Optimal operating policy for a controllable queueing model with a fuzzy environment |
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| Authors: | Chuen-horng Lin Jau-chuan Ke |
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| Institution: | (1) Department of Information Management, National Taichung Institute of Technology, Taichung, 404, Taiwan, China;(2) Department of Applied Statistics, National Taichung Institute of Technology, Taichung, 404, Taiwan, China |
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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 ex-pressed 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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| Keywords: | Controllable queue Fuzzy sets Membership function Nonlinear programming |
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