A Note on a Fully Polynomial-Time Approximation Scheme for Minimizing Makespan of Deteriorating Jobs

In (1998), Kovalyov and Kubiak studied the problem of scheduling n deteriorating jobs on a single machine to minimize makespan. They presented a fully polynomial-time approximation scheme which is based on a dynamic programming. Unfortunately, their dynamic programming is incorrect. So the fully pol...

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Published in:Mathematical problems in engineering Vol. 2013; no. 2013; pp. 1 - 7
Main Author: Wan, Long
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2013
John Wiley & Sons, Inc
Subjects:
Approximation
Construction
Deterioration
Dynamic programming
Job shops
Mathematical analysis
Mathematical problems
Polynomials
Production scheduling
Scheduling
ISSN:1024-123X, 1563-5147
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Abstract In (1998), Kovalyov and Kubiak studied the problem of scheduling n deteriorating jobs on a single machine to minimize makespan. They presented a fully polynomial-time approximation scheme which is based on a dynamic programming. Unfortunately, their dynamic programming is incorrect. So the fully polynomial-time approximation scheme is also invalid. In this paper, we construct an instance to show how their dynamic programming does not work and provide a correct dynamic programming, based on which a new fully polynomial-time approximation scheme is derived.
AbstractList In (1998), Kovalyov and Kubiak studied the problem of scheduling n deteriorating jobs on a single machine to minimize makespan. They presented a fully polynomial-time approximation scheme which is based on a dynamic programming. Unfortunately, their dynamic programming is incorrect. So the fully polynomial-time approximation scheme is also invalid. In this paper, we construct an instance to show how their dynamic programming does not work and provide a correct dynamic programming, based on which a new fully polynomial-time approximation scheme is derived.
Author Wan, Long
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Cites_doi 10.1002/nav.3800030106
10.1016/j.tcs.2006.06.006
10.1016/0377-2217(90)90089-T
10.1016/S0020-0190(03)00262-X
10.1016/j.tcs.2010.09.017
10.1142/S0217595912500194
10.1016/0166-218X(96)00102-3
10.1016/j.tcs.2009.04.018
ContentType Journal Article
Copyright Copyright © 2013 Long Wan.
Copyright © 2013 Long Wan.; This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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SubjectTerms Approximation
Construction
Deterioration
Dynamic programming
Job shops
Mathematical analysis
Mathematical problems
Polynomials
Production scheduling
Scheduling
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