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

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 machi...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 8; no. 1; p. 133
Main Authors: Liu, Xiaofei, Li, Weidong
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.01.2020
Subjects:
Algorithms
Approximation
approximation algorithm
Combinatorial analysis
Design
Fines & penalties
Job shops
Mathematical analysis
Polynomials
Rejection
Release dates
Scheduling
submodular rejection penalty
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math8010133