Dynamic pricing for online hotel demand: The case of resort hotels in Majorca

Abstract

Online customer behavior in terms of price elasticity of demand and the effect of time along the booking horizon are key requirements for the price optimization process that allows hotels to maximize their revenues. In this vein, this study adapts the online transient hotel demand functions to deterministic and stochastic dynamic models—two extended optimal pricing methods existing in the literature—in order to determine the prices that maximize the revenues of two resort hotels located in Majorca. The main findings indicate that (1) seasonality, the number of rooms available, the hotel location, and the tourist profile affect dynamic pricing (DP); (2) the booking horizon limitation leads to larger revenue decreases under elastic demand; (3) higher levels in demand elasticities generally produce lower levels of prices; and (4) the distribution of elasticities across the booking horizon and the natural variability of demand have an impact on DP. Implication for industry revenue managers is that they have to consider the booking horizon duration together with the demand price sensitivity in order to maximize the hotel revenues.

Keywords

Booking horizon demand deterministic model dynamic pricing price elasticity of demand revenue maximization stochastic model

Introduction

In recent years, the study of pricing techniques has become a popular field of research in hotel revenue management (RM) literature. Legohérel et al. (2013) and Ivanov and Zhechev (2012) define RM as the application of information system control and pricing that allows for revenue maximization via the allocation of the right capacity at the right time in the right place. Cross et al. (2011) point out that RM has helped many companies to increase their profits, as they are able to sell a relatively homogeneous product at different prices to different types of customers. The perishability of the hotel product, in conjunction with the capacity limitations of hotel establishments as well as seasonality, makes demand management a crucial factor in the revenue maximization process (Coenders et al., 2003; Ivanov and Zhechev, 2012). Demand management is especially relevant in the short run, due to the impossibility of changing the number of rooms during this period (Coenders et al., 2003). Price variations enable the revenue manager to adjust demand to the desired occupancy levels at any point along the booking horizon which leads to revenue maximization at the date of stay. In the hotel sector, the most common way to segment customers is to set different prices according to tourist booking behaviors (Hanks et al., 2002). The reason for limiting the number of rooms to be sold at any moment on the booking horizon is based on the expectation that they will be sold in the future to a more profitable demand (Aziz et al., 2011). Thus, pricing represents a key tool in hotel RM.

There are two popular dynamic pricing (DP) models used in the literature for the revenue maximization, the first type is the deterministic model which is used to discriminate prices across the booking horizon, thus allowing for revenue maximization (Aziz et al., 2011; Guadix et al., 2010; Lee, 2011). The second type is the stochastic model, mainly a consumer choice framework, which segments the demand into different classes; every class is individually measured, as they are interrelated, and the objective is the determination of market responses to price variations (Ratliff et al., 2008; Suzuki et al., 2001; Talluri and van Ryzin, 2004a).

In this article, we propose an application of these two types of DP models for online transient demand that allow for revenue maximization at the hotel level and consider the demand response to price variation, as well as the seasonal and the booking date effects.

The first step in the revenue maximization process is the measurement of the market reactions to price variations, that is, the demand function estimations (Lee, 2011; Shy, 2008). In order to maximize revenue in this case, we use a demand model that measures the own-price elasticity values under different seasonal demands and across booking horizons.

In practical terms, hotels need to learn how to use the huge amount of information available more efficiently in order to segment the demand, estimate its response to price variations, and maximize revenues. Understanding customer behavior, through an efficient use of data that a hotel is able to collect, represents a key step in the RM context, as well as in the revenue maximization process across the booking horizon and along the different seasons. It is especially relevant in the resort hotel sector, as the implementation of advanced RM techniques is usually low and the level of empirical academic studies with industry implications is quite scarce.

The present article has two main objectives: (1) to adapt and apply the two widespread revenue maximization models used in the literature to the hotel resort segment, that is, the deterministic and stochastic DP models; and (2) to provide an empirical comparison of both models for the emerging online transient segment using data from two resort hotels located in Majorca, which could be useful to answer relevant questions for the island’s resort sector such as: which type of model is more effective in maximizing the resort hotel’s revenue?; how do the different values taken by the price elasticity of demand affect seasonal and booking horizon dynamic prices?; how do the hotels’ characteristics and specific demand behavior affect the estimations of optimal prices and revenues?; which effects may have limitations on the number of rooms allocated to the online transient segment¹?; and what are the effects of the discounts offered along the booking horizon?

