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Server scheduling on parallel dedicated machines with fixed job sequences

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

Abstract

We consider server scheduling on parallel dedicated machines to minimize the makespan. Each job has a loading operation and a processing operation. The loading operation requires a server that serves all the jobs. Each machine has a given set of jobs to process, and the processing sequence is known and fixed. We design a polynomial‐time algorithm to solve the two‐machine case of the problem. When the number of machines is arbitrary, the problem becomes strongly NP‐hard even if all the jobs have the same processing length or all the loading operations require a unit time. We design two heuristic algorithms to treat the case where all the loading times are unit and analyze their performance.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:66:y:2019:i:4:p:321-332
    DOI: 10.1002/nav.21846
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    References listed on IDEAS

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    1. F. Hwang & M. Kovalyov & B. Lin, 2014. "Scheduling for fabrication and assembly in a two-machine flowshop with a fixed job sequence," Annals of Operations Research, Springer, vol. 217(1), pages 263-279, June.
    2. Celia A. Glass & Yakov M. Shafransky & Vitaly A. Strusevich, 2000. "Scheduling for parallel dedicated machines with a single server," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(4), pages 304-328, June.
    3. 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.
    4. Sourd, Francis, 2005. "Optimal timing of a sequence of tasks with general completion costs," European Journal of Operational Research, Elsevier, vol. 165(1), pages 82-96, August.
    5. Y.M. Shafransky & V.A. Strusevich, 1998. "The open shop scheduling problem with a given sequence of jobs on one machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(7), pages 705-731, October.
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    Cited by:

    1. Jesús Isaac Vázquez-Serrano & Leopoldo Eduardo Cárdenas-Barrón & Rodrigo E. Peimbert-García, 2021. "Agent Scheduling in Unrelated Parallel Machines with Sequence- and Agent–Machine–Dependent Setup Time Problem," Mathematics, MDPI, vol. 9(22), pages 1-34, November.

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