Availability management of hotel rooms under cooperation with online travel agencies

International Journal of Hospitality Management 50 (2015) 145–152

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International Journal of Hospitality Management journal homepage: www.elsevier.com/locate/ijhosman

Availability management of hotel rooms under cooperation with online travel agencies Liuyi Ling, Yufeng Dong ∗ , Xiaolong Guo, Liang Liang School of Management, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui Province 230026, PR China

a r t i c l e

i n f o

Article history: Received 28 January 2015 Received in revised form 16 June 2015 Accepted 10 July 2015 Keywords: Hotel marketing Dual-channel distribution Availability management Channel conflict

a b s t r a c t Hotels are required to pay high commission fees when cooperating with online travel agencies (OTAs) to manage online marketing channels. Thus, to maximize their revenues, hotels protect their income through their own (traditional) marketing channels and save on considerable commissions by optimizing room availability for their cooperative OTAs. The present paper proposes a method to manage such availability in the context of a hotel cooperating with an OTA on room booking service. Customers can make reservations directly through the distribution channel of the hotel or indirectly through the OTA, if applicable, during the selling period. The hotel then forecasts room demand base on distribution information after receiving enough room bookings and optimizes room availability with respect to its maximum revenue by determining whether on-hand rooms are available for the OTA. Results indicate when hotel rooms become unavailable for the cooperative OTA. Numerical studies reveal that this method is conducive to the improvement of hotel revenue. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction The Internet has played a significant role in travel behavior, and it has been embraced by travelers as a crucial channel for booking hotel rooms (Gazzoli et al., 2008; Pan et al., 2013). A survey from the China Tourism Academy (2011) indicates that the Chinese tourism e-commerce market in 2010 was as high as CNY 200 billion (approximately USD 32 billion), or nearly 15% of the total tourism revenue. A large percentage of customers booking electronically reserve rooms via OTAs, such as Expedia and Orbitz (Kim et al., 2007; Morosan and Jeong, 2008). Toh et al. (2011a) report that in 2011, 80% of leisure travelers used the web to search for hotel rooms, among which 67% booked rooms online, and as high as 30% of online-booking customers reserved rooms by OTAs. The popularity of OTAs has resulted in their increasingly significant role in the distribution systems of hotels (Pan et al., 2013; Park et al., 2007; Yang et al., 2014a). Efficient and convenient OTAs can attract a large number of customers for hotels and improve their occupancy rates (Guo et al., 2014; Kracht and Wang, 2010; Law and Cheung, 2006). However, hotels must pay high commission for each sold room (Ling et al., 2014). Toh et al. (2011b) reveal that the commission paid to OTAs is as high as 15–30%, especially for small

∗ Corresponding author. E-mail addresses: [email protected] (L. Ling), [email protected] (Y. Dong), [email protected] (X. Guo), [email protected] (L. Liang). http://dx.doi.org/10.1016/j.ijhm.2015.07.005 0278-4319/© 2015 Elsevier Ltd. All rights reserved.

hotels. Thus, numerous hotels, particularly small hotels with less negotiation power, harbor resentment against such commission rates. Consequently, hotels have displayed an ambivalent attitude toward cooperation with OTAs because cooperating with OTAs means having to pay considerable commission fees; however, they risk losing a large online market share in this e-commerce era if they do not cooperate with OTAs. Considering that hotel rooms are highly perishable and cannot be reserved for future use (Hung et al., 2010; Stringam and Gerdes Jr., 2010), hotels must make a tradeoff between potentially higher revenues of reserving rooms by themselves and lower revenues of selling them through OTAs. Hence, hotels have taken the challenge of developing applicable cooperative mechanism with OTAs. It is observed that certain hotel rooms are sold out on the webpage of OTAs while they are available from the brand website of hotels. This phenomenon is practiced commonly. For example, Hotel ICON cooperates with Expedia (http://www.expedia.com/ ?v=b) to sell rooms to online customers. Fig. 1 shows that Club 36 Harbour View Rooms for free cancellation for May 15, 2015 were all sold out on Expedia. By contrast, Fig. 2 illustrates that this type of room was available on the brand website of Hotel ICON (http:// www.hotel-icon.com/) for the same day. In this paper, the same types of rooms with different properties are defined as different products. For example, in Fig. 1, Club 36 Harbour View rooms for free cancellation are different from rooms that are non-refundable. In view of this phenomenon, this paper proposes a new method for a

