Presenting a Mathematical Model for Flexible job-shop Production Scheduling Problem with Reverse Flows and Solving it by Using Genetic Algorithm

The scheduling problems application in today’s competitive world and usage range of its result in industry is indicating its high importance. One of the important issues in the field of flexible job-shop production scheduling is reverse flows within a single production unit, as is the case in the assembly/disassembly plants. In this paper, we conduct a study of the flexible job-shop scheduling with reverse flows approach which consists of two flows of jobs at each stage in opposite directions. The problem can be used only if you have two flows: The first one going from first stage to last stage, and the second flow going from last stage to first stage. We present a mathematical model of problem with the objective is to minimize the maximal completion time of the jobs (i.e., the makespan). Because of the complexity solving and prove that this problem ranked on NP-hard problems, we proposed meta-heuristic algorithm genetic (GA) and then design proposed model chromosome structure. Also, The parameters of these algorithm GA and their appropriate operators are set and determined by the use of the Taguchi experimental design. The computational results validate outperforms proposed algorithm GA.