Solving Assembly Line Balancing Problems by Combining IP and CP

Assembly line balancing problems consist in partitioning the work necessary to assemble a number of products among different stations of an assembly line. We present a hybrid approach for solving such problems, which combines constraint programming and integer programming.Comment: 10 pages, Sixth Annual Workshop of the ERCIM Working Group on Constraints, Prague, June 200

Detecting Infeasibility and Generating Cuts for MIP using CP

Colloque avec actes et comité de lecture. internationale.International audienceWe study a hybrid MIP/CP solution approach in which CP is used for detecting infeasibilities and generating cuts within a branch-and-cut algorithm for MIP. Our framework applies to MIP problems augmented by monotone constraints that can be handled by CP. We illustrate our approach on a generic multiple machine scheduling problem, and compare it to other hybrid MIP/CP algorithms

Module: Game Theory

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The convex hull of the disjunction of polymatroids

Rapport interne.We give a linear characterization of the convex hull of the disjunction of polymatroids. For the family of inequalities defining the convex hull, we present an efficient separation algorithm. Among consequences of this result are the characterization of the convex hull of matroid polyhedra [Conforti/Laurent 88], and the characterization of the convex hull of 0-1 points satisfying logical conditions called cardinality rules [Yan/Hooker 99, Balas 2000]

Network flow problems in constraint programming

Colloque avec actes et comité de lecture. internationale.International audienceWe introduce a new global constraint for modeling and solving network flow problems in constraint programming. We describe the declarative and operational semantics and illustrate its use through a number of applications

On unions and dominants of polytopes

A well-known result on unions of polyhedra in the same space gives an extended formulation whose projection is the convex hull of the union. Here in contrast we study the unions of polytopes in different spaces, giving a complete description of the convex hull without additional variables. When the underlying polytopes are monotone, the facets are described explicitly, generalizing results of Hong and Hooker on cardinality rules, and an efficient separation algorithm is proposed. These results are based on an explicit representation of the dominant of a polytope, and an algorithm for the separation problem for the dominant. For non-monotone polytopes, both the dominant and the union are characterized. We also give results on the unions of polymatroids both on disjoint ground sets and on the same ground set generalizing results of Conforti and Laurent

On unions and dominants of polytopes

A well-known result on unions of polyhedra in the same space gives an extended formulation whose projection is the convex hull of the union. Here in contrast we study the unions of polytopes in different spaces, giving a complete description of the convex hull without additional variables. When the underlying polytopes are monotone, the facets are described explicitly, generalizing results of Hong and Hooker on cardinality rules, and an efficient separation algorithm is proposed. These results are based on an explicit representation of the dominant of a polytope, and an algorithm for the separation problem for the dominant. For non-monotone polytopes, both the dominant and the union are characterized. We also give results on the unions of polymatroids both on disjoint ground sets and on the same ground set generalizing results of Conforti and Laurent

LISCOS Growth Project: Modelling and requirements of PSA test cases

Rapport de contrat.This report describes threee representative problems proposed by the industrial partner PSA