DP models and their empirical testing are quite extended in the airline sector, they are also quite common in the urban hotel sector, but as we pointed out before, their application in the resort hotel sector is more limited. In fact, there is no evidence in the RM literature of such a broad definition of DP models nor is there evidence of empirical testing focused on the hotel resort sector. In addition, these models are easily replicable for the rest of resort hotels due to their characteristics—the wide range of seasonal effects and the variability of prices due to the different types of room and board pricing schemes (Cross et al., 2009)—and because the estimation derived from the two hotels provides sufficient scenarios to test a large range of situations. The hotel industry, particularly the RM departments, will be able to benefit from our research, as our results show that a broad study of an individual resort hotel’s behavior can improve the online demand optimal pricing that allows for revenue maximization and thus leads to an improvement in RM techniques. It could represent a step toward the introduction of DP techniques in the resort segment.

The structure of this article is organized as follows. The section following the “Introduction” section presents a literature review focused on DP and revenue maximization. The third section details the data used from two resort hotels in Majorca. The fourth section describes the methodology, that is, the demand model used and the two different price optimization models analyzed. The fifth section outlines the results of the estimation of prices, sales, and revenues; finally, in the sixth section, we discuss the implications of the results in terms of DP and industry pricing strategies.

Literature review

Classical modeling of hotel revenue maximization focuses on optimal allocation (Aziz et al., 2011). Optimal allocation means selling the right amount of inventory at a given price, where each of these prices is associated with one of various previously identified classes/segments (El Gayar et al., 2011; Pan, 2007). However, more complex models are associated with differences in the customers’ willingness to pay as the date of stay approaches. So, problems arise when trying to set a pricing policy that is able to maximize the company’s revenue, while considering the sensitivity of demand to price variations (Aziz et al., 2011; Badinelli, 2000). These models are called DP models, and they maximize revenue by offering a price that reflects current demand and hotel occupancy levels (Ivanov and Zhechev, 2012), while considering different customer behaviors along the booking horizon. The dynamic models are mainly used to deal with the trade-off between selling a room today and waiting for an expected higher price that a potential customer will pay in the future (Chatwin, 2000; Guadix et al., 2010). In practical terms, Aziz et al. (2011) highlight the advantages of DP models as different price segments for each overnight stay are considered. In order to maximize revenues, they set different price categories along the booking horizon as well as allow for the introduction of dynamic changes when a new reservation takes place. Ratliff et al. (2008) point out that dynamic models vary as a function of time along the booking horizon. Thus, the time before the date of stay plays a key role in price determination.

In that sense, a direct and common way to typify customer behavior is through a demand function, which is able to reflect the consumers’ willingness to pay (Shy, 2008). The demand function estimation is a powerful tool in revenue maximization as demand changes can be measured under different price structures and market conditions (Lee, 2011; Lee and Jang, 2011). In the hotel sector, Hormby et al. (2010) use the demand modeling in order to segment the demand based on the hypothesis that customer sensitivity varies depending on variables such as the booking date, group size, and season. Lee (2011) in order to assess the linear demand models in different hotel typologies—airport, suburban, and urban hotels—uses the following variables: prices, reservation date, length of stay, and the weekday of arrival. Aziz et al. (2011) estimate the demand with a probit function. Guo et al. (2013) study the DP strategy in the hotel sector through online market demand segmentation. They use two types of demand functions, linear and nonlinear, and estimate the optimal number of market segments to be differentiated along the booking horizon that allow the revenue maximization.

The DP models usually consider the willingness to pay as the date of stay approaches and allow the hotel revenue maximization; they can be classified into deterministic and stochastic or probabilistic approaches (Talluri and van Ryzin, 2004b).

The deterministic dynamic models allocate the hotel capacity according to the average demand along the booking horizon (Talluri and van Ryzin, 2004b). Guadix et al. (2010) point out that the deterministic models try to anticipate the price elasticity of each demand segment that allows the hotel revenue maximization. In practical terms, Aziz et al. (2011) develop a DP model that allows for hotel revenue maximization for each overnight stay. The model enables consumer segmentation through daily price variations, which are influenced by the time before the date of stay and the hotel occupancy. Guadix et al. (2010) attempt to anticipate the number of rooms that can be sold for a specific date of stay; they forecast the price elasticity of each demand segment and the expected sales that maximize the hotel revenue. Lee (2011) defines the hotel product as a combination of the following variables: the reservation’s arrival date and the length of stay which are limited by the available capacity at this specific date.

However, the stochastic nature of the tourism demand makes it never perfectly predictable, as the customers book the product before its consumption at the date of stay. Thus, the stochastic processes allow the anticipated demand to differ from the historical average demand levels (Badinelli, 2000; Guadix et al., 2010), where the customer only buys the product if its price is below his or her maximum willingness to pay (Chatwin, 2000; Zhao and Zheng, 2000). Several stochastic dynamic models specify the demand following a Poisson process as the booking horizon draws closer to the date of stay and the inventory diminishes (Chatwin, 2000; Gallego and van Ryzin, 1994; Talluri and van Ryzin, 2004a; Zhao and Zheng, 2000).

