A Mathematical Programming Model and Genetic Algorithm for a Multi-Product Single Machine Scheduling Problem with Rework Processes

In this paper, a multi-product single machine scheduling problem with the possibility of producing defected jobs, is considered. We concern rework in the scheduling environment and propose a mixed-integer programming (MIP) model for the problem.  Based on the philosophy of just-in-time production, minimization of the sum of earliness and tardiness costs is taken into account as the objective function. It is possible to obtain optimal solutions for small-sized problems using the MIP model by operation research solvers. Due to the complexity of the problem, exact algorithms are inefficient for medium and large-sized problems. For large-sized problems, an adapted genetic algorithm (GA) is used to solve them. The implemented GA is compared to the optimal solutions generated by an optimization solver, and to the solutions generated by dispatching rules procedure. Computational experiments are performed to illustrate the efficiency of the adapted GA algorithm.