# American Institute of Mathematical Sciences

April  2016, 12(2): 771-779. doi: 10.3934/jimo.2016.12.771

## Approximate algorithms for unrelated machine scheduling to minimize makespan

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

Received  July 2014 Revised  March 2015 Published  June 2015

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.
Citation: Xianzhao Zhang, Dachuan Xu, Donglei Du, Cuixia Miao. Approximate algorithms for unrelated machine scheduling to minimize makespan. Journal of Industrial & Management Optimization, 2016, 12 (2) : 771-779. doi: 10.3934/jimo.2016.12.771
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