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.
We consider the total weighted completion time minimization for the two-parallel capacitated machines scheduling problem. In this problem, one of the machines can process jobs until a certain time T1 after which it is no longer available. The other machine is continuously available for performing jobs at any time. We prove the existence of a strongly Fully Polynomial Time Approximation Scheme (FPTAS) for the studied problem, which extends the results for the unweighted version (see [I. Kacem, Y. Lanuel and M. Sahnoune, Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem, Int. J. Plann. Sched. 1 (2011) 32–41]). Our FPTAS is based on the simplification of a dynamic programming algorithm. Moreover, we present a set of numerical experiments and we discuss the results.
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