Single-machine group scheduling problems with deterioration and learning effects

In many situations, the skills of workers continuously improve when repeating the same or similar tasks. This phenomenon is known as the ldquolearning effectrdquo in the literature. There exist two kinds of learning effects. The first is position dependent, the learning phenomenon is implemented by assuming the actual job processing time is a function of its scheduled position. And the second is time dependent, the actual job processing time is the function of the total normal processing time of the previous jobs scheduled in front of it. In many realistic situations, a group processed later consumes more setup time than the same group when it is processed earlier; this phenomenon is known as deteriorating phenomenon. However, both the learning effects and deteriorating effects are relatively unexplored together in the context of group technology. In this paper, we consider two models of single-machine scheduling problems in the context of group technology where setup times are simple linear functions of their starting times and the jobs in the same group have learning effect are considered. In the first one, the position dependent learning effect is considered, whereas the second one concerns with the time dependent learning effect. For both of the problems, the makespan minimization objective is discussed.