We consider the problem that consists in maximizing the revenue of a firm operating on a transportation network, and where flow is assigned according to a discrete choice model of user behaviour. Such models arises naturally in the context of revenue managment applied to the airline, rail or hospitality industry. The resulting model admits several local optima, and is computationally challenging. The presentation will focus on algorithmic issues concerning different variants of logit-based assignment models.

This talk discusses the adaptation of a bilevel revenue optimization model to the hotel industry, in an oligopolistic environment. We will focus on features that are specific to this industry, namely "quality of service" and "length of stay".

Consider the problem of approximating a single variable concave function on the unit interval using function and subgradient values. Values and derivatives of the function at the extremities are known a priori and the problem is to find the evaluation points that minimize the worst-case error, mesured either in Lp norm or in a weighted L1 norm. In this paper, the usefulness of adaptation for these problems is discussed and optimal algorithms for their solution are given.

The Toll Setting Problem involves determining a toll vector for a subset of the arcs of a multi-commodity network so as to maximise the revenues raised from those tolls. We propose to solve this problem by a branch-and-bound algorithm where each node is solved by column generation. Each sub-problem corresponds to one or more commodity and is used to generate feasible solutions for those commodities. We also present a family of cuts for the master problem. We discuss strategies for accelerating the solution process and present numerical results.