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Fig. 1. Club 36 Harbour View Rooms for free cancellation of Hotel ICON on Expedia.

hotel to cooperate with an OTA by announcing its room unavailability to cooperative OTA before the target date to cut the commission fee and maximize profit. At the beginning of the booking horizon, the hotel cooperates with the OTA. Thus, customers can book hotel rooms directly through the traditional distribution system of the hotel or indirectly through the OTA. The hotel then forecasts future demands with the observed room bookings and determines the optimal time for announcing the unavailability of its rooms to the OTA. Afterward, the hotel rooms become unavailable on the OTA and can only be booked through the hotel. A mathematical model is developed to describe the decision process of the hotel, and optimal results are obtained. In the numerical example, the hotel utilizes committed orders received to forecast future demands and announces to the OTA that no rooms are available two days before the target. The model proves that hotel revenue is improved compared with when the hotel cooperates with the OTA on room booking throughout the selling period. The rest of the paper is organized as follows. Section 2 reviews related literature on hotel revenue management and cooperation of hotels with OTAs. Section 3 elaborates the cooperation problem

between a hotel and an OTA and proposes a new cooperation method for the hotel. Section 4 presents the optimal solution methodology for the problem. Section 5 provides the numerical example to illustrate the solution process. Section 6 concludes the paper, summarizes its limitations, and provides specific research directions for future study. 2. Literature review Studies related to hotel revenue management and cooperation of hotels with OTAs are discussed in this section. The differences and relationships between these previous studies and the present paper are elaborated. 2.1. Hotel revenue management Hotel revenue management has long been a popular topic not only in academic research but also in practice. Kimes and Chase (1998) consider hotel revenue management as controlling customer demand to improve profits through variable pricing and

Fig. 2. Club 36 Harbour View Rooms for free cancellation of Hotel ICON on its brand website.

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capacity management. Anderson and Xie (2010) outline 25 years of revenue management in the hospitality industry in Cornell Quarterly and regard revenue management as managing customer behavior at an individual level by pricing constrained resources and overseeing availability to maximize profits. Lai and Ng (2005) propose a network optimization model for hotel revenue management by recognizing the demand for multi-night stays and lengths of stay of customers. In practice, Sheraton, Holiday Inn, Hilton Hotels Corp, and Marriott International have been pleased with their profits because of the successful application of revenue management program (Mei and Zhan, 2013). Studies have investigated hotel revenue management by focusing on strategic levers, such as pricing (Baker and Collier, 2003; Bayoumi et al., 2013; Choi and Mattila, 2004; Kimes and Chase, 1998; Noone and Mattila, 2009), overbooking (Liberman and Yechiali, 1978; Noone and Lee, 2011; Phumchusri and Maneesophon, 2014; Rothstein, 1974), customer relationship management (Lo et al., 2010; Noone et al., 2003; Wang, 2012), and demand forecasting (Koupriouchina et al., 2014; Weatherford and Kimes, 2003; Weatherford et al., 2001). Our study discusses hotel revenue management from the perspective of availability management of hotel rooms, that is, optimization of hotel room allocation. Other papers have also considered room allocation as a strategic lever of hotel revenue management. Bitran and Gilbert (1996) develop a model to optimize hotel room allocation among customers and formulate heuristic procedures for deciding the acceptance of reservations. Different from previous studies, they assume that not all of the customers arrive simultaneously on the target date, which is reflected in their model (Bitran and Gilbert, 1996). Koide and Ishii (2005) investigate the optimal room allocation policies for early discount price, overbooking, and normal price. Chen and Kachani (2007) propose a room allocation policy to maximize hotel revenue by setting bookings limits for a particular class of customers (accepting or rejecting a hotel reservation in their case). Their work presents a forecasting framework to optimize room allocation. To maximize hotel revenue, Aziz et al. (2011) develop a dynamic pricing model to allocate room capacity to different customers segments (e.g., types of stay). Instead of setting allocated rooms to different types of stay as decision variables in the classical model, they consider the prices of different segments as decision variables and make significant contribution in increasing the revenue of hotels. By contrast, the present paper optimizes hotel room availability by allocating rooms between the distribution channels of the hotel and OTA. A similar work was conducted by Xu et al. (2014); however, they allocate hotel rooms between a hotel and a thirdparty website by setting online exclusive rooms for the website. In our study, the hotel dynamically determines whether its rooms are available for its cooperative OTA by forecasting future demand base on received room bookings. 2.2. Cooperation with OTAs The essence of cooperation and partnerships among tourism destination communities to sustainable planning and development of tourism destinations has been emphasized in previous studies (Bramwell and Lane, 2000; Byrd, 2007). Pansiri (2013) state that tourism organizations should be encouraged to design and implement tourism marketing plans to enhance collaboration and partnerships. Beritelli (2011) analyzes factors that positively influence cooperative behavior. Czernek (2013) identifies determinants of cooperation and illustrate how they positively or negatively affect this cooperation. Hotels rely heavily on online distribution intermediaries on room booking service (Del Chiappa and Balboni, 2013; Kim et al., 2007). Ma (2009) analyzes e-collaboration in the tourism industry

