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

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 image time complexity (image is the sum of weights, image is the number of jobs and image is the error bound). For this problem, we propose a new approach to obtain a more effective FPTAS of image time complexity. Moreover, a more effective and simpler dynamic programming algorithm is designed.