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Exact and Approximation Algorithms for the Tactical Fixed Interval Scheduling Problem

Author

Listed:
  • Leo G. Kroon

    (Erasmus University, Rotterdam, The Netherlands)

  • Marc Salomon

    (Tilburg University, Tilburg, The Netherlands)

  • Luk N. Van Wassenhove

    (INSEAD, Boulevard de Constance, France)

Abstract

The Tactical Fixed Interval Scheduling Problem (TFISP) is the problem of determining the minimum number of parallel nonidentical machines, such that a feasible schedule exists for a given set of jobs. In TFISP, each job must belong to a specific job class and must be carried out in a prespecified time interval. The problem is complicated by the restrictions that (1) each machine can handle only one job at a time, (2) each machine can handle only jobs from a subset of the job classes, and (3) preemption is not allowed. In this paper we discuss the occurrence of TFISP in practice, we analyze the computational complexity of TFISP, and we present exact and approximation algorithms for solving TFISP. The paper concludes with a computational study.

Suggested Citation

  • Leo G. Kroon & Marc Salomon & Luk N. Van Wassenhove, 1997. "Exact and Approximation Algorithms for the Tactical Fixed Interval Scheduling Problem," Operations Research, INFORMS, vol. 45(4), pages 624-638, August.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:4:p:624-638
    DOI: 10.1287/opre.45.4.624
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    Cited by:

    1. Lin, Shih-Wei & Ying, Kuo-Ching, 2014. "Minimizing shifts for personnel task scheduling problems: A three-phase algorithm," European Journal of Operational Research, Elsevier, vol. 237(1), pages 323-334.
    2. 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.
    3. Siwate Rojanasoonthon & Jonathan Bard, 2005. "A GRASP for Parallel Machine Scheduling with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 32-51, February.
    4. Brucker, Peter & Qu, Rong & Burke, Edmund, 2011. "Personnel scheduling: Models and complexity," European Journal of Operational Research, Elsevier, vol. 210(3), pages 467-473, May.
    5. Borgonjon, Tessa & Maenhout, Broos, 2022. "An exact approach for the personnel task rescheduling problem with task retiming," European Journal of Operational Research, Elsevier, vol. 296(2), pages 465-484.
    6. 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.
    7. Finke, Gerd & Lemaire, Pierre & Proth, Jean-Marie & Queyranne, Maurice, 2009. "Minimizing the number of machines for minimum length schedules," European Journal of Operational Research, Elsevier, vol. 199(3), pages 702-705, December.
    8. 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.
    9. Yim, Seho & Hong, Sung-Pil & Park, Myoung-Ju & Chung, Yerim, 2022. "Inverse interval scheduling via reduction on a single machine," European Journal of Operational Research, Elsevier, vol. 303(2), pages 541-549.
    10. Kovalyov, Mikhail Y. & Ng, C.T. & Cheng, T.C. Edwin, 2007. "Fixed interval scheduling: Models, applications, computational complexity and algorithms," European Journal of Operational Research, Elsevier, vol. 178(2), pages 331-342, April.
    11. 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.
    12. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
    13. Kravchenko, Svetlana A. & Werner, Frank, 2009. "Minimizing the number of machines for scheduling jobs with equal processing times," European Journal of Operational Research, Elsevier, vol. 199(2), pages 595-600, December.
    14. Martin Branda & Štěpán Hájek, 2017. "Flow-based formulations for operational fixed interval scheduling problems with random delays," Computational Management Science, Springer, vol. 14(1), pages 161-177, January.

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