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Preemptive parallel‐machine scheduling with a common server to minimize makespan

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  • T.C.E. Cheng
  • Svetlana A. Kravchenko
  • Bertrand M.T. Lin

Abstract

We consider parallel‐machine scheduling with a common server and job preemption to minimize the makespan. While the non‐preemptive version of the problem is strongly NP‐hard, the complexity status of the preemptive version has remained open. We show that the preemptive version is NP‐hard even if there is a fixed number of machines. We give a pseudo‐polynomial time algorithm to solve the case with two machines. We show that the case with an arbitrary number of machines is unary NP‐hard, analyze the performance ratios of some natural heuristic algorithms, and present several solvable special cases. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 388–398, 2017

Suggested Citation

  • T.C.E. Cheng & Svetlana A. Kravchenko & Bertrand M.T. Lin, 2017. "Preemptive parallel‐machine scheduling with a common server to minimize makespan," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(5), pages 388-398, August.
    • Handle: RePEc:wly:navres:v:64:y:2017:i:5:p:388-398
    DOI: 10.1002/nav.21762
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    References listed on IDEAS

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    1. W. A. Horn, 1974. "Some simple scheduling algorithms," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 21(1), pages 177-185, March.
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    Cited by:

    1. T.C.E. Cheng & Svetlana A. Kravchenko & Bertrand M. T. Lin, 2019. "Server scheduling on parallel dedicated machines with fixed job sequences," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(4), pages 321-332, June.
    2. Wieslaw Kubiak & Yanling Feng & Guo Li & Suresh P. Sethi & Chelliah Sriskandarajah, 2020. "Efficient algorithms for flexible job shop scheduling with parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(4), pages 272-288, June.
    3. Abdelhak Elidrissi & Rachid Benmansour & Nicolas Zufferey & Mohammed Benbrahim & David Duvivier, 2024. "Minimization of maximum lateness on parallel machines with a single server and job release dates," 4OR, Springer, vol. 22(3), pages 351-385, September.

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