More specifically, stochastic models consider that bookings are able to capture the variability in the customers’ product valuation and perception, in terms of the probability of a product being available over time (Yilmaz et al., 2016). Thus, the stochastic models allow hotel rooms reservations different from the mean (historical data), by considering the natural variability of the demand (Guadix et al., 2010). Stochastic models capture customer choice probabilities and measure their utility based on the use of historical data (Ratliff et al., 2008; Talluri and van Ryzin, 2004a). The interdependence of the different segments is considered by the customer choice models; these models are able to represent the heterogeneity of preferences of each segment, while they can also model uncertainty, as a large range of customer behaviors (Talluri and van Ryzin, 2004b). The stochastic models are also able to measure the cross-elasticities effects, and these can involve price variations of a company within a market, a segment class within a product demand, a booking time along the booking horizon, and others. Most of them use multinomial logit (MNL) models, which consider that individual demands are affected by different known attributes, and so their effects influence consumer choices. Therefore, the MNL model allows for the consideration of different variables such as the ability to be refunded, minimum length of stay, and other non-price factors, which are not properly captured by the deterministic models.

When deterministic and stochastic models are compared, Guadix et al. (2010) find that in those situations, when the demand is higher than the supply, the likelihood of a customer accepting higher prices is larger in the stochastic models. They find that the deterministic model obtains better results when analyzing the whole demand hotel behavior. In terms of hotel DP, Zhang and Weatherford (2016) highlight that the deterministic linear programing performs well when the different network effects are considered, that is, the effects on demand and capacity caused by multiple lengths of stay, while the demand uncertainty is ignored. Meanwhile, the stochastic DP formulation is able to solve the demand uncertainty, but the network effects are only captured through bid prices and prices proration. Regarding the dynamic room allocation, Aydin and Birbil (2018) detect that the consideration of the stochastic nature of the demand and the network effect improve the bid price policies for advance bookings. When the authors also consider the stay over room consumption, the stochastic models behave better as they consider the uncertainty of staying more nights beyond the reservation. On another hand, when the customer behavior is compared when facing a price increase or a price discount, Suzuki et al. (2001) use a logit model that considers variables such as the service quality and prices in the airline sector, detect an asymmetric market response, and find a stronger market response to a price increase compared to a price reduction. Guizzardi et al. (2017) highlight that the consideration of the stochastic nature of hotel price trends along the booking horizon is usually not effective, due to the lack of price variability of urban hotels located in Italy. In this context, Oses et al. (2016) find that most of the price changes across the booking horizon of hotels located in Bilbao correspond to competitors’ price variation, demand fluctuation, and inventory changes. Cho et al. (2018) using US luxury-urban hotel database are able to predict the hotel pricing behavior in a dynamic way, as well as the level of bookings and cancellations using a stochastic model. They also observe that revenue managers follow the price competitors’ trends, while they usually do not follow the RM system recommendations. Nevertheless, their results suggest that the pricing strategy followed is competitive, as the hotel considers the demand behavior and the competitors’ price levels in its decision process.

The available literature identifies some problems with DP models. For example, Badinelli (2000) finds that sometimes historical demand data do not offer good predictions of the future and in those cases, real booking data would improve the estimations of future demand. Ratliff et al. (2008) also stress the problem of data availability: most of the time information is only available on the company studied. Meanwhile, the choice models focus on the market-level context. These problems can be mitigated by looking at long historical periods that incorporate the seasonal and booking horizon demand behavior. Additionally, current booking information can introduce demand behavior shifts which are not reflected in historical demand behavior.

Finally, we highlight the main gaps found in the literature. There are just a few academic empirical studies that addressed the issue of advanced RM techniques in the hotel resort sector, especially analyzing industry implications; hence, the DP studies in the sector are even more limited. Furthermore, the articles available comparing the deterministic and stochastic models performance in the DP context are also very few. Thus, the combination of both factors, the scarcity of DP studies in the resort hotel sector and the scarcity of DP models comparison, makes the findings of the present empirical study quite relevant to cover a gap in the literature.

Data

The present study uses data on the online transient segment from two 4-star Majorcan hotels belonging to one of the top four multinational hotel chains in the Balearic Islands. The hotel chain provided the data on the two hotels included in the study, two hotels located in the same destination that allowed a proper comparison of results. Hoteliers need technological solutions that allow them to improve the way they use all the information they are able to collect/generate, while allowing them to increase the customer knowledge, which lead to a better customer segmentation and an increase of revenues.

