A Bilevel Programming Approach to Optimal Price Setting

In this paper, we survey applications and algorithms pertaining to an important class of price setting problems formulated as bilevel programs. Introduction. Bilevel Programming. The present paper focuses on a specific class of bilevel problems that arise naturally when tariffs, tolls or devious taxes are imposed on a set of commodities. Not only does this class encompass several important optimization problems encountered in the transportation, telecommunication and airline industries, but its structure makes it amenable to efficient solution techniques. Our aim is to present several such models and briefly discuss algorithmic approaches, either exact or heuristic, that can be applied to large scale problems within this class. Bilevel programming is the adequate framework for modelling asymmetric games where one player (the leader) calls the shots first, taking into account the optimal reaction of the second player (the follower).