Short Communication: Fully polynomial time approximation scheme for the weighted flow-time minimization on a single machine with a fixed non-availability interval

Authors:
Imed Kacem;A. Ridha Mahjoub
Affiliations:
Université de Technologie de Troyes, ICD, LOSI, CNRS 2848, France;Université Paris-Dauphine, LAMSADE, CNRS 7024, France
Venue:
Computers and Industrial Engineering
Year:
2009

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Abstract

In a recent paper [Theoretical Computer Science 363, 257-265], He, Zhong and Gu considered the non-resumable case of the scheduling problem with a fixed non-availability interval under the non-resumable scenario. They proposed a polynomial time approximation scheme (PTAS) to minimize the total completion time. In this paper, we propose a fully polynomial-time approximation scheme to minimize the total weighted completion time. The FPTAS has O(n^2/@e^2) time complexity, where n is the number of jobs and @e is the required error bound. The proposed FPTAS outperforms all the previous approximation algorithms designed for this problem and its running time is strongly polynomial.