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Improved approximation algorithms for the combination problem of parallel machine scheduling and path

Author

Listed:
  • Li Guan

    (Yunnan University)

  • Jianping Li

    (Yunnan University)

  • Weidong Li

    (Yunnan University)

  • Junran Lichen

    (Yunnan University)

Abstract

In this paper, we study a combination problem of parallel machine scheduling and the s–t path problem, which is to find a s–t path $$P_{st}$$ P st of the given directed graph, and to schedule the jobs corresponding to the arcs of the path $$P_{st}$$ P st on m parallel machines, such that the makespan is minimized. It has been proved that this problem is NP-hard and admits 2-approximation algorithm. We present a polynomial-time algorithm with approximation ratio 1.5. By modifying the dynamic programming method for the restricted shortest path problem, we also give a polynomial time approximation scheme.

Suggested Citation

  • Li Guan & Jianping Li & Weidong Li & Junran Lichen, 2019. "Improved approximation algorithms for the combination problem of parallel machine scheduling and path," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 689-697, October.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:3:d:10.1007_s10878-019-00406-0
    DOI: 10.1007/s10878-019-00406-0
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    References listed on IDEAS

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    1. Arthur Warburton, 1987. "Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems," Operations Research, INFORMS, vol. 35(1), pages 70-79, February.
    2. Refael Hassin, 1992. "Approximation Schemes for the Restricted Shortest Path Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 36-42, February.
    3. Kameng Nip & Zhenbo Wang & Fabrice Talla Nobibon & Roel Leus, 2015. "A combination of flow shop scheduling and the shortest path problem," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 36-52, January.
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    Cited by:

    1. Zohreh Hosseini Nodeh & Ali Babapour Azar & Rashed Khanjani Shiraz & Salman Khodayifar & Panos M. Pardalos, 2020. "Joint chance constrained shortest path problem with Copula theory," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 110-140, July.

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