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Preemptive Scheduling of Independent Jobs with Release and Due Times on Open, Flow and Job Shops

Author

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  • Yookun Cho

    (University of Minnesota, Minneapolis, Minnesota)

  • Sartaj Sahni

    (University of Minnesota, Minneapolis, Minnesota)

Abstract

We study the problem of obtaining feasible preemptive schedules for independent jobs. It is assumed that each job has associated with it a release and due time. No job can begin before its release time. All jobs must be completed by their respective due times. It is shown that determining the existence of feasible preemptive schedules for two processor flow and job shops is NP -hard in the strong sense even when all jobs have the same due time. A linear programming formulation for the open shop problem is obtained. Also, a fast polynomial time algorithm is obtained for a restricted class of open shop problems.

Suggested Citation

  • Yookun Cho & Sartaj Sahni, 1981. "Preemptive Scheduling of Independent Jobs with Release and Due Times on Open, Flow and Job Shops," Operations Research, INFORMS, vol. 29(3), pages 511-522, June.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:3:p:511-522
    DOI: 10.1287/opre.29.3.511
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    Cited by:

    1. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    2. M.A. Kubzin & V.A. Strusevich & J. Breit & G. Schmidt, 2006. "Polynomial‐time approximation schemes for two‐machine open shop scheduling with nonavailability constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(1), pages 16-23, February.
    3. 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.
    4. 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.
    5. Valls, Vicente & Angeles Perez, M. & Sacramento Quintanilla, M., 1998. "A tabu search approach to machine scheduling," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 277-300, April.
    6. Tzafestas, Spyros & Triantafyllakis, Alekos, 1993. "Deterministic scheduling in computing and manufacturing systems: a survey of models and algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(5), pages 397-434.
    7. Shakhlevich, Natalia V. & Sotskov, Yuri N. & Werner, Frank, 2000. "Complexity of mixed shop scheduling problems: A survey," European Journal of Operational Research, Elsevier, vol. 120(2), pages 343-351, January.
    8. Lang, N.A. & Moonen, J.M. & Srour, F.J. & Zuidwijk, R.A., 2008. "Multi Agent Systems in Logistics: A Literature and State-of-the-art Review," ERIM Report Series Research in Management ERS-2008-043-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    9. Cheng, Jinliang & Steiner, George & Stephenson, Paul, 2001. "A computational study with a new algorithm for the three-machine permutation flow-shop problem with release times," European Journal of Operational Research, Elsevier, vol. 130(3), pages 559-575, May.
    10. Blazewicz, Jacek & Domschke, Wolfgang & Pesch, Erwin, 1996. "The job shop scheduling problem: Conventional and new solution techniques," European Journal of Operational Research, Elsevier, vol. 93(1), pages 1-33, August.
    11. Timkovsky, Vadim G., 2003. "Identical parallel machines vs. unit-time shops and preemptions vs. chains in scheduling complexity," European Journal of Operational Research, Elsevier, vol. 149(2), pages 355-376, September.
    12. Dvir Shabtay & Moshe Kaspi, 2006. "Minimizing the makespan in open‐shop scheduling problems with a convex resource consumption function," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(3), pages 204-216, April.
    13. George Vairaktarakis & Sartaj Sahni, 1995. "Dual criteria preemptive open‐shop problems with minimum makespan," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(1), pages 103-121, February.
    14. Matta, Marie E. & Elmaghraby, Salah E., 2010. "Polynomial time algorithms for two special classes of the proportionate multiprocessor open shop," European Journal of Operational Research, Elsevier, vol. 201(3), pages 720-728, March.
    15. Liaw, Ching-Fang, 2005. "Scheduling preemptive open shops to minimize total tardiness," European Journal of Operational Research, Elsevier, vol. 162(1), pages 173-183, April.

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