Single machine group scheduling with general linear deterioration to minimize the makespan

In this paper, we consider a single machine scheduling problem with deteriorating jobs and group technology assumption. By deteriorating jobs and group technology assumption, we mean that the group setup times and job processing times are both increasing functions of their starting times, i.e., group setup times and job processing times are both described by function, which is a general linear function of time. The objective of the scheduling problem is to minimize the makespan. We show that the problem remains solvable in polynomial time when general linear deterioration and group technology are considered simultaneously.