rooms sold this model. total spoi 3 Totallpaogileag e== = SS   i − i 1 i 2– x1 + x2 , on the ith day for two days in a row. the 2(x*1 + x * 2). objective function is to minimize daily therefore, the formulation is as fol- spoilage. lows: Assume that x– –1, x2 are the optimal X3 solutXion for th is model with total spoil- Miin Si −– 2ð(xi 11 ++ xx2Þ,2), (A1-3) 3 –  Total poilaggee= = SS −– 22x(x  ii 1 ++ x– ). i= 1x , i 1 1 2 2 the formulation is as follows: subject to x1, x2 ≥ 0 Min S – x , (A1-1) S1 – x1 1 1 ≥ 0 S2 – x1 – x2 ≥ 0 subject to S3 – x2 ≥ 0. x1 ≥ 0 From the formulation, for a given opti- Si – x1 ≥ 0, where i = 1,2, (A1-2) mal x1(x * 1) , we can get and X3   MMinin SS  – i −– 22(xxi 1*+ x ,Min S – x – x 1 + x22), (A1-4) 2 1 2 i= 1 subject to subject to x2 ≥ 0 x2 ≥ 0 S2 – x – x ≥ 0 S * 1 2 2 – x1 – x2 ≥ 0 S3 – x S – x ≥ 0.2 ≥ 0. 3 2 By observation, we get x–1 = min (S1, S2) then, by observation, x*2 = min(S3, S2 – and x–2 = min (s2 – x – 1, s3). x*1). If S1 ≤ S2, similarly, for optimal x*2, X3   * 1. I f S2 — S1 ≤ S – – X3, x1 = S1, x2 = S2 – S1, total MMinin Si −– 2i (x1 + x22),, (A1-5) i= 1 tostaplsop i 3 olailgagee = ½[Si i− –2 S22S=2] S=3 −S3S 2–= + SSi 1 21 + S1. subject to 2. If S2 – S1 >X S3, x – – 1 = S1, x2 = S3, total spoil 3totals poialaggee = [= ½Si i− – 22SS3 −3 2–S 12S=1]S 2=− SS33 –− S1 x1 ≥ 0i 1 S2 – S1]. S1 – x1 ≥ 0 3. I f S1 > S2, i.e. S2 – s1 < 0X, then x – 1 = S ,– 2 S2 – x1 – x * 2 ≥ 0, x2 = 0, tot alt 3 ostaplopiolialagge = = ½[Si −i –2 2S2S2=] S3 − S2 + S1:i 1 = S3 – S2 + S1. then, by observation, x*2 = min(S1, S2 – x*2). In summary, the results are therefore, · If s2 – s1 ≤ s3, total spoilage = s3 – 1. I f S – x* ≤ S , that is, x*2 1 3 1 ≥ S2 – S3, then s2 + s1, x*2 S1 ≥ S2 – x*1, thXat is, x * 2 + x * 1 = S2. so · If s2 – s1 > s3, total spoilage = s2 – 3totatol taslpsopiolialaggee = = ½SSii −– 2S22 = S31− –S S2 +2 S1i 1 s1 – s3. + S . Also we know that x*3 1 = min(S1, S 2 – x*2), so S1 ≥ x*1 ≥ S2 – S3, that is, S2 – S1 For a whole season model with a three ≤ S3. thXus, when S3 2 – S1 ≤ S3, total spoil- day window, the two decision variables totals poialaggee = = S½Sii –− 2S22 = S31 −– S22+ +S 1Si 1 3. 322 Cornell Hospitality Quarterly August 2009 ROOM-RIsK MANAgEMENt At suNQuEst VACAtIONs HOtEL FINANCE 2. I f S2 – x * * * 1 > S3, then x2 = S3, x1 = subject to min(S1,S2 – S3). so if S1 < S2 –X S3, then x*1 = S1, and totatlo tsaplsopiolailgagee = 3 = ½Sii −– 2S2= S3 − S2 + S1i 1 x2 ≥ 0 2S3 – 2S1 = S2 – S1 – S3. If S –1 ≥ S2 – S3, TS2 – x1 – x2 ≥ 0 tXhen x * 1 = S2 – S3, and total spoilage = TS3 – x2 ≥ 0.3 totals poilage= = ½Sii −– 2S22= =S S3 −1 –S 2S+2 S+1 S3.i 1 By observation, we get x–1 = min (TS1, In summary the results are TS2) and x – 2 = min (TS2 – x – 1, TS3). X If TS1 ≤ TS3 2, then · If S – S ≤ S , totalt ostaplsopiloailgagee = = ½Si − 2S2= S3 − S + S2 1 3 2 1i 1 Si – 2S2 = S1 – S2 + S3. X 1. I f TS2 – TS ≤ TS – 3 1 3 , x–1 = TS1, x2 = TS2 · If S2 – S1 > S3, totalt ostaplsopiloailgagee = = ½Si − 2S2= S3 −– ST2S+ Si 1 1. 1 S – 2S – 2S = S – S – S . t otal spoilage = max(0, S – xi 3 1 2 1 3 1 1) + max(0, S2 – x1 – x2) + max(0, s3 – x2) Which is the same as the one-day rolling- = 0 + 0 + max(0, S3 – TS2 + TS1), since window formulation. Si ≤ TSi for all i. = max(0, s2 – ts2 + ts1). 2. I f TS – –2 – TS1 > TS3, x1 = TS1, xAppendix B 2 = TS2. t otal spoilage = max(0, s1 – x1) + max(0, S2 – x1 – x2) + max(0, S3 – x2) Result II—Nonequivalence of = 0 + max(0, S2 – TS3 – TS1) If TS > TS , that is, TS – TS < 0 < One-Day and Seasonwide 1 –2TS – 2 1 3, then x1 = ts1, x2 = 0. Formulations with Inclusion of total spoilage is then max(0, S1 – x1) Nonrisk Roo + max(0, S – x – x ) + max(0, S – x ) ms 2 1 2 3 2= 0 + 0 + max(0, S3 – 0) = S3. In this case, the one-day rolling-win- In summary, the results are dow model does not necessarily have the same spoilage as the whole-season · If TS1 ≤ TS2, then: if TS2 – TS1 ≤ TS3, model has. similar to Result I, we illus- then total spoilage = max(0, S3 – TS2 trate a simple