Passenger demand modeling under availability constraints and customer segmentation assumptions (2015)

The aim of Revenue Management (RM) is to improve the profitability of a firm through the “optimal” management of its demand, price and inventory. In the airline and train industry this can be achieved by controlling the availability of seats, to transmit customers to products with high profit margins. Policy makings in this context are highly dependent on historical demand forecasts. Especially when there is lack of information resulting from censored demand. In this case, the observed demand does not match the true behavior of the customers, and may yield unreliable estimates. The bias resulting from inaccurate demand forecasts has a negative impact on the level of service that the company can offer. As soon as a product is no longer available, true demand of airlines and trains may differ from registered bookings, thus inducing a negative bias in the estimation results in an artificial increase in demand for substitute products. According to Weatherford and Belobaba (2002), ignoring the data censorship phenomenon can lead to demand underestimation ranging from 12.5% to 25%, and negatively affect revenue by 1% to 3%, a significant amount for major rail or airline operators. Most commonly used uncensoring methods in this context usually try to compensate the missing information by using parametric techniques such as Expectation-Maximization (EM). They are usually costly to be implemented when there is a stochastic process assumption for customer arrival rates at different booking intervals.  These customers come from different segments based on their characteristics. In reality, one product could be more appealing for a customer with certain characteristics comparing to other ones from other segments. In this research, we use aggregated data to predict demand of different products for different customer types. The only information at hand is the number of registered bookings associated with each fare class during different reservation intervals before each departure. Parametric assumptions on demand distribution complicates the process of utility estimation especially when product demands are correlated. Here, we introduce a non-parametric and distribution-free estimation procedure that, based upon historical bookings, takes explicitly into account the set of available products. Although different approaches have been proposed to model demand under availability constraints there are still issues that need to be addressed: 1-      Demand across fare products is not independent. Dealing with dependency yields a complex parameter estimation process that has been considered and tested by small instances (Stefanescu (2009). However, while dealing with large volume of aggregate real data, these types of parametric approaches fail to estimate demand properly because of computation burden caused by correlations between different products demands. 2-       As the proportion of censored demand in historical data grows, the accuracy of the standard estimation methods decreases (see Talluri and van Ryzin (2004); Vulcano et al. (2012); Haensel and Koole (2010)). 3-       Several statistical methods fail to accurately capture seasonal effects. 4-      In order to capture the behavior of different customers within each segment, usually parametric assumptions about choice attributes come into play which complicate optimization models to estimate demand. Hence, we estimate choice probabilities in a more efficient way. In this presentation, we address the problem of demand modeling from a new point of view when customers come from different segments with different willingness to pay and characteristics. We propose an algorithm that takes availability constraints into account via a non-parametric mathematical representation. To solve the problem, first, we linearize the mathematical model by implementing different levels of relaxations. Then, by introducing a tailored branch and bound algorithm and by the help of global optimization techniques to solve the general case, we estimate daily potential demand of each product as well as product utilities. Then, in order to estimate product utilities for customers from different segments we use an Adaptive Large Neighborhood Search (ALNS) approach.  The accuracy of proposed algorithms have been tested and verified.