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Scheduling Jobs on Several Machines with the Job Splitting Property

Author

Listed:
  • Paolo Serafini

    (University of Udine, Italy)

Abstract

This scheduling model is derived from the real problem of scheduling looms in a textile industry. Jobs may be independently split over several specified machines, and preemption is allowed. Deadlines are specified for each job, and jobs are assumed to be available. It is shown that minimizing maximum weighted tardiness can be done in polynomial time. The case of uniform machines (as in the considered application) can be modeled as a network flow, and minimization of maximum tardiness can be done in strongly polynomial time. The case of unrelated machines can be solved either by generalized flow techniques or by Linear Programming. Attention is also focused on the problem of finding so-called Unordered Lexico Optima, in order to schedule nonbinding jobs as early as possible.

Suggested Citation

  • Paolo Serafini, 1996. "Scheduling Jobs on Several Machines with the Job Splitting Property," Operations Research, INFORMS, vol. 44(4), pages 617-628, August.
    • Handle: RePEc:inm:oropre:v:44:y:1996:i:4:p:617-628
    DOI: 10.1287/opre.44.4.617
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    Cited by:

    1. Davila-Pena, Laura & Borm, Peter & Garcia-Jurado, Ignacio & Schouten, Jop, 2023. "An Allocation Rule for Graph Machine Scheduling Problems," Other publications TiSEM 17013f33-1d65-4294-802c-b, Tilburg University, School of Economics and Management.
    2. S. Thomas McCormick, 1999. "Fast Algorithms for Parametric Scheduling Come From Extensions to Parametric Maximum Flow," Operations Research, INFORMS, vol. 47(5), pages 744-756, October.
    3. Davila-Pena, Laura & Borm, Peter & Garcia-Jurado, Ignacio & Schouten, Jop, 2023. "An Allocation Rule for Graph Machine Scheduling Problems," Discussion Paper 2023-009, Tilburg University, Center for Economic Research.
    4. Enrico Bartolini & Mauro Dell’Amico & Manuel Iori, 2017. "Scheduling cleaning activities on trains by minimizing idle times," Journal of Scheduling, Springer, vol. 20(5), pages 493-506, October.
    5. Hongmin Li & Woonghee T. Huh & Matheus C. Sampaio & Naiping Keng, 2021. "Planning Production and Equipment Qualification under High Process Flexibility," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3369-3390, October.
    6. Sedeño-Noda, A. & de Pablo, D. Alcaide López & González-Martín, C., 2009. "A network flow-based method to solve performance cost and makespan open-shop scheduling problems with time-windows," European Journal of Operational Research, Elsevier, vol. 196(1), pages 140-154, July.
    7. Jun-Ho Lee & Hoon Jang, 2019. "Uniform Parallel Machine Scheduling with Dedicated Machines, Job Splitting and Setup Resources," Sustainability, MDPI, vol. 11(24), pages 1-23, December.
    8. Sedeno-Noda, A. & Alcaide, D. & Gonzalez-Martin, C., 2006. "Network flow approaches to pre-emptive open-shop scheduling problems with time-windows," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1501-1518, November.
    9. Qian, Fubin & Strusevich, Vitaly & Gribkovskaia, Irina & Halskau, Øyvind, 2015. "Minimization of passenger takeoff and landing risk in offshore helicopter transportation: Models, approaches and analysis," Omega, Elsevier, vol. 51(C), pages 93-106.
    10. Talla Nobibon, Fabrice & Leus, Roel & Nip, Kameng & Wang, Zhenbo, 2015. "Resource loading with time windows," European Journal of Operational Research, Elsevier, vol. 244(2), pages 404-416.
    11. Öncü Hazır & Safia Kedad-Sidhoum, 2014. "Batch sizing and just-in-time scheduling with common due date," Annals of Operations Research, Springer, vol. 213(1), pages 187-202, February.
    12. Freddy C. Chua & Bernardo A. Huberman, 2016. "Partitioning uncertain workloads," Netnomics, Springer, vol. 17(3), pages 233-253, November.
    13. Jun-Ho Lee & Hyun-Jung Kim, 2021. "A heuristic algorithm for identical parallel machine scheduling: splitting jobs, sequence-dependent setup times, and limited setup operators," Flexible Services and Manufacturing Journal, Springer, vol. 33(4), pages 992-1026, December.
    14. S. Knust & N. V. Shakhlevich & S. Waldherr & C. Weiß, 2019. "Shop scheduling problems with pliable jobs," Journal of Scheduling, Springer, vol. 22(6), pages 635-661, December.

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