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Scheduling parallel dedicated machines with the speeding‐up resource

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  • Hans Kellerer
  • Vitaly A. Strusevich

Abstract

We consider a problem of scheduling jobs on m parallel machines. The machines are dedicated, i.e., for each job the processing machine is known in advance. We mainly concentrate on the model in which at any time there is one unit of an additional resource. Any job may be assigned the resource and this reduces its processing time. A job that is given the resource uses it at each time of its processing. No two jobs are allowed to use the resource simultaneously. The objective is to minimize the makespan. We prove that the two‐machine problem is NP‐hard in the ordinary sense, describe a pseudopolynomial dynamic programming algorithm and convert it into an FPTAS. For the problem with an arbitrary number of machines we present an algorithm with a worst‐case ratio close to 3/2, and close to 3, if a job can be given several units of the resource. For the problem with a fixed number of machines we give a PTAS. Virtually all algorithms rely on a certain variant of the linear knapsack problem (maximization, minimization, multiple‐choice, bicriteria). © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

Suggested Citation

  • Hans Kellerer & Vitaly A. Strusevich, 2008. "Scheduling parallel dedicated machines with the speeding‐up resource," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(5), pages 377-389, August.
    • Handle: RePEc:wly:navres:v:55:y:2008:i:5:p:377-389
    DOI: 10.1002/nav.20292
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    References listed on IDEAS

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    1. Kellerer, H. & Strusevich, V. A., 2003. "Scheduling parallel dedicated machines under a single non-shared resource," European Journal of Operational Research, Elsevier, vol. 147(2), pages 345-364, June.
    2. Shabtay, Dvir & Kaspi, Moshe, 2006. "Parallel machine scheduling with a convex resource consumption function," European Journal of Operational Research, Elsevier, vol. 173(1), pages 92-107, August.
    3. Janiak, Adam & Kovalyov, Mikhail Y., 1996. "Single machine scheduling subject to deadlines and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 94(2), pages 284-291, October.
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    2. Fang, Kan & Wang, Shijin & Pinedo, Michael L. & Chen, Lin & Chu, Feng, 2021. "A combinatorial Benders decomposition algorithm for parallel machine scheduling with working-time restrictions," European Journal of Operational Research, Elsevier, vol. 291(1), pages 128-146.

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