Most research done on the design of cellular production systems also has examined one of the main areas of design including cell formation, cellular layout, and material handling. Some research studies also have been done by considering the lack of independence of these areas, two areas simultaneously, and three areas sequentially. The main goal of this research is to present a mathematical framework for designing and also providing the efficient methods for solving the desired problem. Therefore, the main contribution of this paper is to determine the same component according to the characteristics of designs and production requirements. For this purpose, an overall design of a cellular production system or material handling system with cellular layout is examined. Then, the mathematical formulation is presented for the problem and then an efficient solution is presented for the problem. In the provided model, the interaction effects between designs fields are provided. A branch and bound algorithm is also provided to solve this problem. The performance of the provided algorithm and the performance of the provided approach are investigated by using different numerical samples. The results show the performance of the provided algorithm and approach in the design of cellular production systems.