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Approximation Algorithm for the Single Machine Scheduling Problem with Release Dates and Submodular Rejection Penalty

by Xiaofei Liu 1 and Weidong Li 2,*
1
School of Electronic Engineering and Computer Science, Peking University, Beijing 100871, China
2
School of Mathematics and Statistics, Yunnan University, Kunming 650504, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 133; https://doi.org/10.3390/math8010133
Received: 11 November 2019 / Revised: 5 January 2020 / Accepted: 10 January 2020 / Published: 16 January 2020
In this paper, we consider the single machine scheduling problem with release dates and nonmonotone submodular rejection penalty. We are given a single machine and multiple jobs with probably different release dates and processing times. For each job, it is either accepted and processed on the machine or rejected. 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 nonmonotone submodular function. We design a combinatorial algorithm based on the primal-dual framework to deal with the problem, and study its property under two cases. For the general case where the release dates can be different, the proposed algorithm have an approximation ratio of 2. When all the jobs release at the same time, the proposed algorithm becomes a polynomial-time exact algorithm. View Full-Text
Keywords: scheduling; submodular rejection penalty; approximation algorithm scheduling; submodular rejection penalty; approximation algorithm
MDPI and ACS Style

Liu, X.; Li, W. Approximation Algorithm for the Single Machine Scheduling Problem with Release Dates and Submodular Rejection Penalty. Mathematics 2020, 8, 133.

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