Mathematics of Information Technology and Complex Systems





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Project Highlights


Revenue management is often described as the practice of “selling the right product to the right customer at the right time and the right price”. One of the central aspects of revenue management is pricing, i.e. finding the price of a product which maximizes a company’s revenue in a competitive setting. Until recently, because of theoretical and technical limitations, pricing was mostly ignored by revenue managers. Current revenue management systems consider that price is fixed and use dynamic capacity management in order to increase revenue.

There is however growing interest in the practice of optimal pricing. This project is concerned with the development, implementation and validation of bilevel pricing model in network industries.

   Airlines


The birthplace of revenue management in the seventies, the airline industry faces today new challenges that profoundly impact its traditional business model. The rise of low-cost carriers, the apparition of new distribution channels such as the Internet and the rapidly evolving purchase behaviour of the passengers are all factors that threaten the profitability of established carriers.

Our research aims at developing optimization tools based on bilevel programming that help pricing analysts at an airline in setting the best prices for the fare products they manage, given the current schedule, the attributes of the products offered by the competition and the purchasing habits of the customers. Such a tool can be used in two contexts. On the tactical front, where thousands of fare changes are published three or four times a day, analysts must react quickly and adjust continuously their prices. Since modern airline networks are highly meshed and critically depend on interconnectedness, it is impossible for a human analyst to estimate the impact such fare changes can have on the overall network and to decide whether the capacity on a given leg is used in the most profitable way, whence the need for computerized decision-aid tools.  On the strategic front, when designing new fare products or establishing new routes, airline marketers wish to conduct scenario analyses and perform what is often called “what-if” pricing, that is simulating the impact of new products and prices on the market. By allowing us to explicitly model customer behaviour at the second level, bilevel programming can provide the basis for such a longer-term, strategic tool.

   Rail


Although unpopular in North America, rail travel is part of everyday life in many European countries. Over the last decades, the development of high-speed links between major centres has turned rail into a competitive alternative to air travel for trips less than 1000km, which are very common in densely populated European countries such as France and Germany. Rail operators, most of them partially privatized monopolies, exploit these high-yield lines in a way that is very similar to airlines. Capacity is divided into control classes analogous to airline booking classes and a single train services numerous markets (i.e. origin-destination pairs).

We are currently adapting our model for solving the passenger rail pricing problem and investigating the benefits of its use in this context. This work involves modelling refinements as well as the development of new metrics for measuring performance. One of the challenges we face is the integration of intermodality into the model, that is the possibility for passengers of choosing from more than one means of transportation. For instance, in the case of European high-speed rail links, one must consider car and low-cost airlines as competitors to rail.

   Telecoms


Instead of human passengers, telecommunication companies transport packets of electronic information. In spite of this fundamental difference, telecoms share many common characteristics with the airline and rail industries. Networks are highly meshed and connectivity is crucial. Capacity is limited and must be allocated wisely but, as with airlines, unused capacity can be produced at a very low marginal cost. In many countries, telecoms have been (or are in the process of being) deregulated and competition is fierce.

Our research in the telecoms domain aims at adapting and refining the bilevel model and validating its use in various contexts, for instance in designing new packages and evaluating their impact on the network and ultimately on the profitability of the firm. On the technical side, certain constraints have to be modified or added to satisfy physical network integrity and electrical stability, aspects that are absent when it comes to passenger transportation.