Design of a Knowledge-Based Manufacturing Flow Shop Sequencing System Using Fuzzy Logic

Abstract

This study investigated an approach for incorporating statistics with fuzzy sets in the problem. It considers a flow shop problem with imprecise processing times with the objective to minimize the makespan. This work is based on the assumption that the precise value for the processing time of each job is unknown, but that some sample data are available. A combination of statistics and fuzzy sets provides a powerful tool for modeling and solving this problem. The processing times are described by triangular fuzzy numbers. The issue that arises is how to rank the constructed job sequences with respect to their obtained makespans, which are fuzzy numbers. A new distance measure between fuzzy makespans is introduced which includes an optimism/pessimism indicator and a function related to λ-levels of fuzzy sets, enabling the decision maker to express his/her preference. Our work intends to extend the crisp flowshop sequencing problem into a generalized fuzzy model that would be useful in practical situations. In this study, we constructed a fuzzy sequencing model based on statistical data, which uses level (1-α, 1-β) interval-valued fuzzy numbers to represent the unknown job processing time

Keywords

• Flowshop Sequencing Problem, Fuzzy Flowshop Model, Interval-Valued Fuzzy Number

References

1. Campos, L. and Monoz A.: A Subjective Approach for Ranking Fuzzy Numbers, Fuzzy Sets and Systems, Vol. 29, 145-153, 1989.
2. Czogala, E.: On Distribution Function Description of Probabilistic Sets and its application in Decision Making, Fuzzy Sets and Systems, 10, 21-29, 1983.
3. Czogala, E. and Pedrycz, W.: On the Concept of Fuzzy Probabilistic Controllers, Fuzzy Sets and Systems, 10, 109-121, 1983.
4. Dubois, D. and Prade, H., Operations in a Fuzzy-Valued Logic, Inform, and Control, Vol. , 224-240, 1979.
5. Gorzalezang, M.B.: A Method of Inference in Approximate Reasoning based on Interval Valued Fuzzy Sets, Fuzzy Sets and Systems, 21, 1-17, 1987.
6. Hirota, K., Concept of Probabilistic Sets, Fuzzy Sets and Systems, Vol. 5, 31-46, 1981.
7. Kaufmann, A. and Gupta, M.M.: Introduction to Fuzzy Arithmetic Theory and Applications, van Nostrand Reinhold, New York, 1991.
8. McCahon, S. and Lee, E.S., Job Sequencing with Fuzzy Processing Times, Computers and Mathematics with Applications, Vol. 19, No.7, 31-41, 1990.

9. Nawaz, M., Enscore Jr, E. and Ham I., A Heuristic Algorithm for the m-Machine, n-Job Flow-Shop Sequencing Problem, OMEGA, Int. J. of Management Science, Vol.11, No 1, 95, 1983.
10. Petrovic, S. and Song, X., A New Approach on two-machine Flow Shop Problem with Uncertain Processing Time, Proceedings of the ISUMA, University of Maryland, USA, 115, 2003.
11. Pinedo, M., Scheduling Theory, Algorithm, and Systems, Prentice Hall, 2nd Edition, Sakawa, M. and Kubota, R., Fuzzy Programming for Multi-objective Job Shop Scheduling with Fuzzy Processing Time and Fuzzy Due date through Genetic Algorithm, European J. of Operations Research, Vol. 120, No. 2, 393-407, 2000.
12. Slowinski, R. and Hapke, M. (Eds.), Scheduling Under Fuzziness, Physica-Verlag, Heidelberg, 2000.
13. Song, X. and Petrovic, S., Ranking of makespans in flow shop problems with fuzzy processing times. Tran, L. and Duckstein, L., Comparison of Fuzzy Numbers using a Fuzzy Distance Measure, Fuzzy Sets and Systems, Vol. 130, 331-341, 2002.
14. Yao, J.S. and Lin, F.T., Constructing a fuzzy flowshop sequencing model based on statistical data, Vol. 29, 215-234, 2002.
15. Yao, J.S. and Wu, K.M., Ranking Fuzzy Numbers based on Decomposition Principle and Signed Distance, Fuzzy Sets and Systems, Vol. 116, 275-288, 2000.
16. Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning, I, Inform. Sci., Vol. 8, 199-249, 1975.