Cell formation considering fuzzy demand and machine capacity

The concept of cellular manufacturing requires that machines and parts be grouped together to form cells. Many researchers have addressed this cell formation problem for crisp (or certain) input data. However, if the input data is not exact or is imprecise (fuzzy), how is the decision made to form cells and assign parts determined? In this paper, crisp and fuzzy mathematical models are developed to optimally determine machine grouping and parts assignment under fuzzy demand and machine capacity. The object of these models is to minimise the processing and the material handling costs. Comparisons between the crisp and fuzzy results are made to show how outcomes differ when uncertainty is introduced. The example problems are solved using the Hyperlindo software package to illustrate the ability of the model to react under different input parameters. To reduce the computation time, nonlinear representations of the above crisp and fuzzy models are developed. These nonlinear formulations allow each model to be elegantly decomposed into two submodels. An iterative solution procedure is proposed which utilises these submodels to reduce computation time substantially. Example problems are solved using both the crisp and the fuzzy optimal models and the iterative procedure. The solutions and computational experience for the two approaches are compared.