Journal of Zhejiang University SCIENCE A
ISSN 1673-565X(Print), 1862-1775(Online), Monthly

2009   Vol. 10   No. 2   p. 311~318

On-line Access Date:   Feb. 16, 2009
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Optimal operating policy for a controllable queueing model with a fuzzy environment

Chuen-horng LIN1, Jau-chuan KE2

(1Department of Information Management; 2Department of Applied Statistics, National Taichung Institute of Technology, Taichung 404, Taiwan, China)
E-mail: linch@ntit.edu.tw; jauchuan@ntit.edu.tw
Received June 26, 2008; revision accepted Feb. 28, 2008; Crosschecked Dec. 26, 2008

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.

Key words: Controllable queue, Fuzzy sets, Membership function, Nonlinear programming
doi:10.1631/jzus.A0820139             CLC number: O22

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