Parallel machine earliness/tardiness scheduling problem under the effects of position based learning and linear/nonlinear deterioration

This paper considers a parallel machine earliness/tardiness (ET) scheduling problem with different penalties under the effects of position based learning and linear and nonlinear deterioration. The problem has common due-date for all jobs, and effects of learning and deterioration are considered simultaneously. By the effects of learning we mean that the job processing time decreases along the sequence of partly similar jobs, and by the effects of deterioration we mean slowing performance or time increases along the sequence of jobs. 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 design a mathematical model for the problem under study and algorithm and lower bound procedure to solve larger test problems. The algorithm can solve problems of 1000 jobs and four machines within 3 s on average. The performance of the algorithm is evaluated using results of the mathematical model.