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Cyclic Scheduling via Integer Programs with Circular Ones

Author

Listed:
  • John J. Bartholdi

    (University of Michigan, Ann Arbor, Michigan)

  • James B. Orlin

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • H. Donald Ratliff

    (Georgia Institute of Technology, Atlanta, Georgia)

Abstract

A fundamental problem of cyclic staffing is to size and schedule a minimum-cost workforce so that sufficient workers are on duty during each time period. This may be modeled as an integer linear program with a cyclically structured 0-1 constraint matrix. We identify a large class of such problems for which special structure permits the ILP to be solved parametrically as a bounded series of network flow problems. Moreover, an alternative solution technique is shown in which the continuous-valued LP is solved, and the result rounded in a special way to yield an optimum solution to the ILP.

Suggested Citation

  • John J. Bartholdi & James B. Orlin & H. Donald Ratliff, 1980. "Cyclic Scheduling via Integer Programs with Circular Ones," Operations Research, INFORMS, vol. 28(5), pages 1074-1085, October.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:5:p:1074-1085
    DOI: 10.1287/opre.28.5.1074
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    Cited by:

    1. Yann Ferrand & Michael Magazine & Uday S. Rao & Todd F. Glass, 2011. "Building Cyclic Schedules for Emergency Department Physicians," Interfaces, INFORMS, vol. 41(6), pages 521-533, December.
    2. Lara Turner & Dwi Groß & Horst Hamacher & Sven Krumke, 2015. "Static and dynamic source locations in undirected networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 619-646, October.
    3. Benoist, Thierry, 2008. "Soft car sequencing with colors: Lower bounds and optimality proofs," European Journal of Operational Research, Elsevier, vol. 191(3), pages 957-971, December.
    4. Delorme, Xavier & Dolgui, Alexandre & Kovalev, Sergey & Kovalyov, Mikhail Y., 2019. "Minimizing the number of workers in a paced mixed-model assembly line," European Journal of Operational Research, Elsevier, vol. 272(1), pages 188-194.
    5. 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.
    6. Ingolfsson, Armann & Campello, Fernanda & Wu, Xudong & Cabral, Edgar, 2010. "Combining integer programming and the randomization method to schedule employees," European Journal of Operational Research, Elsevier, vol. 202(1), pages 153-163, April.
    7. Legato, Pasquale & Monaco, M. Flavia, 2004. "Human resources management at a marine container terminal," European Journal of Operational Research, Elsevier, vol. 156(3), pages 769-781, August.
    8. Giovanni Felici & Claudio Gentile, 2004. "A Polyhedral Approach for the Staff Rostering Problem," Management Science, INFORMS, vol. 50(3), pages 381-393, March.
    9. 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.
    10. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    11. Arjan Akkermans & Gerhard Post & Marc Uetz, 2021. "Solving the shift and break design problem using integer linear programming," Annals of Operations Research, Springer, vol. 302(2), pages 341-362, July.
    12. Bentz, Cédric & Cornaz, Denis & Ries, Bernard, 2013. "Packing and covering with linear programming: A survey," European Journal of Operational Research, Elsevier, vol. 227(3), pages 409-422.
    13. Michael J. Brusco & Larry W. Jacobs, 1993. "A simulated annealing approach to the cyclic staff‐scheduling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 69-84, February.
    14. Yang, Yongjie & Dimitrov, Dinko, 2023. "Group control for consent rules with consecutive qualifications," Mathematical Social Sciences, Elsevier, vol. 121(C), pages 1-7.
    15. de Werra, D., 1996. "Extensions of coloring models for scheduling purposes," European Journal of Operational Research, Elsevier, vol. 92(3), pages 474-492, August.
    16. Luca Di Gaspero & Johannes Gärtner & Guy Kortsarz & Nysret Musliu & Andrea Schaerf & Wolfgang Slany, 2007. "The minimum shift design problem," Annals of Operations Research, Springer, vol. 155(1), pages 79-105, November.
    17. Kulkarni, Anand J. & Baki, M.F. & Chaouch, Ben A., 2016. "Application of the cohort-intelligence optimization method to three selected combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 250(2), pages 427-447.
    18. Bentz, Cédric & Costa, Marie-Christine & Létocart, Lucas & Roupin, Frédéric, 2009. "Multicuts and integral multiflows in rings," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1251-1254, August.
    19. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    20. Tristan Becker, 2020. "A decomposition heuristic for rotational workforce scheduling," Journal of Scheduling, Springer, vol. 23(5), pages 539-554, October.
    21. O’Sullivan, Dónal & Newman, Alexandra, 2015. "Optimization-based heuristics for underground mine scheduling," European Journal of Operational Research, Elsevier, vol. 241(1), pages 248-259.
    22. 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.
    23. 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.
    24. 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.

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