Solving bi-level programming problem with fuzzy random variable coefficients

Article type: Research Article

Authors: Singh, Vishnu Pratap | Chakraborty, Debjani^*

Affiliations: Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India

Correspondence: [*] Corresponding author. Debjani Chakraborty, Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721 302, India. Tel.: +91 3222 283638; Fax: +91 3222 282276; E-mail: debjani@maths.iitkgp.ernet.in.

Abstract: This paper represents the bi-level linear programming problem in an imprecise and uncertain mixed environment. The aim of this paper is to introduce coefficients of leader and the follower’s objective function and the constraints as the fuzzy random variable. To determine the optimal value of the leader and follower’s objectives a new methodology is developed for bi-level linear programming model in the presence of fuzzy random variable. A numerical example is solved to demonstrate the methodology.

Keywords: Bi-level programming, fuzzy random variable, two stage stochastic programming, fuzzy goal programming

DOI: 10.3233/JIFS-152354

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 1, pp. 521-528, 2017