Parallel machine earliness/tardiness scheduling problem with setup times under the effects of learning and deterioration

This study sheds light on parallel machine Earliness/Tardiness (E/T) scheduling problem with Past Sequence Dependent Setup Times (PSDST) under the effects of learning and deterioration. We considered linear and nonlinear deterioration and position based and time based learning effect. All jobs have common due-date, and effects of learning and deterioration were considered simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by decreasing function of its position in the sequence and increasing function of its execution start time, respectively. However, PSDST is a new form of setup times which depend on all already scheduled jobs from the current batch. In this study, we show that optimal solution for E/T scheduling problem with PSDST under effects of learning and deterioration is V-shape schedule under certain agreeable conditions. A mathematical model for the problem under study and proposed an algorithm to solve large test problems was designed.