A genetic algorithm for the single machine preemptive scheduling problem with linear earliness and quadratic tardiness penalties

In this paper, we consider the single machine preemptive scheduling problem with linear earliness and quadratic tardiness penalties, with no machine idle time. The problem is strongly NP-hard. We proposed a new mathematical model, with non-linear terms and integer variables. We develop a genetic algorithm for solving the problem in medium and large size. The proposed procedure is compared with optimal solutions for the smaller instance sizes. The genetic procedure is also quite close to the optimum and provided an optimal solution for most of the test problems. Numerical examples show that the proposed algorithm is efficient and effective. Scheduling with early and tardy penalties has received extensive attention from the scheduling community because of its practical significance. Single machine scheduling environments actually occur in several practical applications. Also, the performance of many production systems is often determined by the schedules for a single bottleneck machine. Furthermore, the study of single machine problems frequently provides outcomes that prove functional for more complex scheduling areas.