IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v47y2000i3p185-200.html
   My bibliography  Save this article

Optimal shift scheduling: A branch‐and‐price approach

Author

Listed:
  • Anuj Mehrotra
  • Kenneth E. Murphy
  • Michael A. Trick

Abstract

We present a branch‐and‐price technique for optimal staff scheduling with multiple rest breaks, meal break, and break windows. We devise and implement specialized branching rules suitable for solving the set covering type formulation implicitly, using column generation. Our methodology is more widely applicable and computationally superior to the alternative methods in the literature. We tested our methodology on 365 test problems involving between 1728 and 86400 shift variations, and 20 demand patterns. In a direct comparison with an alternative method, our approach yields significant improvements both in cpu time and in the number of problem instances solved to optimality. The improvements were particularly marked for problems involving larger numbers of feasible shifts. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 185–200, 2000

Suggested Citation

  • Anuj Mehrotra & Kenneth E. Murphy & Michael A. Trick, 2000. "Optimal shift scheduling: A branch‐and‐price approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(3), pages 185-200, April.
    • Handle: RePEc:wly:navres:v:47:y:2000:i:3:p:185-200
    DOI: 10.1002/(SICI)1520-6750(200004)47:33.0.CO;2-7
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/(SICI)1520-6750(200004)47:33.0.CO;2-7
    Download Restriction: no
    File URL: https://libkey.io/10.1002/(SICI)1520-6750(200004)47:33.0.CO;2-7?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
    ---><---

    References listed on IDEAS

    as
    1. Fred F. Easton & Donald F. Rossin, 1991. "Sufficient Working Subsets for the Tour Scheduling Problem," Management Science, INFORMS, vol. 37(11), pages 1441-1451, November.
    2. Turgut Aykin, 1996. "Optimal Shift Scheduling with Multiple Break Windows," Management Science, INFORMS, vol. 42(4), pages 591-602, April.
    3. Thomas J. Holloran & Judson E. Byrn, 1986. "United Airlines Station Manpower Planning System," Interfaces, INFORMS, vol. 16(1), pages 39-50, February.
    4. M. Segal, 1974. "The Operator-Scheduling Problem: A Network-Flow Approach," Operations Research, INFORMS, vol. 22(4), pages 808-823, August.
    5. George B. Dantzig, 1954. "Letter to the Editor---A Comment on Edie's “Traffic Delays at Toll Booths”," Operations Research, INFORMS, vol. 2(3), pages 339-341, August.
    6. Anuj Mehrotra & Michael A. Trick, 1996. "A Column Generation Approach for Graph Coloring," INFORMS Journal on Computing, INFORMS, vol. 8(4), pages 344-354, November.
    7. Leslie C. Edie, 1954. "Traffic Delays at Toll Booths," Operations Research, INFORMS, vol. 2(2), pages 107-138, May.
    8. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    9. 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.
    10. Gary M. Thompson, 1997. "Assigning Telephone Operators to Shifts at New Brunswick Telephone Company," Interfaces, INFORMS, vol. 27(4), pages 1-11, August.
    11. Gary M. Thompson, 1995. "Improved Implicit Optimal Modeling of the Labor Shift Scheduling Problem," Management Science, INFORMS, vol. 41(4), pages 595-607, April.
    12. Stephen E. Bechtold & Larry W. Jacobs, 1990. "Implicit Modeling of Flexible Break Assignments in Optimal Shift Scheduling," Management Science, INFORMS, vol. 36(11), pages 1339-1351, November.
    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. Rana Shariat & Kai Huang, 2024. "A large-scale neighborhood search algorithm for multi-activity tour scheduling problems," Journal of Heuristics, Springer, vol. 30(5), pages 225-267, December.
    2. 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.
    3. Hua Ni & Hernán Abeledo, 2007. "A branch-and-price approach for large-scale employee tour scheduling problems," Annals of Operations Research, Springer, vol. 155(1), pages 167-176, November.
    4. Zhixing Luo & Hu Qin & Wenbin Zhu & Andrew Lim, 2016. "Branch‐and‐price‐and‐cut for the manpower routing problem with synchronization constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 138-171, March.
    5. María I. Restrepo & Bernard Gendron & Louis-Martin Rousseau, 2016. "Branch-and-Price for Personalized Multiactivity Tour Scheduling," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 334-350, May.
    6. Daniel Villeneuve & Jacques Desrosiers & Marco Lübbecke & François Soumis, 2005. "On Compact Formulations for Integer Programs Solved by Column Generation," Annals of Operations Research, Springer, vol. 139(1), pages 375-388, October.
    7. 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.
    8. Jeroen Beliën & Erik Demeulemeester, 2007. "On the trade-off between staff-decomposed and activity-decomposed column generation for a staff scheduling problem," Annals of Operations Research, Springer, vol. 155(1), pages 143-166, November.

