A method of eliminating exceptional elements attaining minimum machine duplications and intercell moves in cellular manufacturing systems

Using the concept of cellular manufacturing systems (CMS) in job shop manufacturing system is one of the most innovative approaches to improving plant productivity. However, several constraints in machine duplication cost, machining capability, cell space capacity, intercell moves and exceptional elements (EEs) are main problems that prevent achieving the goal of maintaining an ideal CMS environment. Minimizing intercell part traffics and EEs are the main objective of the cell formation problem because it is a critical point in improving production efficiency. Because the intercell moves could be changed according to the sequence of operation, it should be considered in assigning parts and machines to a machine cell. This paper presents a method that eliminates EEs under the constraints of machine duplication cost and cell space capacity attaining two goals of minimizing machine duplications and minimizing intercell moves simultaneously. We develop an algorithm that calculates the machine duplications by cell–machine incidence matrix and part–machine incidence matrix, and calculates the exact intercell moves considering the sequence of operation. Based on the number of machine duplications and exact intercell moves, the goal programming model which satisfies minimum machine duplications and minimum intercell moves is developed. A linear programming model is suggested that could calculate more effectively without damaging optimal solution. A numerical example is provided to illustrate these methods.