Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem

Abstract

We study the n–job two–parallel machines scheduling problem with the aim of minimising the total flow–time. In this problem, instead of allowing both machines to be continuously available as it is often assumed in the literature, we consider that one of the machines is available for a specified period of time after which it can no longer process any job. On the basis of the modification of an exact algorithm execution, we establish the existence of a strongly Fully Polynomial Time Approximation Scheme (FPTAS) for the above–mentioned problem.