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Journal of Zhejiang University SCIENCE A 2009 Vol.10 No.2 P.311-318

http://doi.org/10.1631/jzus.A0820139


Optimal operating policy for a controllable queueing model with a fuzzy environment


Author(s):  Chuen-horng LIN, Jau-chuan KE

Affiliation(s):  Department of Information Management; more

Corresponding email(s):   linch@ntit.edu.tw, jauchuan@ntit.edu.tw

Key Words:  Controllable queue, Fuzzy sets, Membership function, Nonlinear programming


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Chuen-horng LIN, Jau-chuan KE. Optimal operating policy for a controllable queueing model with a fuzzy environment[J]. Journal of Zhejiang University Science A, 2009, 10(2): 311-318.

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Abstract: 
We construct the membership functions of the fuzzy objective values of a controllable queueing model, in which cost elements, arrival rate and service rate are all fuzzy numbers. Based on Zadeh’s extension principle, a set of parametric nonlinear programs is developed to find the upper and lower bounds of the minimal average total cost per unit time at the possibility level. The membership functions of the minimal average total cost are further constructed using different values of the possibility level. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the object value is expressed and governed by the membership functions, the optimization problem in a fuzzy environment for the controllable queueing models is represented more accurately and analytical results are more useful for system designers and practitioners.

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