4 Presentations

• 
  10:30 AM - 11:00 AM

  Network Capacity Control under a Non-Parametric Choice Model of Demand

  • Morad Hosseinalifam, presenter, Polytechnique Montréal
  • Patrice Marcotte, Université de Montréal
  • Gilles Savard, Polytechnique Montréal

  One of the most powerful and simple approaches to model a customer’s choice behavior, with the aim to predict his choice decision facing different options, is non-parametric choice modeling of demand. In this approach, each arriving customer chooses from available alternatives according to an ordered preference list of products. If the customer's most preferred product was not available, he substitutes it with a next lower rank product in his ordered preference list.

  In this paper, we propose a new mathematical programming approach to calculate optimal allocation of resources under a non-parametric choice model of demand. In contrast with most proposed approaches in the literature to address this problem, our approach is flexible and can easily accommodate technical and practical side constraints.

  We develop a modified column generation algorithm to efficiently solve large scale, real world practical problems. Moreover, as the complexity of the algorithm increases with the number of the ordered preference lists, we provide an aggregation algorithm to reduce the number of the ordered preference lists without affecting the quality of the solution. Our computational results show that the new approach outperforms alternative proposals from the current literature.

• 
  11:00 AM - 11:30 AM

  Demand Modeling in Revenue Management Systems under Availability Constraints

  • Shadi Sharif Azadeh, presenter, École Polytechnique de Montréal
  • Gilles Savard, Polytechnique Montréal

  Revenue management (RM) can be considered as an application of Operation Research (OR) in transportation industry. For these service companies, it is a difficult task to adjust supply and demand. In order to maximize revenue, RM systems display demand behavior by using historical data. Afterwards, these models are used to determine product availabilities and their associated prices at a given time while maximizing revenue. Therefore, demand forecasting plays an important role as a preprocessing step in revenue management. However, in reality, historical data based on which these models are defined are incomplete. For a given time period, not all alternatives are available to arriving customers due to booking limitations. When a product is unavailable, the registered bookings do not represent the real demand commonly known as censored data. The mathematical and statistical techniques that are used to extrapolate the actual demand from truncated data are called uncensoring or unconstraining methods. These approaches coupled with choice models help researchers to estimate both turn away and recaptured demand causing from unavailability of some alternatives. In the last couple of decades, discrete choice demand models (most notably the multinomial logit (MNL)) have been adapted into revenue management systems. While difficult to calibrate accurately, choice models have an important flexibility advantage in being able to uncensor demand from bookings in almost any combination of open fare classes. Furthermore, it is relatively easy to estimate upsell, downsell, and recapture rates from MNL choice models.
  
  Variation in the size of choice sets across the market is an important source of identification in demand models. Our proposed algorithm is able to extrapolate the actual demand of each product under availability constraints via a non-parametric mathematical representation. This provides consistent estimation of demand even when stock outs imply that the set of available options varies endogenously. In order to solve the original nonlinear non-convex problem, first, we linearize the mathematical representation by implementing different levels of relaxation. Then, we introduce a new approach for demand forecasting which considers daily registered bookings and product availabilities simultaneously. A heuristic method comprising choice models is represented to show a computationally efficient method for demand estimation. The precision of results has been verified by both synthetic and real data that belongs to a major railway company.

• 
  11:30 AM - 12:00 PM

  Accommodating Taste Heterogeneity in the Railway Pricing and Seat Allocation Problem

  • Cinzia Cirillo, presenter, University of Maryland
  • Pratt Hetrakul, University of Maryland

  In this presentation, discrete choice methods in the form of multinomial logit and latent class models are proposed to explain ticket purchase timing decisions of intercity passenger railway. The analysis makes use of online ticket reservation data, which are characterized by limited number of socio-demographic characteristics. The latent class model, which divides passengers based on their departure schedule, overcomes the difficulty of population segmentation identified by individual variables. The passenger demand volume is modeled with a log-linear demand function and is incorporated together with the choice model into an optimization problem which maximizes expected revenue for each train trip. The proposed optimization jointly considers pricing and seat allocation which allows for a realistic representation of passenger behavior and for an efficient utilization of the capacity across the network.

• 
  12:00 PM - 12:30 PM

  Dynamic Discrete Choice Model for Railway Ticket Cancellation and Exchange Behavior

  • Fabian Bastin, presenter, Université de Montréal
  • Pratt Hetrakul, University of Maryland
  • Cinzia Cirillo, University of Maryland

  The increasing use of internet as a major ticket distribution channel has resulted in passengers becoming more strategic to fare policy. This potentially induces passengers to book the ticket well in advance in order to obtain a lower fare ticket, and later adjust their ticket when they are sure about trip scheduling. This is especially true in flexible refund markets where ticket cancellation and exchange behavior has been recognized as having major impacts on revenues. Therefore, when modeling this behavior, it is important to account for the characteristic of the passenger that optimally makes decision over time based on trip schedule and fare uncertainty.

  In this paper, we propose an inter-temporal choice model of ticket cancellation and exchange for railway passengers where customers are assumed to be forward looking agents. A dynamic discrete choice model (DDCM) is applied to predict the timing in which ticket exchange or cancellation occurs in response to fare and trip schedule uncertainty. Passengers’ decisions involve a two-step process. First, the passenger decides whether to keep or adjust the ticket. Once the decision to adjust the ticket has been made, the passenger has the choice to cancel the ticket or to change departure time. The problem is formulated as an optimal stopping problem, and a two-step look-ahead policy is adopted to approximate the dynamic programming problem.

  The approach is applied to simulated and real ticket reservation data for intercity railway trips. Estimations results indicate that the DDCM provides more intuitive results when compared to multinomial logit (MNL) models. In addition, validation results show that DDCM has better prediction capability than MNL. The approach developed here in the context of exchange and refund policies for railway revenue management can be extended and applied to other industries that operate under flexible refund policies.