, Volume 16, Issue 1, pp 54–76 | Cite as

Formal languages for integer programming modeling of shift scheduling problems

  • Marie-Claude Côté
  • Bernard Gendron
  • Claude-Guy Quimper
  • Louis-Martin Rousseau


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.


Constraint programming Integer programming Reformulations Formal languages 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Marie-Claude Côté
    • 1
    • 2
  • Bernard Gendron
    • 2
    • 3
  • Claude-Guy Quimper
    • 4
  • Louis-Martin Rousseau
    • 1
    • 2
  1. 1.Département de mathématiques et génie industrielÉcole Polytechnique de MontréalMontréalCanada
  2. 2.CIRRELT-Interuniversity Research Center on Enterprise NetworksLogistics and TransportationMontréalCanada
  3. 3.Département d’informatique et de recherche opérationnelleUniversité de Montréal, Pavillon André-AisenstadtMontréalCanada
  4. 4.Omega OptimisationMontréalCanada

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