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Approximate and branch-and-bound algorithms for the parallel machine scheduling problem with a single server

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  • Guo-Sheng Liu
  • Jin-Jin Li
  • Hai-Dong Yang
  • George Q. Huang

Abstract

In this paper, we consider the scheduling problem of minimising the total weighted job completion time when a set of jobs must be processed on m parallel machines with a single server. This problem has various applications to networks, manufacturing, logistics, etc. The shortest weighted processing time (SWPT) sequencing by Hasani et al. is (3−2/m)-approximate for general problem cases and (2−1/m)-approximate for problems subjected to regular job restrictions. At present, these findings are the best-known results available for the worst-case analyses. Furthermore, dominance properties are discussed and several rules for improving a given schedule are given. To solve the problem, a branch-and-bound (B&B) algorithm is developed by integrating SWPT sequencing, a new lower bound, and dominance properties. A number of numerical experiments are illustrated to validate the performance of our algorithms and identify implications for the considered problem.

Suggested Citation

  • Guo-Sheng Liu & Jin-Jin Li & Hai-Dong Yang & George Q. Huang, 2019. "Approximate and branch-and-bound algorithms for the parallel machine scheduling problem with a single server," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(9), pages 1554-1570, September.
    • Handle: RePEc:taf:tjorxx:v:70:y:2019:i:9:p:1554-1570
    DOI: 10.1080/01605682.2018.1500976
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    Cited by:

    1. 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.
    2. Jun-Ho Lee & Hyun-Jung Kim, 2021. "A heuristic algorithm for identical parallel machine scheduling: splitting jobs, sequence-dependent setup times, and limited setup operators," Flexible Services and Manufacturing Journal, Springer, vol. 33(4), pages 992-1026, December.

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