Journées de l'optimisation 2007 Optimizations days

We consider a bilateral transportation service procurement market where multiple shippers and multiple carriers trade shipping contracts. Shippers are the retailers, the distributors and other companies that need to move some commodities between specified locations under some restrictions. Carriers are companies that make offers to ensure transportation services. The trading process is modeled as a one-sided iterative combinatorial auction where we have, on one side, carriers submitting package bids, and on the other side, a market maker acting as a shippers' representative. At the end of the auction process, once the final winning bids are determined, one should specify the price that must be paid or received by each participant. From the carriers' perspective, we adopt a "receive what you bid" rule. From the shippers' perspective, the problem is more complex. In fact, the total amount that must be paid by all shippers can be easily deduced. But what does each shipper pay individually? In other words, how this total cost should be shared between shippers? We will present, evaluate and compare different cost allocation methods for this problem.

Consider the tarification problem of maximizing the revenue generated by tolls set on a subset of arcs of a transportation network, where origin-destination flows are assigned to shortest paths with respect to the sum of tolls and initial costs. The Network Pricing Problem with Consecutive Toll Arcs deals with structured networks that takes into account features specific to a highway topology. Our main results concern: the theoretical complexity of the problem and its variants, the design of valid inequalities, and the connection with a pricing problem in economics.

Bilevel programming is used to model this second-best pricing. For practical reasons, the authority can fix the maximum number of toll points. Our model's solution gives the toll points' locations and their amount(s). A variational inequality is used to model the second level problem and we obtain a mathematical program with equilibrium constraints (MPEC). Then, we discretize the congestion in order to obtain a mixed integer program (MIP). We develop an algorithm that adopts the range of flow that is discretized in regards to of the last solution obtained. For the first MIP, the congestion is discretized arbitrarily. Then, a new discretization is constructed while considering the last solution, this new MIP is solved, and so on until some stopping criteria are attained.

Nous considérons un problème de tarification sur un réseau multi produits avec demande élastique. Nous proposons un modèle de programmation mathématique à deux niveaux où les suiveurs réagissent aux tarifs en choisissant le chemin de longueur minimale et ou la demande varie selon le niveau des tarifs imposés par le meneur. Trois reformulations en des programmes linéaires mixtes sont développées et comparées.