Regarding the hotel chain information, it annually sets individual hotel prices which vary according to the seasonal period of stay, type of room, type of board, guest type, booking date, length of stay, and method of payment. The highest prices are found during July and August, the peak season. Concurrently, 32–41% of bookings take place during the peak season, when a 31.5% of international tourist arrivals to Majorca’s airport concentrate (CAIB, 2018). Regarding the price evolution across the booking horizon, each hotel sets three predetermined early booking periods offering discounts of between 5% and 15% depending on the specific date. The multinational hotel chain owns 15 four- or five-star hotels in the island of Majorca and operates over 120 hotels in 16 countries worldwide (Iberostar, 2019), most located next to a beach (97% of them are resort hotels).

Regarding the hotels’ characteristics, hotel 1 has 619 rooms, and almost 33% of the reservations are made online. Hotel 2 has 366 rooms, and slightly more than 35% of the reservations are made online. During the last few years, the growth of the online segment has been substantial in both hotels. Hotel 2 is located in a very popular and highly transited area of Majorca, with more than twice as many beds as the area in which hotel 1 is located (CAIB, 2018). Regarding the tourist profile, the demand for hotel 1 comes mainly from Germany and Spain. Most of the tourists are families, 90% of reservations are made with all-inclusive board, and the length of stay averages almost 7.5 days. The demand for hotel 2 mainly comes from the German and English markets. Most of the tourists are couples, only 50% of reservations are made with all-inclusive board, and the length of stay is 8 days on average.

The hotel chain supplied all of the information necessary for obtaining the different demand functions: the daily room reservations (Q_t ) and daily prices (P_t ). The dates of stay are grouped into homogeneous dates of stay: the dates farther from the dates of stay where the reservations’ pace and prices are low (period I) and the dates closer to the dates of stay where the level of bookings and prices significantly increase (period II). Finally, each of these groups of dates of stay is divided in two differentiated demands functions, which are used in the revenue maximization methodologies, due to the two differentiated booking behaviors found by Vives et al. (2019).

The main limitation of information available is the impossibility to introduce the hotels competitor’s prices and the tour operator’s demand in the demand function and DP models, due to the incompatibility of data sources and/or lack of detailed information.

Methodology

Demand model

As we pointed out in the “Literature review” section, the demand function is a direct way for measuring the customer behavior in the hotel reservation process. In that specific case, the number of online transient bookings (Q^d ) for a specific date of stay (d) is a function of the price set by the hotel (p^d ) and the booking time (r^d ), that is, the distance between the date of stay and the booking date

Q_{t}^{d} = f (p_{t}^{d}, r_{t}^{d})

where time t represents the date along the booking horizon (t = 1, 2,…., d), and d represents the date of stay, that is, the last observation across the booking horizon.

The demand function can be specified by a linear formulation (2) or a linearized Cobb–Douglas formulation which can be linearized with the application of natural logarithms (3) (Guo et al. 2013; Suzuki et al., 2001; Vives et al., 2019)²

Q_{t}^{d} = α_{0} + D u m m i e s + α_{p} \cdot p_{t}^{d} + α_{r} \cdot r_{t}^{d}

Ln Q_{t}^{d} = β_{0} + D u m m i e s + β_{p} \cdot ln p_{t}^{d} + β_{r} \cdot ln r_{t}^{d}

D u m m i e s_{y, d, b} = \sum_{y = 1, 2, \dots, Y} β_{y} D y + \sum_{d = 1, 2, \dots, D} β_{d} D d + \sum_{b = 1, 2, \dots, B} β_{b} D b

The b factor is the booking period and the y factor represents the year when the observation takes place.

Finally, the dummy Dy represents the year of the date of the stay and takes the value 1 when the observation pertains to a specific year and 0 otherwise (yy), as we are working with historical booking data from different years. The booking period (Db) takes the value 1 when the observation pertains to a specific period of time across the booking horizon and 0 otherwise (mm). The date of stay (Dd) takes the value 1 when the observation pertains to a specific date of stay and 0 otherwise (d), which is the last observation along the booking horizon.

The demand function previously defined can be applied to most of the resort hotels, due to the fact that it considers most of the parameters affecting the resort hotel transient demand, while is able to consider the demand behavior.

Price optimization—Deterministic model

The representation of the revenue maximization model (R) is quite common in the DP literature (Aziz et al., 2011; Badinelli, 2000; Guadix et al., 2010; Lee, 2011)

R (t') = Max \sum_{t^{'}} Q_{t'}^{d} \cdot p_{t'}^{d}

Thus, with the number of online transient reservations $(Q_{t'}^{d})$ multiplied by the price $(p_{t'}^{d})$ , we can obtain the number of average daily room reservations (q_t′ ) that t′ maximizes the revenue obtained along the booking horizon t′ and for each date of stay d.

