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Constraint programming for lot-sizing problems

Grigori German 1 
1 G-SCOP_GCSP - Gestion et Conduite des Systèmes de Production
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
Abstract : In this thesis we investigate the potential use of constraint programming to develop a production planning solver. We focus on lot-sizing problems that are crucial and challenging problems of the tactical level of production planning and use one of the main strengths of constraint programming, namely global constraints. The goal of this work is to set the grounds of a constraint programming framework for solving complex lot-sizing problems. We define a LotSizing global constraint based on a generic single-item, single-level lot-sizing problem that considers production and inventory capacities, unitary production and inventory costs and setup costs. This global constraint is an intuitive modeling tool for complex lot-sizing problems as it can model the nodes of lot-sizing networks. We use classical dynamic programming techniques of the lot-sizing field to develop powerful filtering algorithms for the global constraint. Furthermore we model multi-item problems that are natural extensions of the core problem.Finally we introduce a new generic filtering algorithm based on linear programming. We show that arc consistency can be achieved with only one call to a linear programming solver when the global constraint has an ideal formulation and adapt the result to provide partial filtering when no restriction is made on the constraints. This technique can be useful to tackle polynomial lot-sizing underlying flow and sequence sub-problems.
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Submitted on : Tuesday, October 16, 2018 - 9:30:08 AM
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Grigori German. Constraint programming for lot-sizing problems. Computer Arithmetic. Université Grenoble Alpes, 2018. English. ⟨NNT : 2018GREAM015⟩. ⟨tel-01896325⟩

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