In today's competitive environment, it is essential to design a flexible-responsive manufacturing system with automatic material handling systems. In this study, a fuzzy Mixed Integer Linear Programming (MILP) model is designed for Cell Formation Problem (CFP) including the scheduling of parts within cells in a Cellular Manufacturing System (CMS) where several Automated Guided Vehicles (AGVs) are in charge of transferring the exceptional parts. Notably, using these AGVs in CMS can be challenging from the perspective of mathematical modeling due to consideration of AGVs’ collision as well as parts pickup/delivery. This paper tries to investigate the role of AGVs and human factors as indispensable components of automation systems in the cell formation and scheduling of parts under fuzzy processing time. The proposed objective function includes minimizing the makespan and inter-cellular movements of parts. Due to the NP-hardness of the problem, a hybrid Genetic Algorithm (GA/heuristic) and a Whale Optimization Algorithm (WOA) are developed. The experimental results reveal that our proposed algorithms have a high performance compared to CPLEX and other two well-known algorithms, i.e., Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO), in terms of computational efficiency and accuracy. Finally, WOA stands out as the best algorithm to solve the problem.