Before this, we must transform the demand function in order to isolate the price variable, which allows the optimization to be performed over one variable (q_t′ )

- β_{p} \cdot ln p_{t'}^{d} = ln q_{t'}^{d} - β_{0} - D u m m i e s_{y, d, b} - β_{r} \cdot ln r_{t'}^{d}

e^{ln p_{t'}^{d}} = e^{\frac{ln q_{t'}^{d} - β_{0} - D u m m i e s_{y, d, b} - β_{r} \cdot ln r_{t'}^{d}}{- β_{p}}}

f (q_{t'}^{d}, r_{t'}^{d}) \to p_{t'}^{d} = e^{\frac{ln q_{t'}^{d} - β_{0} - D u m m i e s_{y, d, b} - β_{r} \cdot ln r_{t'}^{d}}{- β_{p}}}

In order to simplify the notation, we are going to work with only one date of stay. Additionally, two different demand functions are used as defined in the work of Vives et al. (2019), where they detect two differentiated demand behaviors along the booking horizon for the same dates of stay; therefore, as t′ varies as the date of stay approaches, it is possible to distinguish two different demand functions $f (p_{1, t'}, r_{1, t'})$ and $f (p_{2, t'}, r_{2, t'})$

Max R (t') = \sum_{1, t'} Q_{1, t'} \cdot f (q_{1, t'}, r_{1, t'}) + \sum_{2, t'} Q_{2, t'} \cdot f (q_{2, t'}, r_{2, t'})

s.t. (1) $λ_{1} : \sum_{1, t'} Q_{1, t'} + \sum_{2, t'} Q_{2, t'} \leq r$

s.t. (2)

λ_{2} : p_{1, 1} \leq p_{1, 2} \leq \dots \leq p_{1, n - 1} \leq p_{1, n} \leq p_{2, n + 1} \leq \dots \leq p_{2, d - 1} \leq p_{2, d} = f (q_{1, 1}, r_{1, 1}) \leq f (q_{1, 2}, r_{1, 2}) \leq \dots \leq f (q_{1, n}, r_{1, n}) \leq f (q_{2, n + 1}, r_{2, n + 1}) \leq \dots \leq f (q_{2, d}, r_{2, d}) \forall t'

where n ≤ d.

The Lagrange multiplier is a common approach used to estimate the prices and bookings along the booking horizon that maximize the revenue, while considering the number of reservations subject to the number of rooms, r, the revenue manager is willing to sell (s.t. (1)); the maximum number of rooms that can be sold is the hotel capacity. Vives et al. (2019) group hotel sales into two groups, one for online sales and the other for tour operator sales; the tour operator sales are negotiated a long time in advance, while the online sales take place in the short-run context. Thus, both types of demand are not compatible with each other in the same dynamic model, and the number of rooms allocated for each segment can vary across the different dates of stay, that is, the managers first decide the capacity to be allocated to the tour operator segment and the rest of capacity is assigned to the online transient segment. While the second constraint (s.t. (2)) is an optional pricing policy defined by the revenue managers, they want to know the optimal price that can be set at every moment without the possibility of decreasing prices along the booking horizon policy

L (1) = (q_{1, 1}, q_{1, 2}, \dots, q_{1, n - 1}, q_{1, n}, q_{2, n + 1}, \dots, q_{2, d}, λ_{1})

L (2) = (q_{1, 1}, q_{1, 2}, \dots, q_{1, n - 1}, q_{1, n}, q_{2, n + 1}, \dots, q_{2, d}, λ_{1}, λ_{2})

The final output is the optimal price for each moment of time for each of the predefined periods of time t′ for each demand function. Every price (p_t′ ) is directly linked to the average number of daily room reservations (q_t’ ) that maximizes revenues, subject to the number of rooms available.

Price optimization—Stochastic model

The stochastic models in the hotel DP report a utility that is associated with a probability of sales, usually MNL models (Ratliff et al., 2008; Talluri and van Ryzin, 2004a), and the objective is the utility maximization of each alternative (Anderson and Xie, 2016). In our case, it would be the probability that takes place in each period along the booking horizon. Nevertheless, the dependent variable (Q_t _′) in our demand function (1) takes nonnegative integers. Therefore, the Poisson regression is more suitable as the hotel reservations are an observed count and follow a Poisson distribution as pointed out by several authors (Chatwin, 2000; Gallego and van Ryzin, 1994; Zhao and Zheng, 2000). The Poisson regression is a stochastic model with some similarities to a logistic regression and containing a discrete explanatory variable. In the same way, Wang et al. (2015) indicate that a multivariable linear regression is not a suitable model for estimating the hotel booking as it is not normally distributed. They highlight that the Poisson regression model is more appropriate as it is a discrete variable. Chen et al. (2011) and Karimi et al. (2015) also use a Poisson regression model to forecast aggregate international tourism demand.

