Strongly Fully Polynomial Time Approximation Scheme for the Weighted Completion Time Minimization Problem on Two-Parallel Capacitated Machines*

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 Kacem, Lanuel and Sahnoune (2011)). Our FPTAS is based on the simplification of a dynamic programming algorithm.