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Abstract
Flow line systems with blocking are often seen in the fuzzy real world. This paper proposes a mixed integer nonlinear programming (MINLP) approach for evaluating the performances of the flow line system with blocking in fuzzy environments. The main idea is to model this system as a single-channel, multiple-phase queuing model with finite capacity, wherein the arrival rate and service rates are fuzzy numbers. This model is then transformed to a family of conventional crisp queues by applying the α-cut approach in fuzzy theory. On the basis of α-cut representation and the extension principle, two pairs of mixed integer nonlinear programs are formulated to calculate the lower and upper bounds of the fuzzy performance measures at possibility level α, from which the membership functions of the performance measures are derived. This paper also provides a representative value of the performance measure via the Yager ranking index method. An example is investigated successfully to illustrate the validity and the informative benefits of using the proposed approach. Since the performance measures are expressed by membership functions rather than by crisp values, the fuzziness of input information is conserved completely and more information is provided for capacity planning in flow line systems. Managerial implications of the analyses are also examined.
Acknowledgments
This research is supported by the National Science Council of Taiwan under Contract NSC94-2416-H-194-006.