147

and indicates that e-collaboration widens market and enhances competitive position, creates value, reduces inventories, enables improved communication, and reduces cultural conflicts because players communicate with each other without meeting face-to˜ ´ face daily. Medina-Munoz and Garcıa-Falcón (2000) emphasize that the establishment of cooperative relationships with other organizations improves performance and promotes survival. Considering the important role of OTAs in hotel distribution system, certain researchers develop mathematical model to depict interaction between hotels and OTAs from an individual level. Dong et al. (2014) study the optimal bidding strategy of a tour operator to its cooperative hotels when selling a travel package. Their work provides a theoretical basis for the operation of travel package service between a tour operator and hotels. Guo et al. (2013a) and Ling et al. (2014) examine the optimal pricing strategy of hotels when they cooperate with OTAs by paying commission for a sold room; they depict the cooperation process between hotels and OTAs and provide suggestions for hotels on choosing their cooperative OTAs. However, despite the advantages of applying OTAs to market rooms online, hotels have to address conflicts of distribution channels. Buhalis (2000) studies the conflicts in the distribution channel between hoteliers and tour operators in the Mediterranean region. He identifies the incompatibility and antagonism between targets and goals set by each partner as a major source of conflict (Buhalis, 2000). Myung et al. (2009) examine the influence of ewholesalers on hotel distribution systems and outline that control over room rates, goals of the host website of the hotel, and similar customer bases may lead to channel conflicts. Furthermore, Ivanov et al. (2015) analyze sources of conflicts between accommodation establishments and travel agencies from the perspective of these two parties. Lowest rates from websites of local travel agencies (Law et al., 2007; Tso and Law, 2005) and popularity of third party websites to customers (Morosan and Jeong, 2008) put hotels in a disadvantageous position (Xu et al., 2014). To ease this conflict, Tse (2003) suggests hotels to disintermediate travel agents by building websites to sell hotel rooms directly to customers and then improve their competitive advantage. After examining the conflict between Choice Hotels International and Expedia.com, Lee et al. (2013) advise hotels to select their distribution channels carefully and cooperate with more OTAs to avoid overreliance on one or a few OTAs. They suggest that hotels form consortia to share information about OTA and maintain control over their inventory. Several other papers have studied the conflicts of distribution channels and propose specific solutions (Gazzoli et al., 2008; Grønflaten, 2009; Ivanov et al., 2015; Kaewkitipong, 2010; Law et al., 2015; Toh et al., 2011b). The present paper proposes a new method for hotels to cooperate with OTAs. Different from the aforementioned studies, hotels can handle conflicts between their own distribution channel and OTAs by announcing their room unavailability to OTAs at optimal timing before the target date. Then, the total commission paid to OTA is cut, whereas occupancy rate is maximized.

