Section: New Results

Bi-level multi-objective optimization for pricing problems in long-haul transportation

Participants: M. Diaby, L. Brotcorne and E-G. Talbi

This work is concerned with the problem of pricing for a long-haul full load goods transportation. More precisely, we are interested in the situation where each vehicle delivers single request at a time. In this environment, we study the problem of pricing and valorization of unutilized capacity between two carriers. The first carrier B, cannot serve all the transportation requests and he thus needs to use outsourcing : second carrier A or his competitors. Carrier A, has to define the prices for carrier B transportation requests. Once carrier A has given its prices for the operations, it is B’s decision to turn to A or to another carrier. This sequential and non-cooperative decision-making process can be adequately represented as a bilevel program : carrier B (the follower) wants to minimize transportation cost while A (the leader) seeks to maximize the revenue. Carrier A explicitly incorporates the reaction of carrier B in his optimization process.

Two types of models have been proposed : the bilevel mono-objective model and the bilevel biobjective model. More precisely, two objectives are simultaneously considered for the leader problem : the maximization of revenue and balancing the free load length (limiting the free load distances). We propose exact methods to solve moderate size instance of the problem and the heuristics to solve large-scale instances in reasonable time.