One of the important factors in the design of automated guided vehicle systems (AGVS) is the flow path design. This paper presents a Branch-and-bound algorithm to determining the flow path by considering not only loaded-vehicles, but also empty-vehicles. The objective is to find the flow path, which will minimize total travel of loaded vehicles. We know that in Branch-and-bound method a Branch can be fathomed in different ways, but it sometimes causes infeasible solutions. By Branching on only feasible solutions, the algorithm presented in this paper works effectively. We also use DFS algorithm for finding only feasible solutions of the problem and by testing the objective function, one efficient flow path can be determined.