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An FPTAS for scheduling a two‐machine flowshop with one unavailability interval

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  • C.T. Ng
  • Mikhail Y. Kovalyov

Abstract

We study a deterministic two‐machine flowshop scheduling problem with an assumption that one of the two machines is not available in a specified time period. This period can be due to a breakdown, preventive maintenance, or processing unfinished jobs from a previous planning horizon. The problem is known to be NP‐hard. Pseudopolynomial dynamic programming algorithms and heuristics with worst case error bounds are given in the literature to solve the problem. They are different for the cases when the unavailability interval is for the first or second machine. The existence of a fully polynomial time approximation scheme (FPTAS) was formulated as an open conjecture in the literature. In this paper, we show that the two cases of the problem under study are equivalent to similar partition type problems. Then we derive a generic FPTAS for the latter problems with O(n5/ε4) time complexity. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Suggested Citation

  • C.T. Ng & Mikhail Y. Kovalyov, 2004. "An FPTAS for scheduling a two‐machine flowshop with one unavailability interval," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(3), pages 307-315, April.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:3:p:307-315
    DOI: 10.1002/nav.10107
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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. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
    3. Blazewicz, Jacek & Breit, Joachim & Formanowicz, Piotr & Kubiak, Wieslaw & Schmidt, Günter, 2001. "Heuristic algorithms for the two-machine flowshop with limited machine availability," Omega, Elsevier, vol. 29(6), pages 599-608, December.
    4. Chung-Yee Lee & Lei Lei & Michael Pinedo, 1997. "Current trends in deterministic scheduling," Annals of Operations Research, Springer, vol. 70(0), pages 1-41, April.
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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.

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