In this research, flexible flow shop scheduling with unrelated parallel machines at each stage are considered. The number of stages and machines vary at each stage and each machine can process specific operations. In other words, machines have eligibility and parts have different release times. In addition, the blocking restriction is considered for the problem. Parts should pass each stage and process on only one machine at each stage. In the proposed problem, transportation of parts, loading and unloading parts are done by robots and the objective function is finding an optimal sequence of processing parts and robots movements to minimize the makespan and finding the closest number to the optimal number of robots. The main contribution of this study is to present the mixed integer linear programming model for the problem which considers release times for parts in scheduling area, loading and unloading times of parts which transferred by robots. New methodologies are investigated for solving the proposed model. Ant Colony Optimization (ACO) with double pheromone and genetic algorithm (GA) are proposed. Finally, two meta-heuristic algorithms are compared to each other, computational results show that the GA performs better than ACO and the near optimal numbers of robots are determined. 
Two meta-heuristic algorithms for flexible flow shop scheduling problem with robotic transportation and release time