An FPTAS for scheduling jobs with piecewise linear decreasing processing times to minimize makespan

We study the problems of scheduling a set of nonpreemptive jobs on a single machine and identical parallel machines, where the processing time of a job is a piecewise linear nonincreasing function of its start time. The objective is to minimize makespan. We first give a fully polynomial-time approximation scheme (FPTAS) for the case with a single machine. We then generalize the result to the case with m identical machines.