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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Veröffentlicht in:Mathematical problems in engineering Jg. 2013; H. 2013; S. 1 - 7
1. Verfasser: Wan, Long
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cairo, Egypt Hindawi Publishing Corporation 01.01.2013
John Wiley & Sons, Inc
Schlagworte:
Approximation
Construction
Deterioration
Dynamic programming
Job shops
Mathematical analysis
Mathematical problems
Polynomials
Production scheduling
Scheduling
ISSN:1024-123X, 1563-5147
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Zusammenfassung: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.
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ISSN:1024-123X
1563-5147
DOI:10.1155/2013/957494