Résumé en anglais

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(n2/ε2) time complexity, where n is the number of jobs and ε 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.