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The Fixed Job Schedule Problem with Spread-Time Constraints

Author

Listed:
  • Matteo Fischetti

    (University of Bologna, Bologna, Italy)

  • Silvano Martello

    (University of Bologna, Bologna, Italy)

  • Paolo Toth

    (University of Bologna, Bologna, Italy)

Abstract

We consider a generalization of the fixed job schedule problem in which each processor is available only for a prefixed time interval from the release time of the earliest task assigned to it. The problem can arise in bus driver scheduling. We show that the problem is NP-hard, and introduce polynomial procedures to determine lower bounds, dominance criteria and reductions. We also develop a branch-and-bound algorithm for obtaining the optimal solution of the problem and analyze the algorithm’s average performance in a series of computational experiments. Finally, we investigate the preemptive case and other polynomial special cases.

Suggested Citation

  • Matteo Fischetti & Silvano Martello & Paolo Toth, 1987. "The Fixed Job Schedule Problem with Spread-Time Constraints," Operations Research, INFORMS, vol. 35(6), pages 849-858, December.
    • Handle: RePEc:inm:oropre:v:35:y:1987:i:6:p:849-858
    DOI: 10.1287/opre.35.6.849
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    Citations

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    Cited by:

    1. Markó Horváth & Tamás Kis, 2019. "Computing strong lower and upper bounds for the integrated multiple-depot vehicle and crew scheduling problem with branch-and-price," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(1), pages 39-67, March.
    2. Ingmar Steinzen & Vitali Gintner & Leena Suhl & Natalia Kliewer, 2010. "A Time-Space Network Approach for the Integrated Vehicle- and Crew-Scheduling Problem with Multiple Depots," Transportation Science, INFORMS, vol. 44(3), pages 367-382, August.
    3. Kroon, Leo G. & Salomon, Marc & Van Wassenhove, Luk N., 1995. "Exact and approximation algorithms for the operational fixed interval scheduling problem," European Journal of Operational Research, Elsevier, vol. 82(1), pages 190-205, April.
    4. 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.
    5. Bekki, Özgün BarIs & Azizoglu, Meral, 2008. "Operational fixed interval scheduling problem on uniform parallel machines," International Journal of Production Economics, Elsevier, vol. 112(2), pages 756-768, April.
    6. Antoon W.J. Kolen & Jan Karel Lenstra & Christos H. Papadimitriou & Frits C.R. Spieksma, 2007. "Interval scheduling: A survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 530-543, August.
    7. Krishnamoorthy, M. & Ernst, A.T. & Baatar, D., 2012. "Algorithms for large scale Shift Minimisation Personnel Task Scheduling Problems," European Journal of Operational Research, Elsevier, vol. 219(1), pages 34-48.
    8. Julia Chuzhoy & Rafail Ostrovsky & Yuval Rabani, 2006. "Approximation Algorithms for the Job Interval Selection Problem and Related Scheduling Problems," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 730-738, November.
    9. Stephen E. Bechtold & Larry W. Jacobs, 1996. "The equivalence of general set‐covering and implicit integer programming formulations for shift scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(2), pages 233-249, March.
    10. Lee, Soonhui & Turner, Jonathan & Daskin, Mark S. & Homem-de-Mello, Tito & Smilowitz, Karen, 2012. "Improving fleet utilization for carriers by interval scheduling," European Journal of Operational Research, Elsevier, vol. 218(1), pages 261-269.
    11. 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.
    12. Eliiyi, Deniz Türsel & Ornek, Arslan & Karakütük, SadIk Serhat, 2009. "A vehicle scheduling problem with fixed trips and time limitations," International Journal of Production Economics, Elsevier, vol. 117(1), pages 150-161, January.
    13. Türsel Eliiyi, Deniz & Azizoglu, Meral, 2011. "Heuristics for operational fixed job scheduling problems with working and spread time constraints," International Journal of Production Economics, Elsevier, vol. 132(1), pages 107-121, July.
    14. Bastian Amberg & Boris Amberg & Natalia Kliewer, 2019. "Robust Efficiency in Urban Public Transportation: Minimizing Delay Propagation in Cost-Efficient Bus and Driver Schedules," Service Science, INFORMS, vol. 53(1), pages 89-112, February.
    15. Shyam S. G. Perumal & Jesper Larsen & Richard M. Lusby & Morten Riis & Tue R. L. Christensen, 2022. "A column generation approach for the driver scheduling problem with staff cars," Public Transport, Springer, vol. 14(3), pages 705-738, October.
    16. Kroon, Leo G. & Edwin Romeijn, H. & Zwaneveld, Peter J., 1997. "Routing trains through railway stations: complexity issues," European Journal of Operational Research, Elsevier, vol. 98(3), pages 485-498, May.
    17. A. Mingozzi & M. A. Boschetti & S. Ricciardelli & L. Bianco, 1999. "A Set Partitioning Approach to the Crew Scheduling Problem," Operations Research, INFORMS, vol. 47(6), pages 873-888, December.
    18. Perumal, Shyam S.G. & Larsen, Jesper & Lusby, Richard M. & Riis, Morten & Sørensen, Kasper S., 2019. "A matheuristic for the driver scheduling problem with staff cars," European Journal of Operational Research, Elsevier, vol. 275(1), pages 280-294.

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