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International Conference on Combinatorial Optimization and Applications

COCOA 2018: Combinatorial Optimization and Applications pp 314–328Cite as

Related Machine Scheduling with Machine Speeds Satisfying Linear Constraints

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11346))

Abstract

We propose a related machine scheduling problem in which the speeds of machines are variables and must satisfy a system of linear constraints, and the processing times of jobs are given and known. The objective is to decide the speeds of machines and minimize the makespan of the schedule among all the feasible choices. The problem is motivated by some practical application scenarios. This problem is strongly NP-hard in general, and we discuss various cases of it. In particular, we obtain a polynomial time algorithm when there is one linear constraint. If the number of constraints is more than one and the number of machines is a fixed constant, then we give a \((2+\epsilon )\)-approximation algorithm. For the case where the number of machines is an input of the problem instance, we propose several approximation algorithms, and obtain a PTAS when the number of distinct machine speeds is a fixed constant.

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Acknowledgments

This work has been supported by NSFC No. 11801589, No. 11771245 and No. 11371216. We also thank Tianning Shi for helpful discussions on this work.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, China

    Siyun Zhang & Zhenbo Wang

  2. School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, China

    Kameng Nip

Authors
  1. Siyun Zhang
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  2. Kameng Nip
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  3. Zhenbo Wang
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Corresponding author

Correspondence to Kameng Nip .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Kennesaw State University, Marietta, GA, USA

    Donghyun Kim

  2. Department of Mathematics and Computer Science, North Carolina Central University, Durham, NC, USA

    R. N. Uma

  3. Department of Computer Science, Georgia State University, Atlanta, GA, USA

    Alexander Zelikovsky

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Zhang, S., Nip, K., Wang, Z. (2018). Related Machine Scheduling with Machine Speeds Satisfying Linear Constraints. In: Kim, D., Uma, R., Zelikovsky, A. (eds) Combinatorial Optimization and Applications. COCOA 2018. Lecture Notes in Computer Science(), vol 11346. Springer, Cham. https://doi.org/10.1007/978-3-030-04651-4_21

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  • DOI: https://doi.org/10.1007/978-3-030-04651-4_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04650-7

  • Online ISBN: 978-3-030-04651-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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