IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v125y2016icp139-151.html
   My bibliography  Save this article

Counting and enumerating feasible rotating schedules by means of Gröbner bases

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475414003292
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2014.12.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hesham Alfares, 2004. "Survey, Categorization, and Comparison of Recent Tour Scheduling Literature," Annals of Operations Research, Springer, vol. 127(1), pages 145-175, March.
    2. Brucker, Peter & Qu, Rong & Burke, Edmund, 2011. "Personnel scheduling: Models and complexity," European Journal of Operational Research, Elsevier, vol. 210(3), pages 467-473, May.
    3. Castillo, Ignacio & Joro, Tarja & Li, Yong Yue, 2009. "Workforce scheduling with multiple objectives," European Journal of Operational Research, Elsevier, vol. 196(1), pages 162-170, July.
    4. Laporte, Gilbert & Nobert, Yves & Biron, Jean, 1980. "Rotating schedules," European Journal of Operational Research, Elsevier, vol. 4(1), pages 24-30, January.
    5. G Laporte & G Pesant, 2004. "A general multi-shift scheduling system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(11), pages 1208-1217, November.
    6. G Laporte, 1999. "The art and science of designing rotating schedules," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(10), pages 1011-1017, October.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Marta Rocha & José Oliveira & Maria Carravilla, 2014. "A constructive heuristic for staff scheduling in the glass industry," Annals of Operations Research, Springer, vol. 217(1), pages 463-478, June.
    3. 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.
    4. Tristan Becker, 2020. "A decomposition heuristic for rotational workforce scheduling," Journal of Scheduling, Springer, vol. 23(5), pages 539-554, October.
    5. Sanja Petrovic, 2019. "“You have to get wet to learn how to swim” applied to bridging the gap between research into personnel scheduling and its implementation in practice," Annals of Operations Research, Springer, vol. 275(1), pages 161-179, April.
    6. Emir Hüseyin Özder & Evrencan Özcan & Tamer Eren, 2019. "Staff Task-Based Shift Scheduling Solution with an ANP and Goal Programming Method in a Natural Gas Combined Cycle Power Plant," Mathematics, MDPI, vol. 7(2), pages 1-26, February.
    7. Lin, Shih-Wei & Ying, Kuo-Ching, 2014. "Minimizing shifts for personnel task scheduling problems: A three-phase algorithm," European Journal of Operational Research, Elsevier, vol. 237(1), pages 323-334.
    8. Jaime Miranda & Pablo A. Rey & Antoine Sauré & Richard Weber, 2018. "Metro Uses a Simulation-Optimization Approach to Improve Fare-Collection Shift Scheduling," Interfaces, INFORMS, vol. 48(6), pages 529-542, November.
    9. M Lezaun & G Pérez & E Sáinz de la Maza, 2010. "Staff rostering for the station personnel of a railway company," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(7), pages 1104-1111, July.
    10. Young-Chae Hong & Amy Cohn & Stephen Gorga & Edmond O’Brien & William Pozehl & Jennifer Zank, 2019. "Using Optimization Techniques and Multidisciplinary Collaboration to Solve a Challenging Real-World Residency Scheduling Problem," Interfaces, INFORMS, vol. 49(3), pages 201-212, May.
    11. 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.
    12. Smirnov, Dmitry & Huchzermeier, Arnd, 2020. "Analytics for labor planning in systems with load-dependent service times," European Journal of Operational Research, Elsevier, vol. 287(2), pages 668-681.
    13. Zhang, Zizhen & Qin, Hu & Wang, Kai & He, Huang & Liu, Tian, 2017. "Manpower allocation and vehicle routing problem in non-emergency ambulance transfer service," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 45-59.
    14. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.
    15. R. K. Jha & B. S. Sahay & P. Charan, 2016. "Healthcare operations management: a structured literature review," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 43(3), pages 259-279, September.
    16. Tristan Becker & Maximilian Schiffer & Grit Walther, 2022. "A General Branch-and-Cut Framework for Rotating Workforce Scheduling," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1548-1564, May.
    17. Fang, Kan & Wang, Shijin & Pinedo, Michael L. & Chen, Lin & Chu, Feng, 2021. "A combinatorial Benders decomposition algorithm for parallel machine scheduling with working-time restrictions," European Journal of Operational Research, Elsevier, vol. 291(1), pages 128-146.
    18. Brusco, Michael J., 2015. "A bicriterion algorithm for the allocation of cross-trained workers based on operational and human resource objectives," European Journal of Operational Research, Elsevier, vol. 247(1), pages 46-59.
    19. Oyku Ahipasaoglu & Nesim Erkip & Oya Ekin Karasan, 2019. "The venue management problem: setting staffing levels, shifts and shift schedules at concession stands," Journal of Scheduling, Springer, vol. 22(1), pages 69-83, February.
    20. 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.

    Corrections

    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:eee:matcom:v:125:y:2016:i:c:p:139-151. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.