Multiple-machine scheduling with earliness, tardiness and completion time penalties

This study deals with the problem of scheduling a number of jobs on parallel machines. We assume that companies are mainly interested in two objectives, namely achieving small deviations from a common due date and short flowtimes. Therefore earliness, tardiness and completion time penalties for the jobs are introduced. We are able to show that the problem is intractable and, consequently, develop an efficient heuristic to obtain near-optimal solutions. We consider the problem of scheduling n jobs on m parallel and identical machines. The goal is to find an optimal permutation of the jobs and an optimal due date which jointly minimize an objective function consisting of earliness, tardiness and completion time penalties. We show that the problem is NP-hard and present a polynomially solvable case. Furthermore, a heuristic is developed and computationally demonstrated to be efficient in obtaining near-optimal solutions.