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A Polyhedral Approach to Simplified Crew Scheduling and Vehicle Scheduling Problems

Author

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  • Matteo Fischetti

    (Dipartimento di Elettronica e Informatica, Universitàà di Padova, Italy)

  • Andrea Lodi

    (Dipartimento di Elettronica, Informatica, e Sistemistica, Universitàà di Bologna, Italy)

  • Silvano Martello

    (Dipartimento di Elettronica, Informatica, e Sistemistica, Universitàà di Bologna, Italy)

  • Paolo Toth

    (Dipartimento di Elettronica, Informatica, e Sistemistica, Universitàà di Bologna, Italy)

Abstract

Crew and vehicle scheduling are fundamental issues in public transit management. Informally, they can be described as the problem of determining the optimal duties for a set of crews (e.g., bus drivers) or vehicles (e.g., buses) so as to cover a given set of timetabled trips, satisfying a number of constraints laid down by the union contract and company regulations. We consider the simplified but still NP-hard case in which several depots are specified, and limits on both the total time between the start and the end of any duty (spread time) and the total duty operational time (working time) are imposed. We give a 0-1 linear programming formulation based on binary variables associated with trip transitions, which applies to both crew and vehicle scheduling. The model is enhanced by means of new families of valid inequalities, for which exact and heuristic separation procedures are proposed. These techniques are embedded into an exact branch-and-cut algorithm, which also incorporates heuristic procedures. The performance of two implementations of the method (for vehicle scheduling and crew scheduling, respectively) are evaluated through computational testing on both random and real-world test problems from the literature.

Suggested Citation

  • Matteo Fischetti & Andrea Lodi & Silvano Martello & Paolo Toth, 2001. "A Polyhedral Approach to Simplified Crew Scheduling and Vehicle Scheduling Problems," Management Science, INFORMS, vol. 47(6), pages 833-850, June.
    • Handle: RePEc:inm:ormnsc:v:47:y:2001:i:6:p:833-850
    DOI: 10.1287/mnsc.47.6.833.9810
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    References listed on IDEAS

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    1. Mauro Dell'Amico & Matteo Fischetti & Paolo Toth, 1993. "Heuristic Algorithms for the Multiple Depot Vehicle Scheduling Problem," Management Science, INFORMS, vol. 39(1), pages 115-125, January.
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    2. Michiel A. J. uit het Broek & Albert H. Schrotenboer & Bolor Jargalsaikhan & Kees Jan Roodbergen & Leandro C. Coelho, 2021. "Asymmetric Multidepot Vehicle Routing Problems: Valid Inequalities and a Branch-and-Cut Algorithm," Operations Research, INFORMS, vol. 69(2), pages 380-409, March.
    3. Breugem, T. & van Rossum, B.T.C. & Dollevoet, T. & Huisman, D., 2022. "A column generation approach for the integrated crew re-planning problem," Omega, Elsevier, vol. 107(C).
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    7. Pan, Hanchuan & Liu, Zhigang & Yang, Lixing & Liang, Zhe & Wu, Qiang & Li, Sijie, 2021. "A column generation-based approach for integrated vehicle and crew scheduling on a single metro line with the fully automatic operation system by partial supervision," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
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    9. Francesco P. Deflorio & Jesus Gonzalez-Feliu & Guido Perboli & Roberto Tadei, 2009. "Transportation cost estimation in freight distribution services with time windows: application to an Italian urban area," Post-Print halshs-00758245, HAL.
    10. Lysgaard, Jens, 2006. "Reachability cuts for the vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 175(1), pages 210-223, November.
    11. Han-Lin Li & Yao-Huei Huang & Shu-Cherng Fang, 2013. "A Logarithmic Method for Reducing Binary Variables and Inequality Constraints in Solving Task Assignment Problems," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 643-653, November.
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    13. Francesco P. Deflorio & Jesus Gonzalez-Feliu & Roberto Tadei & Simone Amico, 2009. "Service quality planning for freight distribution with time windows in large networks," Working Papers halshs-01056187, HAL.

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