A fuzzy programming approach for a cell formation problem with dynamic and uncertain conditions

This paper presents an integration of explicit uncertainty for a cell formation problem (CFP) with a dynamic condition in cellular manufacturing systems (CMS). The dynamic condition indicates a multi-period planning horizon, in which product mix and demand in each period are different. As a result, the best cells designed for one period may not be the most efficient for subsequent periods and thus require reconfigurations. Moreover, in real manufacturing systems, some input parameters are fuzzy in nature. In such cases, the fluctuation in part demand and the availability of manufacturing facilities in each period can also be regarded as fuzzy. In this paper, a fuzzy programming-based approach is developed to solve an extended mixed-integer programming model of the dynamic CFP, in which there are piecewise fuzzy numbers as coefficients in the objective function and the technological matrix. The main purpose of this paper is to determine the optimal cell configuration in each period with the maximum degree of satisfying the fuzzy objective under the given constraints. To illustrate the behavior of the proposed model and verify the performance of the developed fuzzy programming-based approach, we introduce a number of numerical examples to illustrate the use of the foregoing approach. Finally, the related computational results are reported and discussed.