example with a one-day + TS1), if TS2 – TS1 > TS3, then total rolling-window model for a three-day spoilage = max(0, S2 – TS3 – TS3). season, selling two-day packages. · If TS1 > TS2, total spoilage = S3. the decision variables xi, i = 1, 2, the number of rooms sold on day i for two similarly, for a model of the entire sea- days in a row, with the objective to mini- son for a three-day window, with the mize each day’s spoilage. Assume that x–1,– objective of minimizing total season x2 are the optimal solution for this model spoilage, assume that x*1, x * 2 are the with total spoilage max(0, S1 – x – 1) +– – – optimal solution for this model. total max(0, S2 – x1 – x2) + max(0, S3 x2). spoilage = max(0, S *1 – x1) + max(0, S2 the formulation is as follows: – x*1 – x * 2) + max(0, S * 3 – x2). the formulation is as follows: Min max(0, S1 – x1), (A2-1) subject to Min [max(0, S1 – x1) + max(0, S2 – x1 – x2) + max(0, S – x ) (A2-3)x1 ≥ 0 3 2 TSi – x1 ≥ 0, where i = 1, 2 subject to x1, x2 ≥ 0 and TS1 – x1 ≥ 0 TS2 – x1 – x2 ≥ 0 Min max(0, S2 – x – 1 – x2) (A2-2) TS3 – x2 ≥ 0. August 2009 Cornell Hospitality Quarterly 323 HOtEL FINANCE ROOM-RIsK MANAgEMENt At suNQuEst VACAtIONs From the formulation, we can get TS2 + S1). so if S3 – TS2 + S1 > 0, then the total spoilage ≤ S3 – TS2 + S1; but recall Min [max(0, S1 – x * 1) + max(0, S2 – that under the same conditions, the x*1 – x2) + max(0, S3 – x2) (A2-4) total spoilage for one-day rolling win- dow = max(S3 – TS2 + TS1, 0) = S3 – TS subject to 2+ TS1 > S3 – TS2 + S1. therefore, we have found a situation x2 ≥ 0 where these two models have different TS2 – x * 1 – x2 ≥ 0 TS – x ≥ 0. spoilage while including the nonrisk 3 2 rooms as supply data. then by observation, we get x*2 = min(TS3, TS *2 – x1). References Min [max(0, S1 – x1) + max(0, S2 – x1 – x * 2) + max(0, S3 – x * 2) (A2-5) Anderson, C. K., and B. Marcus. 2007. Competitive sup- ply chain contracting: Tour operator revenue man- agement. Working Paper, School of Hotel subject to Administration, Cornell University, Ithaca, NY. Belobaba, P. P. 1989. Application of a probabilistic deci- x ≥ 0 sion model to airline seat inventory control. 1 ≥ Operations Research 37 (2): 183-97.TS1 – x1 0 Buhalis, D., and M. Licata. 2002. The future of etourism TS2 – x – x * 1 2 ≥ 0. intermediaries. Tourism Management 23:207-20. Cooper, C., J. Fletcher, A. Fyall, D. Gilbert, and S. then by observation, we get x* = Wanhill. 2005. Tourism principles and practice. 3rd 1 * ed. Upper Saddle River, NJ: Pearson.min(TS1, TS2 – x2). Gallego, G., and R. Phillips. 2004. Revenue management therefore, if TS2 – x * 1 ≤ TS , then x*3 2 = of flexible products. Manufacturing and Service TS – x*, total spoilage = max(0, S – x*) Operations Management 6:321-37.2 1 1 1 + max(0, S – x* – x*) + max(0, S – x*) = Hoontrankul, P., and S. Sahadev. 2006. Morethailand.com: 2 1 2 3 2 Online travel intermediary. International Journal of max(0, S – x*1 1) + max(0, S3 – x * 2). E-Business Research 2:94-114. Also, x*1 = min(TS1, TS2 – x * 2) so TS1 ≥ Littlewood, K. 1972. Forecasting and control of passenger x* ≥ TS – TS that is, TS – TS ≤ TS . bookings. In Proceedings of the 12th Annual 2 2 3 2 1 3 thus, if TS ≤ TS and TS > S > TS AGIFORS Symposium. 1 2 1 1 2 Talluri, K., and G. van Ryzin. 2004. The theory and prac- – TS3, then when S1 = x1, the total spoil- tice of revenue management. Amsterdam: Kluwer age = max(0, S – x ) + max(0, S – x ) = Academic.1 1 3 2 max(0, S – TS + S ), so the optimal Williamson, E. L., and P. P. Belobaba. 1988. Optimization 3 2 1 * techniques for seat inventory control. In Procee-spoilage = max(0, S1 – x1) + max(0, S2 – dings of the 28th Annual AGIFORS Symposium. x*1 – x * 2) + max(0, S3 – x * 2) ≤ max(0, S3 – Chris K. Anderson, Ph.D., is an assistant professor of operations management at the Cornell university school of Hotel Administration (cka9@cornell.edu), where Xiaoqing Xie is a doctoral student (xkx2@ cornell.edu). 324 Cornell Hospitality Quarterly August 2009