    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. Aykin, Turgut, 2000. "A comparative evaluation of modeling approaches to the labor shift scheduling problem," European Journal of Operational Research, Elsevier, vol. 125(2), pages 381-397, September.
    2. Gary M. Thompson, 1997. "Labor staffing and scheduling models for controlling service levels," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(8), pages 719-740, December.
    3. 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.
    4. Brusco, Michael J. & Jacobs, Larry W., 1995. "Cost analysis of alternative formulations for personnel scheduling in continuously operating organizations," European Journal of Operational Research, Elsevier, vol. 86(2), pages 249-261, October.
    5. Robbins, Thomas R. & Harrison, Terry P., 2010. "A stochastic programming model for scheduling call centers with global Service Level Agreements," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1608-1619, December.
    6. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    7. 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.
    8. Brusco, Michael J. & Johns, Tony R., 1996. "A sequential integer programming method for discontinuous labor tour scheduling," European Journal of Operational Research, Elsevier, vol. 95(3), pages 537-548, December.
    9. Giovanni Felici & Claudio Gentile, 2004. "A Polyhedral Approach for the Staff Rostering Problem," Management Science, INFORMS, vol. 50(3), pages 381-393, March.
    10. Tolga Çezik & Oktay Günlük & Hanan Luss, 2001. "An integer programming model for the weekly tour scheduling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(7), pages 607-624, October.
    11. Thompson, Gary M. & Pullman, Madeleine E., 2007. "Scheduling workforce relief breaks in advance versus in real-time," European Journal of Operational Research, Elsevier, vol. 181(1), pages 139-155, August.
    12. 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.
    13. Michael J. Brusco & Larry W. Jacobs, 1998. "Personnel Tour Scheduling When Starting-Time Restrictions Are Present," Management Science, INFORMS, vol. 44(4), pages 534-547, April.
    14. 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.
    15. Easton, F. F. & Rossin, D. F., 1997. "Overtime schedules for full-time service workers," Omega, Elsevier, vol. 25(3), pages 285-299, June.
    16. Easton, Fred F. & Mansour, Nashat, 1999. "A distributed genetic algorithm for deterministic and stochastic labor scheduling problems," European Journal of Operational Research, Elsevier, vol. 118(3), pages 505-523, November.
    17. Melanie Erhard, 2021. "Flexible staffing of physicians with column generation," Flexible Services and Manufacturing Journal, Springer, vol. 33(1), pages 212-252, March.
    18. Ernst, A. T. & Jiang, H. & Krishnamoorthy, M. & Sier, D., 2004. "Staff scheduling and rostering: A review of applications, methods and models," European Journal of Operational Research, Elsevier, vol. 153(1), pages 3-27, February.
    19. S Casado & M Laguna & J Pacheco, 2005. "Heuristical labour scheduling to optimize airport passenger flows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 649-658, June.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:47:y:2000:i:3:p:185-200. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.