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Chance Constrained Linear Plus Linear Fractional Bi-level Programming Problem
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 56 - Number 16 |
| Year of Publication: 2012 |
| Authors: Surapati Pramanik, Durga Banerjee, Bibhas C. Giri |
10.5120/8978-3189
|
Surapati Pramanik, Durga Banerjee, Bibhas C. Giri . Chance Constrained Linear Plus Linear Fractional Bi-level Programming Problem. International Journal of Computer Applications. 56, 16 ( October 2012), 34-39. DOI=10.5120/8978-3189
Abstract
We present fuzzy goal programming approach to solve chance constrained linear plus linear fractional bi-level programming problem. The chance constraints with right hand parameters as random variables of prescribed probability distribution functions are transformed into equivalent deterministic system constraints. We construct nonlinear membership functions based on deterministic system constraints. The nonlinear membership functions are transformed into linear membership functions by using first order Taylor's series approximation. In the bi-level decision making context, decision deadlock may arise due to the dissatisfaction of the lower level decision maker with the decision of upper level decision maker. To overcome this problem, decision maker of each level gives his preference bounds on decision variables under his/her control to provide some relaxation on their decisions. Fuzzy goal programming model is used to achieve highest membership goals by minimizing negative deviational variables. Euclidean distance function is used in order to find out the most satisfactory solution. We solve a chance constrained linear plus linear fractional bi-level programming problem to illustrate the proposed approach.
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