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Financial mathematics

Laurent Rabier - Technoscope - 28/09/2010

Mathematical models to sell the right product at the right price at the right time… and to the right customer

Luce Brotcorne Luce Brotcorne - © Inria

Luce Brotcorne, a junior research scientist at Inria since 2009, is a member of the DOLPHIN project-team. Her field is revenue management, in particular price setting, a discipline in which she proposes an innovative approach which explicitly takes into account the behaviour of consumers. 

What issues does your research concern?

Luce Brotcorne:  It is a field widely designated by the English term, even in France: yield management . Most of the researchers working on this issue are from English-speaking countries. It is about developing a strategy to sell the right product to the right customer at the right price and at the right time. For example, for an airline, this would mean knowing how many seats to offer during a given period, and at what price. The example of aviation is not chosen at random. The discipline first emerged in the eighties, at a time when the airline industry was being deregulated. It can be subdivided into four areas: estimating demand, overbooking, allocating capacity, and finally pricing. I have specialised in the last of these.

What are you trying to achieve?

L. B.: A new approach to pricing, which I initially developed with colleagues from Brussels and Montreal but am now continuing at Inria. Traditionally, airlines used their historic data to estimate demand, and determined their prices accordingly. This approach has now become obsolete because, with the Internet, customers can compare prices and see the effect of flying sooner or later, etc. In short, they can develop a strategy that can depend on factors other than the price itself, such as timetables, waiting times between connections and loyalty to a particular airline. What is original about our approach is that it involves expressly taking this behaviour into account when determining prices. We are the only ones taking this approach at present. It has led us to consider mathematical optimisation problems at two levels.

Why two levels?

L. B.: Because, when it comes to maximising a company's yield, demand is calculated by solving a second problem: the issue of optimising the number of customers that maximise their utility functions. Those are the two levels I'm talking about. It's the main subject of my habilitation to advise doctoral theses. Using this kind of complex tool allows decision-makers to see interactions that would not have been as clearly visible in the past.

Who uses this pricing approach today?

L. B.: At present, it is mainly Thalys, via the start-up Expretio, set up in Montreal. We have contacts with airlines but it will take them some time to change their practices to this extent, particularly for the heavyweights among them. Unlike rail transport, it's a field in which a great deal of software is already available. This is why it was easier for us to impose our two-level mathematical optimisation approach in the railways market.

So you have transposed a tool designed for airlines into the rail sector?

L. B.: No, it's a new tool because we had to adapt to the particularities of rail transport. The paradigm itself is quite general, which means it can be suitable for use in a number of contexts, but it must always be tailored to the specificities of each individual field. A rail network is very different from that of an airline. The constraints in terms of passenger load factor are completely different, the prices change less often, etc. This is even more obvious when it comes to energy, where the particularities are even more marked. Maximising revenue is important, but companies are also faced with potential congestion of their networks if all of their customers choose to buy at the same time. Spreading out peaks in customer numbers is therefore an objective that should be taken into account when determining prices. For the moment, we are still only at the exploratory stage, but this means developing a tool that has both two levels and multiple objectives, which falls completely within the scope of Inria's Dolphin team.

Keywords: Luce Brotcorne Yield management Tarifs Clients Transport aérien Ferroviaire