research-article

Related machine scheduling with machine speeds satisfying linear constraints

Authors:

Zhenbo WangAuthors Info & Claims

Journal of Combinatorial Optimization, Volume 44, Issue 3

Pages 1724 - 1740

https://doi.org/10.1007/s10878-020-00523-1

Published: 01 October 2022 Publication History

Abstract

We propose a related machine scheduling problem in which the processing times of jobs are given and known, but the speeds of machines are variables and must satisfy a system of linear constraints. 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 polynomial time algorithms for two special cases. If the number of constraints is more than one and the number of machines is a fixed constant, then we give a

(2 + ϵ)

-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 polynomial time approximation scheme when the number of distinct machine speeds is a fixed constant.

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Cited By

Nip KXie P(2024)Computational complexity and algorithms for two scheduling problems under linear constraintsJournal of Combinatorial Optimization10.1007/s10878-024-01122-047:4Online publication date: 14-Apr-2024
https://dl.acm.org/doi/10.1007/s10878-024-01122-0
Nip K(2023)On the NP-Hardness of Two Scheduling Problems Under Linear ConstraintsFrontiers of Algorithmics10.1007/978-3-031-39344-0_5(58-70)Online publication date: 14-Aug-2023
https://dl.acm.org/doi/10.1007/978-3-031-39344-0_5

Index Terms

Related machine scheduling with machine speeds satisfying linear constraints
1. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Scheduling algorithms
    2. Online algorithms
      1. Online learning algorithms
        Scheduling algorithms
  2. Theory and algorithms for application domains
    1. Machine learning theory
      1. Reinforcement learning
        Sequential decision making

Index terms have been assigned to the content through auto-classification.

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cover image Journal of Combinatorial Optimization

Journal of Combinatorial Optimization Volume 44, Issue 3

Oct 2022

790 pages

ISSN:1382-6905

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© Springer Science+Business Media, LLC, part of Springer Nature 2020.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 October 2022

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Cited By

Nip KXie P(2024)Computational complexity and algorithms for two scheduling problems under linear constraintsJournal of Combinatorial Optimization10.1007/s10878-024-01122-047:4Online publication date: 14-Apr-2024
https://dl.acm.org/doi/10.1007/s10878-024-01122-0
Nip K(2023)On the NP-Hardness of Two Scheduling Problems Under Linear ConstraintsFrontiers of Algorithmics10.1007/978-3-031-39344-0_5(58-70)Online publication date: 14-Aug-2023
https://dl.acm.org/doi/10.1007/978-3-031-39344-0_5

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