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.

Balancing the project’s time, cost, and quality involves deciding on different implementation methods for each project activity. Time and cost are minimized simultaneously, and the quality of the final product or service is maximized. Indeed, the use of search methods to determine the optimal execution methods of each activity requires the evaluation and review of various performance criteria such as time, cost, and especially the final quality of each activity. These performance measures, especially the quality of the different implementation methods, are reported and recorded in inaccurate, ambiguous, and vague numbers or concepts. In this research, new methods have been proposed to evaluate and investigate the trade-off of time, cost, and quality of the project in conditions of uncertainty. This means that by fuzzy number theory, the specifications and conditions of a project are included in the problem of balancing time, cost, and quality. In fact, time, cost, and quality are considered triangular and trapezoidal fuzzy numbers. Also, the fuzzy multiattribute utility function approach (in which the concept of fuzzy computational operators is included) has been used to evaluate different combinations of execution methods of project activities. Since different quality combinations can be obtained with different combinations of parameters involved in the implementation of an algorithm, the Taguchi experimental design method has been used to adjust the parameters of the proposed algorithm. To solve the proposed model, particle mass optimization algorithms and artificial bee colonies have also been studied.