The common due-date early/tardy scheduling problem on a parallelmachine under the effects of time-dependent learning and linear and nonlinear deterioration

This paper considers earliness/tardiness (ET) scheduling problem on a parallel machine environment with common due-date under the effects of time-dependent learning and linear and nonlinear deterioration. In this paper, the effects of learning and deterioration are considered simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. This study shows that optimal solution for ET scheduling problem under effects of learning and deterioration is V-shape schedule under certain agreeable conditions. Furthermore, we present a mathematical model for the problem under study and an algorithm for solving large test problems. The algorithm can solve problems of 1000 jobs and four machines within 3 s on average.