An extended fuzzy parametric programming-based approach for designing cellular manufacturing systems under uncertainty and dynamic conditions

• Authors: N. Safaei;R. Tavakkoli-Moghaddam
• Venue: International Journal of Computer Integrated Manufacturing
• Year: 2008

This paper proposes an extended fuzzy parametric programming (FPP) approach to solve a dynamic cell formation problem considering the uncertain part demand and machine capacity. The classical FPP approach gives the decision maker a number of alternative decisions for different grades of precision. Linear membership functions such as trapezoid, triangular and other piecewise forms have widely been used to express the uncertain parameters in the different engineering fields. Especially, to our best of knowledge, all researches related to the use of the fuzzy programming-based approaches for cellular manufacturing systems (CMSs) have been applied to the piecewise membership functions. In the case of lack of sufficient knowledge, there is a section in the piecewise forms called 'core', consisting of the fully included members (i.e. members with membership degree equal to one). This section, which represents the expert's ignorance, is not considered in the fuzzy programming-based approaches presented in the literature. In a highly cost-intensive production system, such as cellular manufacturing systems, the decision maker wants to know how big the changes of the cell configuration from one period to another are. These changes are caused by the fluctuations in some parameters of the system, such as part demand and machine capacity. However, when these parameters are uncertain as well as dynamic, the risk of decision making will increase significantly. On the other hand, in practice, a domain of uncertainty of data corresponds to a unique decision and hence the whole uncertainty in the system can be covered by only a few numbers of the alternative decisions, called 'applicable decisions'. This reduction in the decision space gives a better idea to the decision maker to make the final decision. The extended FPP proposed in this paper uses a simple strategy to extract all possible applicable solutions resulting from the core of the membership functions of the uncertain parameters. To verify the performance and applicability of the proposed approach, a comprehensive numerical example is solved and experimental results are presented.