A heuristic approach for two-machine no-wait flowshop scheduling with due dates and class setups

This paper studies the two-machine flowshop scheduling problem with class setups in a no-wait processing environment to minimize the maximum lateness. The jobs are divided into job classes and a setup is required at the initial processing of a job or between the processing of jobs of different classes. In a no-wait environment, a job must be processed from start to finish without interruptions on a machine or between the machines. A batch is a maximal subset of consecutively processed jobs of the same class. Several properties concerning the beneficial merging of batches and some dominance rules that improve the objective function are derived. Since the problem is NP-hard, a heuristic is proposed and evaluated computationally. The numerical results demonstrate that the heuristic can produce near-optimal solutions quickly for realistic-sized problems.