An FPTAS for two performance measures for the relocation scheduling problem subject to fixed processing sequences

In this paper we consider a resource-constrained scheduling problem on two parallel dedicated machines with given fixed processing sequences of jobs assigned to each one of the machines. The problem is to determine the starting times of all jobs, subject to the resource constraint, in order to minimize some given performance measure. Lin et al. (J Sched 19(2):153–163, 2016) showed that the problem is NP-hard in the ordinary sense under the performance measures of weighted total tardiness and weighted number of tardy jobs, and questioned the existence of approximation schemes. In this paper we answer their question in the affirmative by designing fully polynomial time approximation schemes.