Manufacturing cell formation in a fuzzy environment

Abstract

<p>The main objective of this study is to develop useful mathematical programming (FMP) models to solve cell formation (CF) problems in fuzzy environments. The dissertation was divided into three major parts. First, two mathematical programming models were developed to formulate the cell formation problems under consideration. The first model was a linear programming (LP) model for grouping parts and machines simultaneously into cells and solving the CF problem for dealing with exceptional elements (EEs). In second, a goal programming (GP) model to obtain a trade off between minimizing total cost of dealing with EEs and maximizing GE, a new similarity coefficient formula between parts also has been developed;In the second part, the fuzzy linear programming (FLP) methodology was applied to solve CF problems involving fuzzy situations. A new fuzzy operator, add-min, was proposed and its performances evaluated against the other six operators. Robustness and excellent performance in terms of clustering results and CPU executing time were verified for the FLP with the new operator. Fuzzy multiobjective linear programming (FMLP) then was used (1) to find the optimal trade-off between multiple goals in the proposed goal programming and (2) to compare the performance with the GP results. Numerical illustrations show that FMLP with the proposed operator performed much better than the GP did in terms of computational efficiency;Finally, an efficient heuristic genetic algorithm (HGA) was developed to solve all mathematical programming models, including the fuzzy models, presented in this dissertation. New heuristic crossover and mutation operators based on the special characteristics of CF were proposed to enhance computational performance. Our experiment showed that the proposed GA heuristic outperformed both the traditional GA approach and the mathematical programming models in terms of clustering results, computational time, and ease of use.</p>