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Using Benders Decomposition to Implicitly Model Tour Scheduling

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  • Monia Rekik
  • Jean-François Cordeau
  • François Soumis

Abstract

This paper introduces a new integrated model for the combined days-off and shift scheduling problem (the tour scheduling problem). This model generalizes the forward and backward constraints, previously introduced by Bechtold and Jacobs for the shift scheduling problem, to the tour scheduling problem. This results in a general and compact formulation that can handle several types of scheduling flexibility. We also provide a new proof of the correctness of forward and backward constraints based on Benders decomposition. The latter approach is interesting in itself because it can be used to solve the problem when extraordinary overlap of break windows or start-time bands is present. A discussion of model size for a set of hypothetical test problems is presented to show the merits of the new formulation. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Monia Rekik & Jean-François Cordeau & François Soumis, 2004. "Using Benders Decomposition to Implicitly Model Tour Scheduling," Annals of Operations Research, Springer, vol. 128(1), pages 111-133, April.
    • Handle: RePEc:spr:annopr:v:128:y:2004:i:1:p:111-133:10.1023/b:anor.0000019101.29692.2c
    DOI: 10.1023/B:ANOR.0000019101.29692.2c
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    Citations

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    Cited by:

    1. Ferdinand Kiermaier & Markus Frey & Jonathan F. Bard, 2020. "The flexible break assignment problem for large tour scheduling problems with an application to airport ground handlers," Journal of Scheduling, Springer, vol. 23(2), pages 177-209, April.
    2. Chapados, Nicolas & Joliveau, Marc & L’Ecuyer, Pierre & Rousseau, Louis-Martin, 2014. "Retail store scheduling for profit," European Journal of Operational Research, Elsevier, vol. 239(3), pages 609-624.
    3. Lusby, Richard Martin & Range, Troels Martin & Larsen, Jesper, 2015. "A Benders decomposition-based Matheuristic for the Cardinality Constrained Shift Design Problem," Discussion Papers on Economics 9/2015, University of Southern Denmark, Department of Economics.
    4. 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.
    5. Henrik Andersson & Marielle Christiansen & Guy Desaulniers, 2016. "A new decomposition algorithm for a liquefied natural gas inventory routing problem," International Journal of Production Research, Taylor & Francis Journals, vol. 54(2), pages 564-578, January.
    6. Lusby, Richard Martin & Range, Troels Martin & Larsen, Jesper, 2016. "A Benders decomposition-based matheuristic for the Cardinality Constrained Shift Design Problem," European Journal of Operational Research, Elsevier, vol. 254(2), pages 385-397.
    7. Idris Addou & François Soumis, 2007. "Bechtold-Jacobs generalized model for shift scheduling with extraordinary overlap," Annals of Operations Research, Springer, vol. 155(1), pages 177-205, November.
    8. 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.
    9. 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.
    10. Jonathan F. Bard & Lin Wan, 2008. "Workforce Design with Movement Restrictions Between Workstation Groups," Manufacturing & Service Operations Management, INFORMS, vol. 10(1), pages 24-42, November.
    11. Alex Bonutti & Sara Ceschia & Fabio De Cesco & Nysret Musliu & Andrea Schaerf, 2017. "Modeling and solving a real-life multi-skill shift design problem," Annals of Operations Research, Springer, vol. 252(2), pages 365-382, May.
    12. 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.
    13. Restrepo, María I. & Lozano, Leonardo & Medaglia, Andrés L., 2012. "Constrained network-based column generation for the multi-activity shift scheduling problem," International Journal of Production Economics, Elsevier, vol. 140(1), pages 466-472.
    14. 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.
    15. Marie-Claude Côté & Bernard Gendron & Louis-Martin Rousseau, 2013. "Grammar-Based Column Generation for Personalized Multi-Activity Shift Scheduling," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 461-474, August.
    16. Youngbum Hur & Jonathan F. Bard & Markus Frey & Ferdinand Kiermaier, 2019. "An investigation of shift and break flexibility with real-time break assignments using a rolling horizon approach," Flexible Services and Manufacturing Journal, Springer, vol. 31(1), pages 174-211, March.
    17. 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.
    18. 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.
    19. Wasakorn Laesanklang & Dario Landa-Silva, 2017. "Decomposition techniques with mixed integer programming and heuristics for home healthcare planning," Annals of Operations Research, Springer, vol. 256(1), pages 93-127, September.
    20. 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.

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