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Chance Constrained Linear Plus Linear Fractional Bi-level Programming Problem

by Surapati Pramanik, Durga Banerjee, Bibhas C. Giri
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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

@article{ 10.5120/8978-3189,
author = { Surapati Pramanik, Durga Banerjee, Bibhas C. Giri },
title = { Chance Constrained Linear Plus Linear Fractional Bi-level Programming Problem },
journal = { International Journal of Computer Applications },
issue_date = { October 2012 },
volume = { 56 },
number = { 16 },
month = { October },
year = { 2012 },
issn = { 0975-8887 },
pages = { 34-39 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume56/number16/8978-3189/ },
doi = { 10.5120/8978-3189 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:59:02.814878+05:30
%A Surapati Pramanik
%A Durga Banerjee
%A Bibhas C. Giri
%T Chance Constrained Linear Plus Linear Fractional Bi-level Programming Problem
%J International Journal of Computer Applications
%@ 0975-8887
%V 56
%N 16
%P 34-39
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
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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Index Terms

Computer Science
Information Sciences

Keywords

Bi-level programming linear plus linear fractional programming chance constraints fuzzy goal programming Taylor's series.

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