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Work Force Size and Single Shift Schedules with Variable Demands

Author

Listed:
  • R. N. Burns

    (School of Business, Queen's University, Kingston, Ontario, Canada K7L 3N6)

  • M. W. Carter

    (School of Business, Queen's University, Kingston, Ontario, Canada K7L 3N6)

Abstract

In recent years, labour negotiations for seven-day-week organizations such as hospitals, mining companies and chemical industries have seen an increased emphasis on improving shift schedules. This paper gives an exact lower bound on the number of workers required to satisfy such primary contractual commitments as ensuring that each employee receives at least A out of every B weekends off, everyone works exactly five days per week, and no one works more than six consecutive days. The model addressed is general in that it allows the number of workers required each day to vary. The proof that the bound is the best possible is constructive. A linear time algorithm is presented that generates schedules satisfying all the primary objectives. Extensions discuss means of incorporating secondary objectives such as giving pairs of adjacent days off.

Suggested Citation

  • R. N. Burns & M. W. Carter, 1985. "Work Force Size and Single Shift Schedules with Variable Demands," Management Science, INFORMS, vol. 31(5), pages 599-607, May.
    • Handle: RePEc:inm:ormnsc:v:31:y:1985:i:5:p:599-607
    DOI: 10.1287/mnsc.31.5.599
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    Citations

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    Cited by:

    1. Richard N. Burns & Rangarajan Narasimhan & L. Douglas Smith, 1998. "A set‐processing algorithm for scheduling staff on 4‐day or 3‐day work weeks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(8), pages 839-853, December.
    2. 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.
    3. 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.
    4. 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.
    5. Jens Brunner & Jonathan Bard & Rainer Kolisch, 2009. "Flexible shift scheduling of physicians," Health Care Management Science, Springer, vol. 12(3), pages 285-305, September.
    6. Hung, Rudy, 2006. "Using compressed workweeks to save labour cost," European Journal of Operational Research, Elsevier, vol. 170(1), pages 319-322, April.
    7. Michael J. Brusco & Larry W. Jacobs, 2000. "Optimal Models for Meal-Break and Start-Time Flexibility in Continuous Tour Scheduling," Management Science, INFORMS, vol. 46(12), pages 1630-1641, December.
    8. G Beddoe & S Petrovic, 2007. "Enhancing case-based reasoning for personnel rostering with selected tabu search concepts," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(12), pages 1586-1598, December.
    9. Hadi W. Purnomo & Jonathan F. Bard, 2007. "Cyclic preference scheduling for nurses using branch and price," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(2), pages 200-220, March.
    10. Mark W. Isken & Osman T. Aydas, 2022. "A tactical multi-week implicit tour scheduling model with applications in healthcare," Health Care Management Science, Springer, vol. 25(4), pages 551-573, December.
    11. Jonathan Bard & David Morton & Yong Wang, 2007. "Workforce planning at USPS mail processing and distribution centers using stochastic optimization," Annals of Operations Research, Springer, vol. 155(1), pages 51-78, November.
    12. Hertz, Alain & Lahrichi, Nadia & Widmer, Marino, 2010. "A flexible MILP model for multiple-shift workforce planning under annualized hours," European Journal of Operational Research, Elsevier, vol. 200(3), pages 860-873, February.
    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. Broos Maenhout & Mario Vanhoucke, 2017. "A resource type analysis of the integrated project scheduling and personnel staffing problem," Annals of Operations Research, Springer, vol. 252(2), pages 407-433, May.
    15. 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.
    16. Narasimhan, Rangarajan, 1997. "An algorithm for single shift scheduling of hierarchical workforce," European Journal of Operational Research, Elsevier, vol. 96(1), pages 113-121, January.
    17. David Sinreich & Ola Jabali, 2007. "Staggered work shifts: a way to downsize and restructure an emergency department workforce yet maintain current operational performance," Health Care Management Science, Springer, vol. 10(3), pages 293-308, September.
    18. L Wan & J F Bard, 2007. "Weekly staff scheduling with workstation group restrictions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(8), pages 1030-1046, August.
    19. Azmat, Carlos S. & Widmer, Marino, 2004. "A case study of single shift planning and scheduling under annualized hours: A simple three-step approach," European Journal of Operational Research, Elsevier, vol. 153(1), pages 148-175, February.
    20. Eiji Mizutani & Kevin Alexander Sánchez Galeano, 2023. "A note on a single-shift days-off scheduling problem with sequence-dependent labor costs," Journal of Scheduling, Springer, vol. 26(3), pages 315-329, June.
    21. Rudy Hung, 1999. "A multiple‐shift workforce scheduling model under annualized hours," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 726-736, September.
    22. Andreas Fügener & Jens O. Brunner, 2019. "Planning for Overtime: The Value of Shift Extensions in Physician Scheduling," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 732-744, October.
    23. 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.
    24. Drexl, Andreas & Mundschenk, Martin, 2005. "Long-term staffing based on qualification profiles," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 592, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    25. Smet, Pieter & Brucker, Peter & De Causmaecker, Patrick & Vanden Berghe, Greet, 2016. "Polynomially solvable personnel rostering problems," European Journal of Operational Research, Elsevier, vol. 249(1), pages 67-75.

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