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Grammar-Based Integer Programming Models for Multiactivity Shift Scheduling

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Author Info

  • Marie-Claude Côté

    ()
    (CIRRELT and Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal, Montréal, Québec H3C 3A7, Canada)

  • Bernard Gendron

    ()
    (CIRRELT and Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, Montréal, Québec H3C 3J7, Canada)

  • Louis-Martin Rousseau

    ()
    (CIRRELT and Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal, Montréal, Québec H3C 3A7, Canada)

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    Abstract

    This paper presents a new implicit formulation for shift scheduling problems, using context-free grammars to model the rules for the composition of shifts. From the grammar, we generate an integer programming (IP) model having a linear programming relaxation equivalent to that of the classical set covering model. When solved by a state-of-the-art IP solver on problem instances with a small number of shifts, our model, the set covering formulation, and a typical implicit model from the literature yield comparable solution times. On instances with a large number of shifts, our formulation shows superior performance and can model a wider variety of constraints. In particular, multiactivity cases, which cannot be modeled by existing implicit formulations, can easily be handled with grammars. We present comparative experimental results on a large set of instances involving one work activity, as well as on problems dealing with up to 10 work activities. This paper was accepted by Dimitris Bertsimas, optimization.

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    File URL: http://dx.doi.org/10.1287/mnsc.1100.1264
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 57 (2011)
    Issue (Month): 1 (January)
    Pages: 151-163

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    Handle: RePEc:inm:ormnsc:v:57:y:2011:i:1:p:151-163

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    Related research

    Keywords: shift scheduling; implicit models; mixed integer programming; context-free grammars;

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    Cited by:
    1. Restrepo, María I. & Lozano, Leonardo & Medaglia, Andrés L., 2012. "Constrained network-based column generation for the multi-activity shift scheduling problem," International Journal of Production Economics, Elsevier, vol. 140(1), pages 466-472.

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