In the Poisson regression model, the expected value of the dependent variable, bookings (Q_t _′), is denoted by E(Q_t _′) = µ_t _′

Where the probability (Pr) of the Poisson regression model in the booking moment t′ is drawn from Chen et al. (2011)

Pr ({Bookings}_{t'} = Q_{t'}) = \frac{e^{- µ_{t'}} µ^{Q_{t'}}}{Q_{t'}!} (Q_{t'} = 0, 1, 2, \dots .)

The Poisson is a log-linear model

log µ_{t′} = f (p_{t′}, r_{t′})

µ_{t′} = e^{f (p_{t′}, r_{t′})}

Again a revenue maximization model (R) with the Lagrange multiplier method is used, similar to the deterministic model

R (t') = Max \sum_{t'} p_{t'} \cdot e^{f (p_{t'}, r_{t'})}

s.t. (1) $λ_{1} : \sum_{1, t'} Q_{1, t'} + \sum_{2, t'} Q_{2, t'} \leq r$

s.t. (2)

λ_{2} : p_{1, 1} \leq p_{1, 2} \leq \dots \leq p_{1, n - 1} \leq p_{1, n} \leq p_{2, n + 1} \leq \dots \leq p_{2, d - 1} \leq p_{2, d}

And again the two demand behaviors are introduced in the maximization process

R (t') = Max \sum_{1, t'} p_{1, t'} \cdot e^{f (p_{1, t'}, r_{1, t'})} + \sum_{2, t'} p_{2, t'} \cdot e^{f (p_{2, t'}, r_{2, t'})}

Results

In this section we present some illustrative examples from all of the cases obtained in our study. Firstly, Figures 1 and 2 present two estimations examples from both hotels’ optimal prices, daily number of room reservations from online transient demand, and elasticities, as well as the observed prices and reservations for the season 2016 and the average from the last three seasons (2014–2016). Four different estimations are presented: the deterministic and stochastic models subject only to the first constraint, the limitation in the number of rooms (s.t. (1)), and both models again but subject to the limitation in number of rooms (s.t. (1)) plus the policy of not decreasing prices across the booking horizon (s.t. (2)).

Figure 1.

Examples showing hotel 1’s seasonal optimal prices, daily number of room reservations, and elasticities (estimated and observed; example). Source: Own elaboration.

Figure 2.

Examples showing hotel 2’s seasonal dynamic prices, daily number of room reservations, and elasticities (estimated and observed). Source: Own elaboration.

In general, the deterministic dynamic model present larger levels of price variability, but lower levels of variability in bookings compared to the stochastic model. Thus, Figures 1 and 2 show that the estimated reservations across the booking horizon of the stochastic model are more irregular. However, the price levels are usually higher in the deterministic model, and the trend that they follow is more similar to the average prices when the last three seasons (2014–2016) are considered, while the prices in the stochastic model are lower and present more similarities to the prices of the last season (2016). The main reasons for these outcomes are explained by the fact that the deterministic dynamic models estimate the bookings according to the average demand of the historical data (Talluri and van Ryzin, 2004b), while the stochastic models allow the estimations of bookings different from the average demand, by allowing the natural variability of demand (Guadix et al., 2010). Similarly, Guadix et al.’s (2010) results indicate that the deterministic models obtain better estimations in terms of revenue.

In general terms, both models present lower levels of reservations on the earliest booking dates, and they increase as the date of stay approaches, while the prices were always higher on average during period II (Aziz et al., 2011). Furthermore, the second constraint in the model (s.t. (2)) led to maintenance or reduction of prices in the maximization processes depending on the elasticities disposition across the booking horizon and their values, in general the behavior is similar in both types of models.

When comparing the elasticities of both hotels with their specific booking and prices levels across the booking horizon, it is clear that none of these factors is directly related with the differential pricing. The pricing differences are also explained by the specific booking characteristics, the type of tourist, and the hotel location. Nevertheless, higher levels of demand elasticities usually produce lower levels of prices in the models’ estimations, in the same way as observed by Perakis and Sood (2004).

In terms of revenue projections from both models, which are obtained by multiplying the price and booking estimations, we can say that on average the deterministic model provides revenues 14.1% higher than the observed revenues from the last season (2016) in hotel 1, and a 14.7% higher in hotel 2, while the stochastic model provides revenues a 3.1% higher in Hotel 1, and a 0.4% higher in Hotel 2. Thus, the price and booking forecasts of the deterministic framework is more optimistic compared with the stochastic one, where forecasts are closer to the observed revenues from the last season.

Secondly, what happens when the number of rooms available for booking in a specific hotel is limited? Figure 2 shows the result of hotel 2 expanding the availability of rooms to 425 instead of 325 (Figure 3).

Figure 3.

Hotel 2’s dynamic prices, daily number of room reservations, and elasticities (300 rooms vs. 400 rooms). Dates of stay: July 16 to August 7. Source: Own elaboration.

