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An approximation algorithm for multi-agent scheduling on two uniform parallel machines

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Abstract

This paper considers a multi-agent scheduling problem, in which each agent has a set of non-preemptive jobs, and all jobs are to be processed on two uniform parallel machines with the objective to minimize the makespan of each agent. Given an instance of the multi-agent scheduling problem, we first devise a measure on the optimal makespan of the single-agent instance for each agent. Then an approximation algorithm is proposed for the multi-agent scheduling problem, in which agents are scheduled in the non-decreasing order of the measure values, and all jobs of each agent are scheduled generally subject to the longest processing time first (LPT) rule. In the obtained schedule, we prove the makespan of the ith completed agent is at most \(i+ \frac{\sqrt{17}-3}{4}\) times its optimal makespan, in which \(\frac{\sqrt{17}-3}{4}\) is the relative error of the LPT rule for the single-agent problem \(Q2||C_{\max }\). Furthermore, an example is introduced to show the tightness of the performance analysis.

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Acknowledgements

The authors thank the referees for reviewing the paper. This work is supported by National Natural Science Foundation of China (Grant Nos. 11201282, 61304209, and 11371137), Innovation Program of Shanghai Municipal Education Commission (Grant No. 14YZ127), Humanities and Social Sciences planning fund of Ministry of Education (Grant No. 17YJAZH024), Pre-research project for young teachers from SUFE, and National project follow-up research project from SUFE.

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Authors and Affiliations

  1. School of Mathematics, Shanghai University of Finance and Economics, Shanghai, China

    Manzhan Gu

  2. Department of Mathematics, East China University of Science and Technology, Shanghai, China

    Xiwen Lu

  3. School of Economics and Management, Shanghai University of Electric Power, Shanghai, China

    Jinwei Gu

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  1. Manzhan Gu
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  2. Xiwen Lu
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  3. Jinwei Gu
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Correspondence to Jinwei Gu.

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Gu, M., Lu, X. & Gu, J. An approximation algorithm for multi-agent scheduling on two uniform parallel machines. Optim Lett 13, 907–933 (2019). https://doi.org/10.1007/s11590-018-1298-y

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  • DOI: https://doi.org/10.1007/s11590-018-1298-y

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