We develop a method for computing facet-defining valid inequalities for any mixed-integer set PJ . While our practical implementation does not return only facet-defining inequalities, it is able to find a separating cut whenever one exists. The separator is not comparable in speed with the specific cutting-plane generators used in branch-and-cut solvers, but it is general-purpose. We can thus u...

Full terms and conditions of use:

In this paper we analyze the optimal joint decisions of when, how and howmuch to replenish customers with products of varying ages. We discuss the main features of the problem arising in the joint replenishment and delivery of perishable products, and we model them under general assumptions. We then solve the problem by means of an exact branch-and-cut algorithm, and we test its performance on ...

In this paper the Fixed Charge Transportation Problem is considered. A new heuristic approach is proposed, based on the intensive use of Lagrangean relaxation techniques. The more novel aspects of this approach are new Lagrangean relaxation and decomposition methods, the consideration of several core problems, defined from the previously computed Lagrangean reduced costs, the heuristic selectio...

This is a summary of the author’s PhD thesis supervised by Philippe Chrétienne and Safia Kedad-Sidhoum and defended in December 2005 at the Université Pierre et Marie Curie (Paris VI). The thesis is written in French and is available from http://absi.nabil.free.fr/ABSI-Thesis.pdf. This work mainly deals with multi-item capacitated lot-sizing problems with setup times, shortages on demand and sa...

We study the problem of designing at minimum cost a two-connected network such that each edge belongs to a cycle using at most K edges. This problem is a particular case of the two-connected networks with bounded meshes problem studied by Fortz, Labbé and Maffioli [6]. In this paper, we compute a lower bound on the number of edges in a feasible solution, we show that the problem is strongly NP-...

This paper proposes the framework of branch-and-check with explanations (BCE), a branch-and-cut method where combinatorial cuts are found by general-purpose conflict analysis, rather than by specialized separation algorithms. Specifically, the method features a master problem that ignores combinatorial constraints, and a feasibility subproblem that uses propagation to check the feasibility of t...

We consider the problem of designing a two level telecommunications network at minimum cost. The decisions involved are the locations of concentrators, the assignments of user nodes to concentrators and the installation of links connecting concentrators in a reliable backbone network. We define a reliable backbone network as one where there exist at least 2-edge disjoint paths between any pair ...

Combinatorial optimization problems arise commonly in logistics applications. The most successful approaches to date for solving such problems involve modeling them as integer programs and then applying some variant of the branch and bound algorithm. Although branch and bound is conceptually easy to parallelize, achieving scalability can be a challenge. In more sophisticated variants, such as b...

Branch & Cut is today’s state-of-the-art method to solve 0/1-integer linear programs. Important for the success of this method is the generation of strong valid inequalities, which tighten the linear programming relaxation of 0/1IPs and thus allow for early pruning of parts of the search tree. In this paper we present a novel approach to generate valid inequalities for 0/1-IPs which is based on...