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A new approximation algorithm for unrelated parallel machine scheduling with release dates

Author

Listed:
  • Zhi Pei

    (Zhejiang University of Technology)

  • Mingzhong Wan

    (Zhejiang University of Technology
    Northern Illinois University)

  • Ziteng Wang

    (Northern Illinois University)

Abstract

In the current study, an unrelated parallel machine scheduling problem with release dates is considered, which is to obtain a job assignment with minimal sum of weighted completion times. Although this problem is NP-hard in the strong sense, which renders the optimality seeking a formidable task within polynomial time, a 4-approximation algorithm based on the constant worst-case bound is devised and proved in comparison with the existing 16/3-approximation (Hall et al. in Math Oper Res 22(3):513–544, 1997). In the newly proposed algorithm, the original scheduling problem is divided into several sub-problems based on release dates. For each sub-problem, a convex quadratic integer programming model is constructed in accordance with the specific problem structure. Then a semi-definite programming approach is implemented to produce a lower bound via the semi-definite relaxation of each sub-problem. Furthermore, by considering the binary constraint, a branch and bound based method and a local search strategy are applied separately to locate the optimal solution of each sub-problem. Then the solution of the original scheduling problem is derived by integrating the outcomes of the sub-problems via the proposed approximation algorithm. In the numerical analysis, it is discovered that the proposed methods could always obtain a scheduling result within $$1\%$$1% of the optimal solution. And an asymptotic trend could be observed where the quality of solutions improves even further as the scale of the scheduling problem increases.

Suggested Citation

  • Zhi Pei & Mingzhong Wan & Ziteng Wang, 2020. "A new approximation algorithm for unrelated parallel machine scheduling with release dates," Annals of Operations Research, Springer, vol. 285(1), pages 397-425, February.
    • Handle: RePEc:spr:annopr:v:285:y:2020:i:1:d:10.1007_s10479-019-03346-4
    DOI: 10.1007/s10479-019-03346-4
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    References listed on IDEAS

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