Minimizing the number of tardy jobs in a dynamic flexible flow shop

This paper considers an m-stage dynamic hybrid flow shop scheduling problem with minimizing the number of tardy jobs. There is at least one machine in each production stage in series, each of which has multiple identical parallel machines. Jobs with deterministic process times and due dates randomly arrive to the system. It is assumed that the release dates of jobs are not known in advance. To solve the problem, we use the combination of two methods. First, a dynamic method is proposed by which the m-stage flexible flow shop problem is decomposed into several parallel machines or single machine sub-problems. Second, each single machine sub-problem is solved by a variation of the Moore-Hodgson algorithm. Moreover, the machine-focus heuristic approach which is an extension of Moore-Hodgson algorithm is used to solve each parallel machines sub-problem. To show the performance of the heuristic algorithm suggested in this paper, computational experiments are done on a number of test problems, and the results are reported.