Using a family of critical ratio-based approaches to minimize the number of tardy jobs in the job shop with sequence dependent setup times

This paper addresses the job shop scheduling problem to minimize the number of tardy jobs, considering the sequence dependent setup time. This problem is taken as a sequencing problem, and a family of approaches with different levels of intricacy is proposed. The simplest form is a critical ratio-based dispatching rule, which leads to satisfactory solutions by taking into account the group information rather than only the individual information of jobs. Then, an enhanced approach consisting of an iterative schedule refining mechanism will be given. Its feature is to iteratively adjust the estimation of the remaining processing times of jobs in a dynamic and operation-specific manner. Finally, a genetic algorithm which takes the dispatching rule and the refining mechanism as the core is proposed. The performance of these approaches is carefully examined by a comprehensive experimental study.