3. Problem description A hotel cooperates with an OTA to attract more online customers. Hence, the customer market for the hotel consists of two segments: h-customer who books rooms from the hotel directly through telephone calls, from the front desk, or through the hotel-owned website and o-customer who books rooms through the OTA. The hotel charges the same room rate of p for both h-customers and o-customers because customers can easily compare room rates offered by different distribution channels. A booking fee is not exacted. The hotel owns a capacity of C identical

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rooms. The different types of rooms in the hotel are not considered because they can be analyzed separately. Three business models are mostly used between hotels and OTAs, that is, the agency model, the merchant model, and the opaque model (Law et al., 2007; Tso and Law, 2005). Under the agency model, the OTA distributes hotel rooms at agreed-on prices and receives an agreed-on commission for each sold room (Denizci, 2008; Tranter, 2009). Under the merchant model, the OTA purchases a given quantity of rooms from the hotel at a wholesale price, and then marks them up and sells them to o-customers for a profit (Toh et al., 2011b). Under the opaque model, the OTA distributes hotel rooms at an agreed price offered by the hotel; o-customers bid for hotel rooms, and the OTA matches the bids of customers with the lowest bid from hotels and makes a profit through price differentials once the hotel accepts the transaction (Lee et al., 2013). The agency model is used between the hotel and OTA in this paper, and a mathematical model is proposed for the hotel to announce its room unavailability to the OTA at optimal timing to maximize hotel revenue. This mathematical model only works for the agency model. Under the merchant model, the OTA bears the risk of unsold inventory (Lee et al., 2013) and the amount of room allocated to the OTA is determined during contract signing. Thus, the hotel cannot announce its room unavailability to the OTA. Under the opaque model, the hotel usually has low forecasted occupancy rate and sells rooms at discounted prices; that is, the hotel has more rooms than needed (Anderson, 2009). Hence, the hotel no longer needs to announce room unavailability to the OTA. The OTA bills the hotel for commission of ω for each transaction. Usually, the commission is a given proportion of earned room revenue (Toh et al., 2011b). Hence, we assume the commission is  proportion of the room price (i.e., ω = p). The hotel announces that no rooms are available for the OTA after a certain period of cooperation to cut the total commission fee. More specifically, at the beginning of the selling period, rooms can be booked through both the hotel’s direct channel as well as the OTA’s distribution system. The hotel then forecasts future demand base on received room bookings and determines the timing when rooms become unavailable to the OTA. As a result, the occupancy rate of the hotel increases by accepting o-customers.

(t)

Fig. 3. Updated decision-making process.

assumed to follow an exponential distribution with respect to t (Chen and Kachani, 2007), as shown in Fig. 3. Therefore, let the forecasted demand take the form of xi (t) = ai e−bi t + εi (t),

i = 1, 2,

(1)

which is widely used in academic research (Guo et al., 2013b). The stochastic component, εi (t), reflects the fluctuation of demand and follows a normal distribution with mean value i = 0 and standard deviation  i (t). Parameters ai and bi can be obtained by using curvefitting method with the previous received room bookings x˜ i (t). On the other hand, a longer forecasting period results in lower prediction accuracy (Alvarez-Diaz et al., 2009; Burger et al., 2001). Hence, the standard deviation of forecasted demands is set as  i (t) =  i (t0 − t)/(T − t0 ), which is widely used in demand forecasting (Chen and Chuang, 2000).  i is the standard deviation of the set of demand data x˜ i (t), t = t0 , t0 + 1, ..., T. Assuming that the hotel announces room unavailability to the OTA at time t, where t < t0 , then the forecasted demands for time period [0,t] and [t,t0 ] are xi (0 − t) = xi (0) − xi (t) and xi (t − t0 ) = xi (t) − xi (t0 ), respectively. Hence, the expected revenue of the hotel in [0,t0 ] is given as +

¯ + pE min{x1 (0 − t), [C¯ − x1 (t − t0 ) − x2 (t − t0 )] } = pE min{x1 (t − t0 ) + x2 (t − t0 ), C}



