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Parallel machines scheduling with deteriorating jobs and availability constraints

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Abstract

We consider parallel machines scheduling problem in which the actual processing time of the job is a proportional function of its starting time and each machine is not available in a specified time period. We consider the non-resumable case. The objective is to minimize the weighted sum of completion times. We show that the general case of the problem is inapproximable unless P = NP and present a pseudo-polynomial dynamic programming algorithm. We also present a fully polynomial-time approximation scheme for the special case of the problem where only one machine is not available in a specified time period.

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Acknowledgments

The authors wish to thank two anonymous referees for their constructive comments and suggestions that improved an early version of this paper.

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Authors and Affiliations

  1. School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, 110034, Liaoning, People’s Republic of China

    Chuanli Zhao & Hengyong Tang

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  1. Chuanli Zhao
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  2. Hengyong Tang
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Correspondence to Chuanli Zhao.

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Zhao, C., Tang, H. Parallel machines scheduling with deteriorating jobs and availability constraints. Japan J. Indust. Appl. Math. 31, 501–512 (2014). https://doi.org/10.1007/s13160-014-0150-8

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  • DOI: https://doi.org/10.1007/s13160-014-0150-8

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