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Formal languages for integer programming modeling of shift scheduling problems

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Abstract

This paper approaches the problem of modeling optimization problems containing substructures involving constraints on sequences of decision variables. Such constraints can be very complex to express with Mixed Integer Programming (MIP). We suggest an approach inspired by global constraints used in Constraint Programming (CP) to exploit formal languages for the modeling of such substructures with MIP. More precisely, we first suggest a way to use automata, as the CP regular constraint does, to express allowed patterns for the values taken by the constrained sequence of variables. Secondly, we present how context-free grammars can contribute to formulate constraints on sequences of variables in a MIP model. Experimental results on both approaches show that they facilitate the modeling, but also give models easier to solve by MIP solvers compared to compact assignment MIP formulations.

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Authors and Affiliations

  1. Département de mathématiques et génie industriel, École Polytechnique de Montréal, PO Box 6079, succ. Centre-Ville, Montréal, H3C 3A7, Canada

    Marie-Claude Côté & Louis-Martin Rousseau

  2. CIRRELT-Interuniversity Research Center on Enterprise Networks, Logistics and Transportation, Montréal, Canada

    Marie-Claude Côté, Bernard Gendron & Louis-Martin Rousseau

  3. Département d’informatique et de recherche opérationnelle, Université de Montréal, Pavillon André-Aisenstadt, PO Box 6128, succ. Centre-Ville, Montréal, H3C 3J7, Canada

    Bernard Gendron

  4. Omega Optimisation, 4200 St-Laurent 301, Montréal, H2W 2R2, Canada

    Claude-Guy Quimper

Authors
  1. Marie-Claude Côté
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  2. Bernard Gendron
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  3. Claude-Guy Quimper
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  4. Louis-Martin Rousseau
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Correspondence to Marie-Claude Côté.

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Côté, MC., Gendron, B., Quimper, CG. et al. Formal languages for integer programming modeling of shift scheduling problems. Constraints 16, 54–76 (2011). https://doi.org/10.1007/s10601-009-9083-2

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