Approximation algorithm for the parallel-machine scheduling problem with release dates and submodular rejection penalties |
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Authors: | Zheng Hongye Gao Suogang Liu Wen Wu Weili Du Ding-Zhu Hou Bo |
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Institution: | 1.School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, People’s Republic of China ;2.Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75080, USA ; |
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Abstract: | In this paper, we consider the parallel-machine scheduling problem with release dates and submodular rejection penalties. In this problem, we are given m identical parallel machines and n jobs. Each job has a processing time and a release date. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on one of the m identical parallel machines. The objective is to minimize the sum of the makespan of the accepted jobs and the rejection penalty of the rejected jobs which is determined by a submodular function. Our main work is to design a 2-approximation algorithm based on the primal-dual framework. |
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