Complexity and approximability of scheduling resumable proportionally deteriorating jobs

A set of independent, resumable and proportionally deteriorating jobs is to be executed on a single machine. The machine is not continuously available for processing but the number of non-availability periods, the start time and end time of each period are known in advance. The criterion of schedule...

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Bibliographic Details
Published in:European journal of operational research Vol. 200; no. 1; pp. 305 - 308
Main Authors: Gawiejnowicz, Stanisław, Kononov, Alexander
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 2010
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Algorithms
Approximation
Complexity theory
Deteriorating jobs
Fully polynomial-time approximation scheme
Job shops
Operations research
Production scheduling
Scheduling
Scheduling Deteriorating jobs Complexity theory Fully polynomial-time approximation scheme
Studies
Fully polynomial-time approximation scheme
Scheduling
Complexity theory
Deteriorating jobs
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:A set of independent, resumable and proportionally deteriorating jobs is to be executed on a single machine. The machine is not continuously available for processing but the number of non-availability periods, the start time and end time of each period are known in advance. The criterion of schedule optimality is the maximum completion time. It is proved that the decision version of the problem with a single non-availability period is ordinarily NP -complete. It is also proved that for the problem with a single non-availability period there exists a fully polynomial-time approximation scheme. Finally, it is proved that for the problem with two or more non-availability periods there does not exist a polynomial-time approximation algorithm with a constant worst-case ratio, unless P = NP .
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2008.12.014