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Polynomial‐time approximation schemes for two‐machine open shop scheduling with nonavailability constraints

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  • M.A. Kubzin
  • V.A. Strusevich
  • J. Breit
  • G. Schmidt

Abstract

This paper addresses a two‐machine open shop scheduling problem, in which the machines are not continuously available for processing. The processing of an operation affected by a non‐availability interval can be interrupted and resumed later. The objective is to minimize the makespan. We present two polynomial‐time approximation schemes, one of which handles the problem with one non‐availability interval on each machine and the other for the problem with several non‐availability intervals on one of the machines. Problems with a more general structure of the non‐availability intervals are not approximable in polynomial time within a constant factor, unless $\cal{P = NP}$. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:53:y:2006:i:1:p:16-23
    DOI: 10.1002/nav.20122
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    References listed on IDEAS

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    1. Schmidt, Gunter, 2000. "Scheduling with limited machine availability," European Journal of Operational Research, Elsevier, vol. 121(1), pages 1-15, February.
    2. Shakhlevich, N. V. & Strusevich, V. A., 1993. "Two machine open shop scheduling problem to minimize an arbitrary machine usage regular penalty function," European Journal of Operational Research, Elsevier, vol. 70(3), pages 391-404, November.
    3. Bo Chen & Vitaly A. Strusevich, 1993. "Approximation Algorithms for Three-Machine Open Shop Scheduling," INFORMS Journal on Computing, INFORMS, vol. 5(3), pages 321-326, August.
    4. 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.
    5. 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.
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    Cited by:

    1. Mosheiov, Gur & Sarig, Assaf & Strusevich, Vitaly A & Mosheiff, Jonathan, 2018. "Two-machine flow shop and open shop scheduling problems with a single maintenance window," European Journal of Operational Research, Elsevier, vol. 271(2), pages 388-400.
    2. Yuan Yuan & Yan Lan & Ning Ding & Xin Han, 2022. "A PTAS for non-resumable open shop scheduling with an availability constraint," Journal of Combinatorial Optimization, Springer, vol. 43(2), pages 350-362, March.
    3. 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.

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