−ω

E

x1 (t−t0 )+x2 (t−t0 )≤C¯

[x2 (t − t0 )] +

Moreover, the total commission fee paid to the OTA is cut and the hotel revenue is improved. The present paper aims to determine the optimal timing when hotel rooms become unavailable to the OTA. A special selling period T is considered in this paper. Assume time t is measured from the target date, that is, t = 0 represents the target date and t = T represents the start of the selling period. The hotel cooperates with the OTA on room booking service until time t0 , and the received room bookings for previous T − t0 + 1 days (may be measured by hour and so on without affecting the results) of the selling period are observed as x˜ i (t), where t = t0 ,t0 + 1, . . ., T and i = 1,2 represent the hotel and OTA, respectively. The hotel forecasts future demands base on these received room bookings. Denote the forecasted demand at time t before the target date as xi (t), where t = 0, 1, ..., t0 . The total demand increases as the time to the target date becomes shorter. In addition, as the target date draws nearer, more customers make room reservations in each period. Therefore, the expected part of the forecasted demand is

E

x1 (t−t0 )+x2 (t−t0 )>C¯



¯ 2 (t − t0 )/(x1 (t − t0 ) + x2 (t − t0 ))] [Cx

,

(2)

where C¯ = C − x˜ 1 (t0 ) − x˜ 2 (t0 ) is the remaining unsold rooms. The first expression is the revenue obtained from reserved rooms from both the hotel and OTA in [t,t0 ]. The second expression represents the revenue obtained from room bookings when the hotel sells the remaining rooms alone in [0,t]. As hotel rooms become unavailable to the OTA after the timing t, the third expression is the total commission fee paid to the OTA in [t,T]. Section 4 elaborates the solution methodology to obtain the optimal timing for the hotel to announce room unavailability to the OTA. 4. Research methodology This section outlines the solution methodology for determining the optimal timing for the hotel to announce room unavailability to the OTA. With the received room bookings in time period [t0 ,T], the hotel forecasts future demands and obtains the optimal t by maximizing its expected revenue in time period [0,t0 ].

L. Ling et al. / International Journal of Hospitality Management 50 (2015) 145–152

Table 1 Observed room bookings for h-customers and o-customers during the sample period.

220 200

1st fitting for h-customer demand 2nd fitting for h-customer demand

180

3rd fitting for h-customer demand 4th fitting for h-customer demand 1st fitting for o-customer demand 2nd fitting for o-customer demand

160

Demands

140

3rd fitting for o-customer demand 4th fitting for o-customer demand Observed room bookings for h-customers

120 100

Observed room bookings for o-customers 80 60 40 20 0 0 2 4 7 10 11 Target date

20

30

40

50

149

60

t

Fig. 4. Fitting results for room demands.

Differentiating Eq. (2) with respect to t, the hotel optimizes room availability for the OTA and obtains t from the first-order condition and t ∗ = arg {∂(t)/∂t = 0}. Details are given in the Appendix. t

However, the calculation of t* is not a one-time decision problem. The hotel reaches a more accurate decision with the following update process. With the received room bookings in time period [t0 ,T], the hotel estimates ai and bi using curve-fitting method and then calculates optimal time as t1∗ . If t1∗ < t0 , then the hotel rooms remain available for the OTA until t1∗ . Hence, the hotel updates the observed  room  bookings and obtains a new set of demand data in period t1∗ , T , with which the hotel re-estimates parameters ai and bi and obtains a new optimal decision as t2∗ . This process is repeated until the optimal timing reached for the hotel to announce its room unavailability to the OTA is merely the decision-making timing, that is, t* = t0 . With more data obtained, the demand forecasting accuracy is improved, leading to a more accurate decision. The updated decision-making process is shown in Fig. 3. The decision process is conducted as follows: Step 1. The numbers of room reservation for h-customers and ocustomers in time period [t0 ,T] are obtained as x˜ i (t), where i = 1,2 and t = t0 , t0 + 1, ..., T. Step 2. Based on the observed room bookings, the hotel forecasts future demands as xi (t), t = 0, 1, . . . t0 , and obtains optimal timing t* for announcing the unavailability of its rooms to the OTA with respect to its maximum revenue. Step 3. If t* < t0 , the hotel continues cooperating with the OTA and re-estimates future demands with updated demands in period [t* , T]. The hotel then obtains a new optimal timing by maximizing its revenue. This updating process is repeated until t* = t0 . Step 4. The hotel announces its room availability to the OTA at timing t* and sells the on-hand rooms through its own marketing channel after that timing. A numerical example is conducted in the next section to illustrate the updated decision-making process, and optimal results are obtained.

