A genetic Algorithm for the Single Machine Scheduling Problem with Linear Earliness and Quadratic Tardiness Penalties with Consideration of Preemption and Idle Time

In this paper, a non linear mathematical model has been proposed for solving a single machine scheduling problem with a linear earliness and quadratic tardiness cost, where machine idle time and preemptions are allowed. As the model is complex and cannot be solved in polynomial time, it has been assumed to be a NP hard problem, so the known optimal solution methods may not be applicable for its solution. A Genetic Algorithm approach has been developed for solving the model and numerical examples has been presented, which imply that the proposed method is efficient and effective.