Title: Bilevel linear programming with fuzzy random variables through absolute deviation minimisation

Authors: Masatoshi Sakawa; Takeshi Matsui

Addresses: Department of System Cybernetics, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527, Japan ' Department of System Cybernetics, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527, Japan

Abstract: This paper considers bilevel linear programming with fuzzy random variables. Through the introduction of a novel optimisation model that is to minimise the absolute deviation of degree of possibility and necessity that each fuzzy goal is fulfilled, the original bilevel programming problems with fuzzy random variables can be transformed into deterministic bilevel fractional programming problems. It is shown that the extended Stackelberg solutions can be obtained by solving the transformed bilevel linear programming problem through the combined use of the variable transformation method and the Kth best algorithm. A numerical example of bilevel purchase problem for food retailing is provided to illustrate the usefulness of the proposed methods.

Keywords: bilevel linear programming; fuzzy random variables; Stackelberg solutions; absolute deviation minimisation; possibility; necessity; optimisation; bilevel purchasing; food retailing.

DOI: 10.1504/IJOR.2016.073249

International Journal of Operational Research, 2016 Vol.25 No.1, pp.1 - 27

Received: 21 Aug 2013
Accepted: 21 Dec 2013
Published online: 30 Nov 2015 *

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