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《Acta Mathematicae Applicatae Sinica》 2018-03
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Approximation Algorithm on Two Stage Flexible Flow-shop Scheduling with Parallel Machines

ZHANG MINGHUI;HAN XIN;School of Software Technology, Dalian University of Technology;Software Engineering Department, Dalian Neusoft University of Information;School of Software Technology,Dalian University of Technology;  
In this paper we consider a two-stage flow-shop scheduling model which combines flexible flow shop with parallel scheduling. There is only one machine at the first stage and m identical parallel executing machines at the other. Each task needs size_i parallel machines execute simultaneously at the second stage. The objective is to minimize the makespan. This model has been proved to be NP-hard and an approximation algorithm has been proposed as well. In this paper we describe the process of the previous algorithm and point out the limitations of algorithm approximate ratio analysis. Then we propose a 3-approximation algorithm based on parallel scheduling results. Our algorithm discards the constraints of previous 3-approximation algorithm analysis. Lastly we study the two special cases with two parallel machines and three parallel machines in the second stage respectively. We propose two approximation algorithms with 2.5 and 2.67 approximate ratio correspondingly according to list scheduling rules.
【Fund】: 国家自然科学基金(11570160 11701062);; 辽宁省自然科学基金(20170540050);; 大连市高层次人才创新支持计划(2015R095)资助项目
【CateGory Index】: TP301.6
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