Approximate algorithms for unrelated machine scheduling to minimize makespan

Xianzhao  Zhang; Dachuan  Xu; Donglei  Du; Cuixia  Miao

doi:10.3934/jimo.2016.12.771

Article Contents

2016, Volume 12, Issue 2: 771-779. Doi: 10.3934/jimo.2016.12.771

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Approximate algorithms for unrelated machine scheduling to minimize makespan

1.
School of Science, Linyi University, Linyi 276005
2.
Department of Information and Operations Research, Beijing University of Technology, Beijing 100124
3.
Faculty of Business Administration, University of New Brunswick, Fredericton, NB, E3B 5A3
4.
School of Mathematical Sciences, Qufu Normal University, Qufu 273165

Received: June 30, 2014

Revised: February 28, 2015

Published: March 2016

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Abstract

We study two unrelated machine scheduling problems with machine dependent release dates to minimize the makespan. For the case with fixed processing time where processing job $j$ on machine $i$ requires time $p_{ij}$ and incurs a cost of $c_{ij}$, we derive a $2$-approximation algorithm. For the problem with variable processing times where the cost increases linearly as the processing time decreases, we propose a $(2+\epsilon)$-approximation algorithm.

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Mathematics Subject Classification: Primary: 90C27, 90B35; Secondary: 68W25, 68W40.

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