t

x˜ 1 (t)

x˜ 2 (t)

t

x˜ 1 (t)

x˜ 2 (t)

t

x˜ 1 (t)

x˜ 2 (t)

60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40

8 8 9 10 11 11 12 13 13 14 16 16 17 18 21 23 23 24 26 29 30

6 7 7 8 9 9 10 11 11 12 13 14 14 15 17 18 19 19 21 22 23

39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19

31 34 38 41 45 46 50 52 54 59 62 63 66 68 72 75 80 82 87 89 92

24 26 29 30 31 33 36 38 40 43 43 44 48 51 53 54 59 62 63 65 69

18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

93 96 100 103 106 111 113 115 120 126 132 138 142 147 154 160 166 173 181

72 73 75 76 79 81 84 87 89 93 98 100 102 106 110 114 119 123 129

Table 2 Optimal results for our method and the benchmark model. [t0 , T˜ ]

a1 /b1

a2 /b2

 1 / 2

t*

*

B

[11,60] [7,60] [4,60] [2,60]

212.2/0.04668 197.2/0.04419 190.6/0.04291 187.6/0.04227

156.3/0.04620 144.8/0.04359 138.2/0.04188 135.4/0.04105

34.41/25.16 38.39/28.00 41.80/30.18 44.32/31.82

7 4 2 2

9415.7 5933.1 3433.3 1448.9

9228.3 5825.4 3377.0 1410.0

the number of room bookings may be very small. Hence, received room bookings of the last two months are chosen to forecast future demands, and the sample period is set as T˜ = 60, without affecting the results. Moreover, hotels can conduct demand forecasting from the beginning of the selling period. Nevertheless, in practice, hotels usually announce the unavailability of their rooms to the OTA several days before the target date. Thus, t0 = 11 is chosen in the first fitting. The input data of the observed room bookings for h-customers and o-customers during the sample period are given in Table 1. A scenario where the hotel cooperates with the OTA throughout the selling period is set as a benchmark. A comparison is conducted between the cooperative form proposed by the present paper and the benchmark to determine whether this new method generates higher hotel revenue. Considering the relationship between the total number of room bookings and room capacity, the expected revenue of the hotel in the benchmark in period [0,t0 ] is as follows:

⎧

⎪ p [˜xi (0) − x˜ i (t0 )] − ω[˜x2 (0) − x˜ 2 (t0 )], if [˜xi (0) − x˜ i (t0 )] ≤ C¯ ⎪ ⎨ i i B



 = ¯ ¯ ⎪ [˜xi (0)− x˜ i (t0 )] , if [˜xi (0) − x˜ i (t0 )] > C¯ ⎪ ⎩ pC − ωC [˜x2 (0) − x˜ 2 (t0 )] / i

i

(3)

5. Numerical example

The optimal results are shown in Table 2. By observing the achieved  room  bookings for h-customers and o-customers in period t0 , T˜ , ai and bi are estimated by applying curve-fitting

In this section, we take a hotel with a capacity of C = 300 rooms as an example, where the room rate is p = 100 and the commission paid to the OTA is  = 15% of the room rate, that is, ω = p = 15. In practice, hotel rooms can be booked as early as one year before the target date. However, during the early part of the selling period,

method using the Cftool of Matlab 2011b (® 7.13.0.564). The fitting results are shown in Fig. 4. The decision process is as follows. First, based on the room bookings in period [11,60], that is, t0 = 11, the cooperation between the hotel and OTA is forecasted to continue until seven days before the target date because the optimal timing for announcing room unavailability to the OTA is calculated

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Fig. 5. Number of rooms sold by the hotel and OTA at different timings.

