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Grammar-Based Integer Programming Models for Multiactivity Shift Scheduling

Author

Listed:
  • 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)

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.

Suggested Citation

  • Marie-Claude Côté & Bernard Gendron & Louis-Martin Rousseau, 2011. "Grammar-Based Integer Programming Models for Multiactivity Shift Scheduling," Management Science, INFORMS, vol. 57(1), pages 151-163, January.
  • Handle: RePEc:inm:ormnsc:v:57:y:2011:i:1:p:151-163
    DOI: 10.1287/mnsc.1100.1264
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Ağralı, Semra & Taşkın, Z. Caner & Ünal, A. Tamer, 2017. "Employee scheduling in service industries with flexible employee availability and demand," Omega, Elsevier, vol. 66(PA), pages 159-169.
    2. Volland, Jonas & Fügener, Andreas & Brunner, Jens O., 2017. "A column generation approach for the integrated shift and task scheduling problem of logistics assistants in hospitals," European Journal of Operational Research, Elsevier, vol. 260(1), pages 316-334.
    3. Arpan Rijal & Marco Bijvank & Asvin Goel & René de Koster, 2021. "Workforce Scheduling with Order-Picking Assignments in Distribution Facilities," Transportation Science, INFORMS, vol. 55(3), pages 725-746, May.
    4. Chapados, Nicolas & Joliveau, Marc & L’Ecuyer, Pierre & Rousseau, Louis-Martin, 2014. "Retail store scheduling for profit," European Journal of Operational Research, Elsevier, vol. 239(3), pages 609-624.
    5. Jens O. Brunner & Jonathan F. Bard & Jan M. Köhler, 2013. "Bounded flexibility in days‐on and days‐off scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 678-701, December.
    6. Restrepo, María I. & Gendron, Bernard & Rousseau, Louis-Martin, 2017. "A two-stage stochastic programming approach for multi-activity tour scheduling," European Journal of Operational Research, Elsevier, vol. 262(2), pages 620-635.
    7. Hassani, Rachid & Desaulniers, Guy & Elhallaoui, Issmail, 2021. "Real-time bi-objective personnel re-scheduling in the retail industry," European Journal of Operational Research, Elsevier, vol. 293(1), pages 93-108.
    8. Mark W. Isken & Osman T. Aydas, 2022. "A tactical multi-week implicit tour scheduling model with applications in healthcare," Health Care Management Science, Springer, vol. 25(4), pages 551-573, December.
    9. Banu Sungur & Cemal Özgüven & Yasemin Kariper, 2017. "Shift scheduling with break windows, ideal break periods, and ideal waiting times," Flexible Services and Manufacturing Journal, Springer, vol. 29(2), pages 203-222, June.
    10. Hernández-Leandro, Noberto A. & Boyer, Vincent & Salazar-Aguilar, M. Angélica & Rousseau, Louis-Martin, 2019. "A matheuristic based on Lagrangian relaxation for the multi-activity shift scheduling problem," European Journal of Operational Research, Elsevier, vol. 272(3), pages 859-867.
    11. Restrepo, María I. & Rousseau, Louis-Martin & Vallée, Jonathan, 2020. "Home healthcare integrated staffing and scheduling," Omega, Elsevier, vol. 95(C).
    12. Alex Bonutti & Sara Ceschia & Fabio De Cesco & Nysret Musliu & Andrea Schaerf, 2017. "Modeling and solving a real-life multi-skill shift design problem," Annals of Operations Research, Springer, vol. 252(2), pages 365-382, May.
    13. 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.
    14. Sana Dahmen & Monia Rekik & François Soumis, 2018. "An implicit model for multi-activity shift scheduling problems," Journal of Scheduling, Springer, vol. 21(3), pages 285-304, June.
    15. Douglas S. Altner & Anthony C. Rojas & Leslie D. Servi, 2018. "A two-stage stochastic program for multi-shift, multi-analyst, workforce optimization with multiple on-call options," Journal of Scheduling, Springer, vol. 21(5), pages 517-531, October.

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