Sequencing two-stage flowshop with nonidentical job sizes

This study addresses the two-machine flowshop in which a batch processor is followed by a discrete processor. The batch machine processes a batch of jobs simultaneously and the discrete machine processes one job at a time. Each job has a certain size or capacity requirements. The capacity of the batch processor is limited. The objective is to minimize the makespan. This problem is shown to be nondeterministic polynomial time hard. A heuristic algorithm and a branch-and-bound algorithm are presented. Computational results show that the proposed heuristic algorithm works effectively compared to the optimal solution, with an overall average quality of 99.42%.