Pricing out demand

To manage the traffic on a telecommunication or road network, it is important to take into account user reactions to the service offered. This question boils down to a sequence of nested, particularly hard to solve, optimization problems that integrate a complex model of demand.

What do you mean objective parameters that make me take this shuttle? I'm the driver!

Will an express bus shuttle service taking highway A14 from Orgeval to La Défense attract any users? What should the fares be, which bus sizes and frequencies are needed to achieve this goal? These are the kind of questions that the work initiated by Laura Wynter at the Prism laboratory of the University of Versailles is intending to answer. She is currently continuing her research at INRIA within the project Metalau. The research concerns the development of tools to solve such problems makind use of, in particular, the Scilab scientific computing environment.

Make no mistake: behind the practical aspects of the question lurk extremely complex modeling problems. To give an example, consider an administrator from a transportation company. He or she wants to determine the parameters that will maximize profits. The solution however must take into account user demand since the latter react to the criteria fixed by the administrator by modifying their choices. This so-called hierarchical relation between a service provider and users is expressed mathematically by nested optimization problems. The second level, which consists in describing the path taken by the user in terms of the characteristics offered by the network, is especially delicate. The problem can be summed up by a variational inequality in often more than 10,000 variables! Additionally, the definition of an optimal solution to the hierarchical system is a challenge because it combines nondifferentiability and nonconvexity of the functions and feasible regions.

Demand modeling brings additional complexity. Indeed, the basic assumption is that users always make the best choice, which is far from being the case. Economists have been working hard on this question for about twenty years and have refined demand models by introducing a random factor into user responses. It is thus necessary to integrate models from such work, taking into account the numerous parameters that describe individual behavior and the nature of the supply (how attractive is the route, travel time, car ownership, salary and so on). In practice, certain databases like the National transportation global survey, give statistics on the transportation habits of families—transportation modes, routes, frequency, etc—that can be used to calibrate the models.

For the time being, Laura Wynter and her coworkers are developing such a model in partnership with the CGEA Connex in the framework of the National Program for Research and Innovation in Ground Transportation (PREDIT*). This approach is also applied to other fields such as the management of Internet congestion. The researchers are already working in collaboration with France Télécom R&D on the design of optimal price setting methods.

* A program at the initiative of the Ministries in charge of Research, Transportation, the Environment and Industry, as well as the Ademe and the Anvar.

Contact:

Laura Wynter, on leave from the University of Versailles, project Metalau,
INRIA Rocquencourt

Tel.: +33 1 39 63 55 38, Laura.Wynter@inria.fr
http://www.prism.uvsq.fr/~wynter