Abstract
A practical solution method for a flow shop scheduling problem to minimize makespan on serial machines under different due date constraints is described. In the flow shop scheduling, when the due date of all jobs is equal, the minimum makespan schedule automatically minimizes the total tardiness of jobs. However, the minimum makespan schedule does not always satisfy the due date constraints when the due date of each job is different. Both the makespan and the tardiness of each job are influenced by the machine idle time and the waiting time of each operation. The idle time and the waiting time depend on the dispersion in processing time as well as the processing sequence. The idle time and waiting time may decrease, if the dispersion in the processing time is made small by dividing each job into some smaller size jobs. Therefore, by dividing jobs, it is possible to generate the desirable schedule which reduces not only the makespan but also the number of tardy jobs and the total tardy time. In this paper, we propose a solution method to generate the smaller makespan schedule satisfying the due date constraints by the application of this approach in the flow shop scheduling problem. This problem may be formulated as a large-scale combinatorial problem to simultaneously decide how to divide each job and in what kind of order to process the divided jobs. An effective solution method does not exist for a large-scale optimal combinatorial problem, so we propose an efficient solution method applying the Genetic Algorithms.
