A PTAS for non-resumable open shop scheduling with an availability constraint

Shop scheduling problem is one of the most classical problems in combinatorial optimization. In this paper, we study two-machine open shop scheduling problem, provided that one machine is subject to maintenance period which has to be performed in a fixed time interval. The target is to minimize the...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 43; no. 2; pp. 350 - 362
Main Authors: Yuan, Yuan, Lan, Yan, Ding, Ning, Han, Xin
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2022
Springer Nature B.V
Subjects:
Combinatorial analysis
Combinatorics
Convex and Discrete Geometry
Job shops
Maintenance
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Polynomials
Scheduling
Theory of Computation
Open shop scheduling
Machine non-availability
Polynomial time approximation scheme
Approximation algorithm
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary:Shop scheduling problem is one of the most classical problems in combinatorial optimization. In this paper, we study two-machine open shop scheduling problem, provided that one machine is subject to maintenance period which has to be performed in a fixed time interval. The target is to minimize the makespan. This paper considers non-resumable scenario, i.e., if a job which starts before the maintenance period cannot be completed before the maintenance period, then it must be restarted after the interval from scratch. We only discuss the case that the maintenance period is performed on the first machine, while the case of the maintenance period on the second machine is symmetric. We obtain a polynomial time approximation scheme, which is better than the best previous result 4 3 .
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-021-00773-7