Note: Fully polynomial time approximation scheme for the total weighted tardiness minimization with a common due date

Authors:
Imed Kacem
Affiliations:
Laboratoire d'Informatique Théorique et Appliquée (LITA), Université Paul Verlaine Metz (UPVM), France
Venue:
Discrete Applied Mathematics
Year:
2010

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Note: A note on "Fully polynomial time approximation scheme for the total weighted tardiness minimization with a common due date"

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Abstract

This paper deals with the total weighted tardiness minimization with a common due date on a single machine. The best previous approximation algorithm for this problem was recently presented in [H. Kellerer, V.A. Strusevich, A fully polynomial approximation scheme for the single machine weighted total tardiness problem with a common due date, Theoretical Computer Science 369 (2006) 230-238] by Kellerer and Strusevich. They proposed a fully polynomial time approximation scheme (FPTAS) of O((n^6logW)/@e^3) time complexity (W is the sum of weights, n is the number of jobs and @e is the error bound). For this problem, we propose a new approach to obtain a more effective FPTAS of O(n^2/@e) time complexity. Moreover, a more effective and simpler dynamic programming algorithm is designed.