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Polynomial‐time approximation scheme for concurrent open shop scheduling with a fixed number of machines to minimize the total weighted completion time

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  • T.C. Edwin Cheng
  • Qingqin Nong
  • Chi To Ng

Abstract

In this article, we consider the concurrent open shop scheduling problem to minimize the total weighted completion time. When the number of machines is arbitrary, the problem has been shown to be inapproximable within a factor of 4/3 ‐ ε for any ε > 0 if the unique games conjecture is true in the literature. We propose a polynomial time approximation scheme for the problem under the restriction that the number of machines is fixed. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

Suggested Citation

  • T.C. Edwin Cheng & Qingqin Nong & Chi To Ng, 2011. "Polynomial‐time approximation scheme for concurrent open shop scheduling with a fixed number of machines to minimize the total weighted completion time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(8), pages 763-770, December.
    • Handle: RePEc:wly:navres:v:58:y:2011:i:8:p:763-770
    DOI: 10.1002/nav.20484
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    1. Chang Sup Sung & Sang Hum Yoon, 1998. "Minimizing total weighted completion time at a pre-assembly stage composed of two feeding machines," International Journal of Production Economics, Elsevier, vol. 54(3), pages 247-255, May.
    2. Leung, Joseph Y.-T. & Li, Haibing & Pinedo, Michael, 2006. "Scheduling orders for multiple product types with due date related objectives," European Journal of Operational Research, Elsevier, vol. 168(2), pages 370-389, January.
    3. Wagneur, E. & Sriskandarajah, C., 1993. "Openshops with jobs overlap," European Journal of Operational Research, Elsevier, vol. 71(3), pages 366-378, December.
    4. Reza Ahmadi & Uttarayan Bagchi & Thomas A. Roemer, 2005. "Coordinated scheduling of customer orders for quick response," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 493-512, September.
    5. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
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