Single machine batch scheduling with two non-disjoint agents and splitable jobs

We investigate the scheduling problem on a single bounded parallel-batch machine where jobs belong to two non-disjoint agents (called agent A and agent B) and are of equal length but different size. Each job’s size can be arbitrarily split into two parts and processed in the consecutive batches. It...

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Published in:	Journal of combinatorial optimization Vol. 40; no. 3; pp. 774 - 795
Main Authors:	Geng, Zhichao, Liu, Jiayu
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.10.2020 Springer Nature B.V
Subjects:	Algorithms Combinatorics Completion time Convex and Discrete Geometry Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Pareto optimum Polynomials Schedules Scheduling Theory of Computation Splitable jobs Polynomial-time algorithm Parallel-batch Pareto optimal
ISSN:	1382-6905, 1573-2886
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Abstract	We investigate the scheduling problem on a single bounded parallel-batch machine where jobs belong to two non-disjoint agents (called agent A and agent B) and are of equal length but different size. Each job’s size can be arbitrarily split into two parts and processed in the consecutive batches. It is permitted to process the jobs from different agents in a common batch. We show that it is unary NP-hard for the problem of minimizing the total weighted completion time of the jobs of agent A subject to the maximum cost of the jobs of agent B being upper bounded by a given threshold. For the case of the jobs of agent A having identical weights, we study the version of Pareto problem, and give a polynomial-time algorithm to generate all Pareto optimal points and a Pareto optimal schedule corresponding to each Pareto optimal point.
AbstractList	We investigate the scheduling problem on a single bounded parallel-batch machine where jobs belong to two non-disjoint agents (called agent A and agent B) and are of equal length but different size. Each job’s size can be arbitrarily split into two parts and processed in the consecutive batches. It is permitted to process the jobs from different agents in a common batch. We show that it is unary NP-hard for the problem of minimizing the total weighted completion time of the jobs of agent A subject to the maximum cost of the jobs of agent B being upper bounded by a given threshold. For the case of the jobs of agent A having identical weights, we study the version of Pareto problem, and give a polynomial-time algorithm to generate all Pareto optimal points and a Pareto optimal schedule corresponding to each Pareto optimal point.
Author	Geng, Zhichao Liu, Jiayu
Author_xml	– sequence: 1 givenname: Zhichao orcidid: 0000-0002-1443-9554 surname: Geng fullname: Geng, Zhichao email: zcgeng@zzu.edu.cn organization: School of Mathematics and Statistics, Zhengzhou University – sequence: 2 givenname: Jiayu surname: Liu fullname: Liu, Jiayu organization: Henan College of Transportation
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SubjectTerms	Algorithms Combinatorics Completion time Convex and Discrete Geometry Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Pareto optimum Polynomials Schedules Scheduling Theory of Computation
Title	Single machine batch scheduling with two non-disjoint agents and splitable jobs
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