Single machine group scheduling with decreasing time-dependent processing times subject to release dates

In this paper we investigate a single machine scheduling problem with decreasing time-dependent processing times and group technology assumption. By the decreasing time-dependent processing times and group technology assumption, we mean that the group setup times and job processing times are both decreasing linear functions of their starting times. We want to minimize the makespan subject to release dates. We show that the problem can be solved in polynomial time.