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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 957494, 7 pages
http://dx.doi.org/10.1155/2013/957494
Research Article

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

School of Information Technology, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 330013, China

Received 12 June 2013; Accepted 9 August 2013

Academic Editor: Yunqiang Yin

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.

Abstract

In (1998), Kovalyov and Kubiak studied the problem of scheduling 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.