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A matheuristic based on Lagrangian relaxation for the multi-activity shift scheduling problem

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  • Hernández-Leandro, Noberto A.
  • Boyer, Vincent
  • Salazar-Aguilar, M. Angélica
  • Rousseau, Louis-Martin

Abstract

The multi-activity shift scheduling problem involves assigning a sequence of activities to a set of employees. In this paper, we consider the variant where the employees have different qualifications and each activity must be performed in a specified time window; i.e., we specify the earliest start period and the latest finish period. We propose a matheuristic in which Lagrangian relaxation is used to identify a subset of promising shifts, and a restricted set covering problem is solved to find a feasible solution. Each shift is represented by a context-free grammar. Computational tests are carried out on two sets of instances from the literature. For the first set, the matheuristic finds a solution with an optimality gap less than 0.01% for 70% of the instances and improves the best-known solution for 16% of them; for the second set, the matheuristic reaches the best-known solutions for 55% of the instances and finds better solutions for 37.5% of them.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:272:y:2019:i:3:p:859-867
    DOI: 10.1016/j.ejor.2018.07.010
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    References listed on IDEAS

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    1. Egon Balas & Maria C. Carrera, 1996. "A Dynamic Subgradient-Based Branch-and-Bound Procedure for Set Covering," Operations Research, INFORMS, vol. 44(6), pages 875-890, December.
    2. Robert E. Bixby & John W. Gregory & Irvin J. Lustig & Roy E. Marsten & David F. Shanno, 1992. "Very Large-Scale Linear Programming: A Case Study in Combining Interior Point and Simplex Methods," Operations Research, INFORMS, vol. 40(5), pages 885-897, October.
    3. 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.
    4. 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.
    5. Marie-Claude Côté & Bernard Gendron & Louis-Martin Rousseau, 2013. "Grammar-Based Column Generation for Personalized Multi-Activity Shift Scheduling," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 461-474, August.
    6. Alberto Caprara & Matteo Fischetti & Paolo Toth, 1999. "A Heuristic Method for the Set Covering Problem," Operations Research, INFORMS, vol. 47(5), pages 730-743, October.
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    Cited by:

    1. Nikzad, Erfaneh & Bashiri, Mahdi & Abbasi, Babak, 2021. "A matheuristic algorithm for stochastic home health care planning," European Journal of Operational Research, Elsevier, vol. 288(3), pages 753-774.

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