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Minimizing the makespan in open‐shop scheduling problems with a convex resource consumption function

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  • Dvir Shabtay
  • Moshe Kaspi

Abstract

We consider open‐shop scheduling problems where operation‐processing times are a convex decreasing function of a common limited nonrenewable resource. The scheduler's objective is to determine the optimal job sequence on each machine and the optimal resource allocation for each operation in order to minimize the makespan. We prove that this problem is NP‐hard, but for the special case of the two‐machine problem we provide an efficient optimization algorithm. We also provide a fully polynomial approximation scheme for solving the preemptive case. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

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  • Dvir Shabtay & Moshe Kaspi, 2006. "Minimizing the makespan in open‐shop scheduling problems with a convex resource consumption function," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(3), pages 204-216, April.
    • Handle: RePEc:wly:navres:v:53:y:2006:i:3:p:204-216
    DOI: 10.1002/nav.20133
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    Cited by:

    1. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.

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