Pan (2007) points out that a higher hotel capacity negatively affects optimal prices, while Perakis and Sood (2004) observe that prices are lower for a larger inventory level for the whole booking horizon. We also observed similar results when analyzing the information from Figure 3, where the increase of room availability led to lower levels of prices. The increase in number of rooms finally led to lower levels of revenue raise compared to the growth in room availability. In the maximization model estimations from Figure 3 when the number of rooms available were increased by 30%, the optimal level of prices decreased on average by 14%, while the total revenue increased only by 12.5%. Nevertheless, when comparing the prices of both hotels, hotel 1 presents higher levels of prices despite having much larger capacity, as we point out before this is caused by the hotels’ differences.

Thirdly, what happens when the seasonal estimations from the two different hotels are compared? The results can be seen in Figure 4. The hotel location, hotel size, and the tourist profile were other factors that affected the DP that allowed for revenue maximization. Hotel 2 has a considerably lower capacity than hotel 1. It is located in a more popular area, and as we mentioned in the previous section, there are differences in the tourist profile.

Figure 4.

Comparison of seasonal average prices from hotels 1 and 2, estimations and observed prices. Source: Own elaboration.

Considering that hotel 2 offers online more or less half the number of rooms than are being offered by hotel 1, when comparing the estimations for both hotels (Figure 4), the results indicate that in the maximization process, hotel 1 sets prices between a 3% and a 6% higher and earned between a 63% and a 73% more revenue, depending on the type of model estimation used (deterministic or stochastic) and on the observed price.³ In this sense, Aguiló et al. (2003), Juaneda et al. (2011), and Papatheodorou (2002) support the hypothesis that a hotel resort’s location is a source of price variability. Additionally, Pan (2007) and Thrane (2005) point out that hotel capacity is another cause of price variability. Finally, hotel booking options such as the type of board (Juaneda et al., 2011; Papatheodorou, 2002; Thrane, 2005) or tourist nationality (Abrate et al., 2011) also affect DP.

When comparing the seasonal prices (Figure 4), the peak season prices double the low season prices in both hotels. Additionally, during the peak season is when the differences between the observed and estimated prices are higher, especially in the case of hotel 1. Juaneda et al. (2011) point out that the seasonality can be a source of price differences when considering different types of establishments.

Fourthly, what happens when the booking horizon is limited? Figure 5 shows an estimation of the revenue loss in the DP maximization process due to booking horizon limitations, that is, limiting the number of days before which a room can be booked for a certain date of stay. Three different scenarios under different elasticity values are considered.

Figure 5.

Expected change in revenue when the booking horizon is limited under different elasticity levels. Source: Own elaboration.

Figure 5 shows that inelastic demand produces larger revenue reductions compared to elastic demands when the booking horizon is limited. This is due to the fact that via elastic demand, it is possible to alter reservation levels with small price variations, while with inelastic demand it is not possible to reach certain levels of occupation with low price variations.

Finally, we compared and analyzed a range of situations: the effect of various elasticity values on optimal prices and reservations across the booking horizon, that is, period I—the earliest dates along the booking horizon—and period II—the dates closer to the date of stay.

In general terms, more inelastic demands during period II lead to increasing pricing trends along the booking horizon (Table 1); the opposite situation draws to a pricing contention and an irregular variability across the booking horizon; and similar elasticities during the two periods result in flat and slightly increasing pricing trends and differences in elasticities in both periods. Regarding the bookings, they depend on the levels of prices estimated in the models. However, time variable also influences the booking levels, this is the natural demand variability along the booking horizon that is not directly related to the price elasticity of demand, for example, the reservation peaks that take place after the Christmas and Easter holidays and at the beginning of summer.

Table 1.

Price elasticity of demand and DP path across the booking horizon.

Demands			Figures placement	Booking horizon prices
Period I		Period II	Figures placement	Booking horizon prices
Elastic		Inelastic	Figure 2: May 14 to Jun 3—Deterministic and stochastic models
Elastic		Inelastic	Figure 1: Jun 4 to Jun 22—Deterministic and stochastic models
Elastic		Unitary	Figure 2: Jun 4 to Jun 22—Deterministic model

			Figure 1: May 10 to Jun 3—Deterministic model

			Figure 1: Sep 12 to Oct 12—Stochastic model
Elastic	≃	Elastic	Figure 1: May 10 to Jun 3—Stochastic model

			Figure 1: Jul 16 to Aug 7—Stochastic model

			Figure 1: Jul 16 to Aug 7—Deterministic and stochastic models
Elastic	>	Elastic	Figure 2: Jun 23 to Jul 3——Deterministic and stochastic models
			Figure 2: Jul 4 to Aug 28—Stochastic models
			Figure 1: Jun 23 to Jul 3—Stochastic models
Elastic	<	Elastic	Figure 1: Jun 23 to Jul 3—Deterministic model

