Solving a new mathematical model for a hybrid flow shop scheduling problem with a processor assignment by a genetic algorithm

This paper presents a new mathematical model for a hybrid flow shop scheduling problem with a processor assignment that minimizes makespan (i.e., C _max) and cost of assigning a number of processors to stages. In this problem, it is assumed that there are a number of parallel identical processors which are assigned to all of the stages with an unlimited intermediate storage between any two successive stages. To solve such a hard problem, first a new heuristic algorithm is proposed to compute the makespan that is embedded in the proposed genetic algorithm in order to find the best sequence of jobs, and then processors are assigned to the stages simultaneously. A number of test problems have been solved and related results are illustrated and analyzed.