as t* = 7 < t0 . Next, the hotel re-estimates future demands with the achieved room bookings in [7,60] (t0 is updated and t0 = 7), and obtains the optimal timing as t* = 4 with respect to its maximum revenue. Given that t* = 4 < t0 , the hotel continues to cooperate with the OTA on room booking service until four days before the target date. The hotel then updates the received room bookings to period [4,60] (i.e., t0 = 4) and forecasts future demands base on these bookings. To maximize its revenue, the hotel calculates the optimal timing for announcing room unavailability to the OTA as t* = 2. The cooperation between the hotel and OTA is continued because t* = 2 < t0 . Finally, with the committed room bookings in [2,60] (i.e., t0 = 2), the hotel optimizes its room availability with respect to its maximum revenue, and the optimal timing is obtained as t* = 2. The hotel decides to announce its room unavailability to the OTA two days before the target date because t* = 2 = t0 . The results shown in Table 2 indicate that the revenue of the hotel using the new cooperation method is larger than that of the benchmark scenario. Thus, this new cooperation will result in an improvement of 2.76% in hotel revenue. The number of rooms sold by the hotel and OTA at different decision-making timings are shown in Fig. 5. In summary, the hotel cooperates with the OTA on room booking service from the beginning of selling period until two days before the target date. Through a four-round tradeoff, the hotel announces its room unavailability to the OTA two days before the target date. By then, 119 of 300 rooms are sold by the OTA, while 166 ones are sold by the hotel. The hotel does not share the remaining rooms with the OTA after that time because the forecast indicates that the hotel can sell out all the on-hand rooms through its own marketing channel. This method can indeed result in the improvement of hotel revenue. 6. Conclusions 6.1. Findings and managerial implications High commissions paid to OTAs cause financial problems to hotels when cooperating with OTAs (Gazzoli et al., 2008). An effective way for hotels to solve this problem is to induce online customers to make room reservations through their own direct channel rather than through OTAs (Toh et al., 2011b; Tso and Law, 2005). The present paper proposes a new method for hotels to cooperate with an OTA on room booking service by managing the availability of hotel rooms for the partner OTA. In this method, the hotel cooperates with the OTA at the beginning of the selling period and then forecasts future demand base on achieved room bookings. Based on the forecasting results, the hotel determines whether onhand rooms are available for the OTA with respect to its maximum revenue. To obtain a more accurate decision, the hotel updates the received room bookings dynamically and forms new decisions. A numerical example is conducted to illustrate this decision process, and results indicate that the hotel decides to announce its room unavailability to the OTA two days before the target date after a

four-round tradeoff. Hotel revenue is improved through the application of this new cooperation method. Theoretical and managerial implications of this paper are as follows. First, hotels should conduct accurate demand forecasting to improve revenue management. Curve-fitting method is proposed in this paper to forecast future demands base on received room bookings. Demand forecasting is crucial in hotel revenue management activity (Lim et al., 2009; Tse and Poon, 2012), and an improved forecast of room demand provides insightful instruction for developing room reservation strategies (Rajopadhye et al., 2001; Yang et al., 2014b). In addition, based on earlier observations collected from customer reservation system, hotels need to adjust forecasted demands dynamically to obtain accurate decisions. Second, this paper proposes a new method for hotels to manage their room availability for cooperative OTAs. Instead of setting exclusive rooms for third-party websites (Xu et al., 2014), this paper advises hotels to forecast future demands base on observed room bookings and then determine the optimal timing for announcing room availability to OTAs repeatedly. Third, although hotels appreciate OTAs for increasing their visibility and online sales (Inversini and Masiero, 2014; Lee et al., 2013; Yacouel and Fleischer, 2012), profit margins of hotels significantly decrease as a result of high payment to OTAs (Thakran and Verma, 2013; Toh et al., 2011b). To cut the total commission paid to OTAs and earn more revenue, hotels can announce their room unavailability to OTAs at optimal timing before the target date. The numerical results indicate an improvement of 2.76% in hotel revenue. Fourth, a large proportion of customers appreciate OTAs as a convenient channel to search travel information and make room reservations (Kim et al., 2007). However, this paper suggests that if customers cannot find their desired hotel rooms from OTAs, they can turn to the brand website of hotels to make reservations. This fact will increase click traffic of the brand website of hotels. Once customers book rooms successfully from the brand website after learning that their preferred rooms are sold out on the webpage of OTAs, their goodwill toward the brand website will be enhanced. Then, more online customers are induced to book rooms in the hotel website. 6.2. Limitations and future research directions The present paper is limited in several aspects. First, the cooperation method between a hotel and an OTA is discussed only from the perspective of the hotel (by maximizing its revenue). In recent years, however, OTAs have had an increasingly strong bargaining position in their interaction with hotels. As a result, discussing the cooperation between the two parties in the context of game theory is a pragmatic approach. Second, hotels usually cooperate with a number of OTAs. Thus, utilizing a one (hotel)-more (OTAs) model can be interesting. Third, in this paper, we assume that all rooms are identical although hotels actually have different types of rooms.

