La semaine de l’IMB

La conjecture de Littlewood P(t)-adique est une version sur les corps de fonctions de la conjecture du même nom (datant des années 1930) en approximation diophantienne. Elle a été proposée par De Mathan et Teulié en 2004. Nous la réfutons ici sur lorsque le corps de base est de caractéristique congruente à 3 modulo 4. 

Toutes les notions utiles seront introduites au cours de l'exposé. Travail en commun avec Dzmitry Badziahin (University of Sydney)

We study the Vehicle Routing Problem with Stochastic Demands (VRPSD), which involves optimizing delivery routes for vehicles with limited capacity to serve customers whose demands are unknown when designing the routes. The routes are designed taking into account the possibility that a route may have too much demand for the capacity of a vehicle to be delivered, in that case recourse actions can be taken, inducing a cost. This problem seeks to minimize routing costs and the expected recourse costs.

The Vehicle Routing Problem with Stochastic Demands is relevant as it addresses the need for efficient logistics under uncertainty in transportation and supply chain management. As a result, research on this problem is very active, and recent advances in exact resolution methods allow for tackling larger instances more efficiently and with greater generality regarding the different hypotheses surrounding recourse and uncertainty modeling.

In this talk, we present the state-of-the-art methods for solving the VRPSD. We first provide a definition of the problem and list its various components that can vary, such as recourse actions and different ways to model uncertainty. Then, we present different methods from the literature to solve the VRPSD, with a focus on the Disaggregated L-shaped method.