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Single machine parallel batch scheduling subject to precedence constraints

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  • T.C.E. Cheng
  • C.T. Ng
  • J.J. Yuan
  • Z.H. Liu

Abstract

We consider the single machine parallel batch scheduling problems to minimize makespan and total completion time, respectively, under precedence relations. The complexities of these two problems are reported as open in the literature. In this paper, we settle these open questions by showing that both problems are strongly NP‐hard, even when the precedence relations are chains. When the processing times of jobs are directly agreeable or inversely agreeable with the precedence relations, there is an O(n2) time algorithm to minimize the makespan. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Suggested Citation

  • T.C.E. Cheng & C.T. Ng & J.J. Yuan & Z.H. Liu, 2004. "Single machine parallel batch scheduling subject to precedence constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(7), pages 949-958, October.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:7:p:949-958
    DOI: 10.1002/nav.20035
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    References listed on IDEAS

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    1. Chung-Yee Lee & Reha Uzsoy & Louis A. Martin-Vega, 1992. "Efficient Algorithms for Scheduling Semiconductor Burn-In Operations," Operations Research, INFORMS, vol. 40(4), pages 764-775, August.
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    Cited by:

    1. M Ozlen & M Azizoğlu, 2011. "Rescheduling unrelated parallel machines with total flow time and total disruption cost criteria," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 152-164, January.
    2. Yuan Gao & Jinjiang Yuan, 2019. "Unbounded parallel-batch scheduling under agreeable release and processing to minimize total weighted number of tardy jobs," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 698-711, October.
    3. Yuan Gao & Jinjiang Yuan & Zhigang Wei, 2019. "Unbounded parallel-batch scheduling with drop-line tasks," Journal of Scheduling, Springer, vol. 22(4), pages 449-463, August.
    4. Evgeny Gafarov & Alexander Lazarev & Frank Werner, 2014. "Approximability results for the resource-constrained project scheduling problem with a single type of resources," Annals of Operations Research, Springer, vol. 213(1), pages 115-130, February.

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