Skip to Main content Skip to Navigation

Étude théorique et numérique du problème de la gestion de la diversité

Abstract : The diversity management problem is defined on a partially ordered set. The objective is to produce a subset of $k$ reference elements, $k$ being a given number, while minimizing the cost. Demands and unit costs of production are known. Each non produced element must be replaced by a reference which is higher in the partial order, and this implies an overcost. After a theoretical study on the complexity of this problem, we describe and justify the model we chose. This model is an integer linear program close to that commonly used for the $k$-median problem. To solve this program, we present a Lagrangean approach, and various criteria of variable fixing. We exploit also this approach to build feasible solutions of good quality. Finally, we design a Branch and Cut type algorithm to solve our problem to optimality. To do so, we first do a polyhedral study of the convex hull of the solutions. We present a particular type of cuts that eliminate fractional solutions, as well as a heuristic to generate them. We conclude by numerical tests carried out on real world instances.
Document type :
Complete list of metadatas

Cited literature [45 references]  Display  Hide  Download
Contributor : Thèses Imag <>
Submitted on : Tuesday, February 17, 2004 - 10:59:18 AM
Last modification on : Friday, November 6, 2020 - 4:39:27 AM
Long-term archiving on: : Wednesday, September 12, 2012 - 1:25:32 PM


  • HAL Id : tel-00004710, version 1




Olivier Briant. Étude théorique et numérique du problème de la gestion de la diversité. Mathématiques [math]. Institut National Polytechnique de Grenoble - INPG, 2000. Français. ⟨tel-00004710⟩



Record views


Files downloads