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Counting and enumerating feasible rotating schedules by means of Gröbner bases

Author

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  • Falcón, Raúl
  • Barrena, Eva
  • Canca, David
  • Laporte, Gilbert

Abstract

This paper deals with the problem of designing and analyzing rotating schedules with an algebraic computational approach. Specifically, we determine a set of Boolean polynomials whose zeros can be uniquely identified with the set of rotating schedules related to a given workload matrix subject to standard constraints. These polynomials constitute zero-dimensional radical ideals, whose reduced Gröbner bases can be computed to count and even enumerate the set of rotating schedules that satisfy the desired set of constraints. Thereby, it enables to analyze the influence of each constraint in the same.

Suggested Citation

  • Falcón, Raúl & Barrena, Eva & Canca, David & Laporte, Gilbert, 2016. "Counting and enumerating feasible rotating schedules by means of Gröbner bases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 125(C), pages 139-151.
    • Handle: RePEc:eee:matcom:v:125:y:2016:i:c:p:139-151
    DOI: 10.1016/j.matcom.2014.12.002
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    References listed on IDEAS

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    7. Van den Bergh, Jorne & Beliën, Jeroen & De Bruecker, Philippe & Demeulemeester, Erik & De Boeck, Liesje, 2013. "Personnel scheduling: A literature review," European Journal of Operational Research, Elsevier, vol. 226(3), pages 367-385.
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    Cited by:

    1. Tristan Becker & Pia Mareike Steenweg & Brigitte Werners, 2019. "Cyclic shift scheduling with on-call duties for emergency medical services," Health Care Management Science, Springer, vol. 22(4), pages 676-690, December.

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