IDEAS home Printed from
   My bibliography  Save this article

Grammar-Based Integer Programming Models for Multiactivity Shift Scheduling


  • 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)


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

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Turgut Aykin, 1996. "Optimal Shift Scheduling with Multiple Break Windows," Management Science, INFORMS, vol. 42(4), pages 591-602, April.
    2. Larry P. Ritzman & LeRoy J. Krajewski & Michael J. Showalter, 1976. "The Disaggregation of Aggregate Manpower Plans," Management Science, INFORMS, vol. 22(11), pages 1204-1214, July.
    3. Willie B. Henderson & William L. Berry, 1976. "Heuristic Methods for Telephone Operator Shift Scheduling: An Experimental Analysis," Management Science, INFORMS, vol. 22(12), pages 1372-1380, August.
    4. Gary M. Thompson, 1995. "Improved Implicit Optimal Modeling of the Labor Shift Scheduling Problem," Management Science, INFORMS, vol. 41(4), pages 595-607, April.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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. 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.
    4. repec:eee:ejores:v:262:y:2017:i:2:p:620-635 is not listed on IDEAS
    5. Rodolfo Cuevas & Juan-Carlos Ferrer & Mathias Klapp & Juan-Carlos Muñoz, 2016. "A mixed integer programming approach to multi-skilled workforce scheduling," Journal of Scheduling, Springer, vol. 19(1), pages 91-106, February.
    6. repec:spr:annopr:v:252:y:2017:i:2:d:10.1007_s10479-016-2175-7 is not listed on IDEAS
    7. 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.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:57:y:2011:i:1:p:151-163. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.