			Figure 1: Jul 4 to Jul 15—Stochastic model

			Figure 1: Aug 7 to Aug 28—Deterministic model

			Figure 1: Aug 29 to Sep 11—Deterministic and stochastic models
Unitary		Unitary	Figure 2: Sep 12 to Oct 12—Deterministic model
Unitary		Inelastic	Figure 2: Jul 4 to Jul 15—Deterministic model
Inelastic		Elastic	Figure 2: Jul 16 to Aug 7—Stochastic model
Inelastic	<	Inelastic	Figure 1: Sep 12 to Oct 12—Deterministic model
Inelastic	>	Inelastic	Figure 2: Aug 8 to Aug 28—Deterministic model
Inelastic	>	Inelastic	Figure 2: Aug 29 to Sep 11—Deterministic model

Source: Own elaboration.

Conclusions

The starting point of the study is that hotels need to improve the use of all the data they are able to collect/generate in order to improve their understanding of the customer behavior, while it helps hotels in the customers’ segmentation and the revenue maximization process across the booking horizon and along the different seasons. It is especially relevant in the resort hotels, as advanced RM techniques implementation is usually low in the sector and the level of empirical academic studies is quite scarce.

The two hotels located in Majorca represent an excellent opportunity for the empirical testing of models detailed in the article, due to the importance of the island of Majorca, a well-known mature mass tourism Mediterranean destination mainly specialized in resort tourism, and the focus on the resort tourism segment; furthermore, we have the opportunity to directly compare the outcomes from both hotels and to derive industry implications. It has to be pointed out that the models described in the article can be applied to other resort hotels, as these have been designed to be generalizable in the sector.

The first objective of this study was to apply and adapt two extended models used in the literature to estimate optimal prices in the transient demand segment for two Majorcan resort hotels. The seasonality and variability of prices present in the sector, in combination with the lack of development of specific models and their empirical testing in the resort hotel specific context, places the subject in an interesting field of study. In this specific case, DP allows for the hotel to maximize seasonal revenue with limited capacity and for the definition and estimation of different online demand functions, where the own-price elasticities and the effect of the time along the booking horizon are considered.

The comparison of the models’ outcomes for two Majorcan hotels shows that both models meet the objective of defining the optimal price for obtaining maximum hotel revenue for each date of stay. However, deterministic models usually provide higher levels and more variability in pricing, while they present lower level of reservation variability across the booking horizon. In accordance with the evidence provided by the literature, when the two model estimations are compared with the observed prices, we observe that the price estimations obtained from the stochastic model are more similar to the observed prices from the last season (year 2016). Meanwhile, the average prices from the last three seasons (years 2014–2016) are more similar with the estimations obtained from the deterministic model.

The second objective of the article was to compare the outcomes of both models and their estimations. The results obtained indicate the following.

Seasonality, the number of rooms available, the hotel location, and the tourist profile affect DP are factors that affect hotel pricing, and thus, for revenue maximization in hotels, it is important to improve the knowledge of the customer, as well as the knowledge of customer valuation of hotel attributes, which allows a better customer segmentation.

The booking horizon limitation leads to larger revenue decreases under elastic demand, that is, revenue managers have to consider the booking horizon duration together with the demand price sensitivity in order to maximize the hotel revenues.

When demand is more elastic, it is observed that generally the models produce lower levels of prices, even when the capacity limitation factor of the hotel sector (the optimal path may not be always the price decrease) is considered.

In the pricing process, the revenue manager should consider not only the demand price sensitivity distribution across the booking horizon, but also the natural variability of demand, as it impacts the level of bookings and so the revenue maximization.

Further research will focus on testing empirical models in similar hotels located in different destinations, the results will be used to check both the deterministic and stochastic models performance, as well as to detect which are the hotel/demand factors that have more impact on pricing. A second step will be the introduction of information on competitors’ prices and hotel ratings in the demand models—this is external data to the hotel that were not available for the present study—in order to improve the bookings estimations. Finally, these models will be tested in other types of hotels—different star rating, hotel segments, demand composition, and so on—in order to check the models performance in different contexts.

Some limitations of the study are that the availability of competitors’ information, the consideration of additional booking information, such as the number of guests, room type, board, cancellation policies, loyalty programs, and so on, as well as other segment data, such as tour operator demand. All this additional data could improve the models estimations; however, at the moment, the data requirements did not allow the inclusion of additional hotel information, which hopefully will lead future direction of our research.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors received funding for the research of this paper from Research Fellowship from the Balearic Government (Grant Number: FPI/1574/2013), Spanish Ministry for the Economy and Competitiveness (Grant Number: ECO2013-47301-R) and Spanish Ministry for Science and Innovation (Grant Number: ECO2011-28999).

ORCID iD

Aldric Vives

Notes

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