Formal languages for integer programming modeling of shift scheduling problems

Authors:
Marie-Claude Côté;Bernard Gendron;Claude-Guy Quimper;Louis-Martin Rousseau
Affiliations:
Département de mathématiques et génie industriel, École Polytechnique de Montréal, Montréal, Canada H3C 3A7 and CIRRELT-Interuniversity Research Center on Enterprise ...;CIRRELT-Interuniversity Research Center on Enterprise Networks, Logistics and Transportation, Montréal, Canada and Département d'informatique et de recherche opérationnelle, Univers ...;Omega Optimisation, Montréal, Canada H2W 2R2;Département de mathématiques et génie industriel, École Polytechnique de Montréal, Montréal, Canada H3C 3A7 and CIRRELT-Interuniversity Research Center on Enterprise ...
Venue:
Constraints
Year:
2011

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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.