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Consequently, in future studies, different types of rooms can be considered when hotels adopt upgrade or downgrade strategies to improve the total occupancy rate of all of the rooms. Finally, the last room availability has long been the main issue for OTAs and hotels. Future research on this topic may solve the controversy between hotels and OTAs. Acknowledgements This work was supported by the National Natural Science Foundation of China (Nos. 71271197; 71371086), the Foundation for International Cooperation and Exchange of the National Natural Science Foundation of China (No. 71110107024), the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (No. 71121061), the Scientific Fund for Innovative Research Groups of USTC (No. WK2040160008), the China Postdoctoral Science Foundation (No. 2014M560523) and the China National Tourism Administration (No. 15TAAK009). Appendix. Normalize the random variables in the stochastic component as z0 =

ε1 (0) ε1 (t) , z1 = , 1 t0 /(T − t0 ) 1 (t0 − t)/(T − t0 ) ε2 (t) 2 (t0 − t)/(T − t0 )

z2 =

Set (z) as the standard normal probability density function while ˚(z)√ as the standard normal distribution function. Since 2 (z) = (1/ 2)e−z /2 , we have  (z) =

√ d 2 [(1/ 2)e−z /2 ] = −z (z) dz

Differentiate the hotel revenue with respect to t and apply the above equation, the optimal time for the hotel to announce the room unavailability to the OTA, t* , is obtained as t ∗ = arg {g(t) = 0}, t

where g(t)



∞

= b2 A2

(z2 )˚(X)( − ˚(Y ))dz2 − −∞

−

−



t0 M (t0 − t)

∞

(z2 ) (X) (Y )dz2 −

2 −∞

(C¯ + A10 + A20 − a1 − A2 (t))M





∞



− C¯

∞

˚(X)( − ˚(Y ))d (z2 ) −∞



∞

(X)˚(Y )d (z2 ) −∞

(z2 ) (X)˚(Y )dz2 −∞



∞

h(z1 , z2 ) (z1 )dz1 −∞

M2 (t0 − t)1



∞

2

(t0 − t) 1 /(T − t0 )

2 T − t0

(z2 )dz2

X

with 2 C¯ + A10 + A20 − A1 (t) − A2 (t) − z2 , 1 1 (t0 − t)/(T − t0 )

A10

= a1 e−b1 t0 , A20 = a2 e−b2 t0 , X =

Y

=

M

= C¯ + A10 + A20 − A1 (t) − A2 (t) + (t0 − t)(b1 A1 (t) + b2 A2 (t)), and

C¯ + A10 + A20 − a1 − A2 (t) (t0 − t)2 z2 , − t0 1 1 t0 /(T − t0 )

h(z1 , z2 ) =

+



b1 A1 (t)(A2 (t) − A20 ) − b2 A2 (t)(A1 (t) − A10 )

2

A1 (t) − A10 + A2 (t) − A20 + (t0 − t)(z1 1 + z2 2 )/(T − t0 )

.

(A2 (t) − A20 − b2 A2 (t)(t0 − t))z1 1 − (A1 (t) − A10 − b1 A1 (t)(t0 − t))z2 2 (T − t0 )(A1 (t) − A10 + A2 (t) − A20 + (t0 − t)(z1 1 + z2 2 )/(T − t0 ))

2

151

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