Interactive fuzzy programming for two-level stochastic linear programming problems through expectation and variance models

Article type: Research Article

Authors: Kato, Kosuke^{a; *} | Sakawa, Masatoshi^b | Katagiri, Hideki^b

Affiliations: [a] Department of Computer Science, Faculty of Applied Information Science, Hiroshima Institute of Technology, Japan | [b] Department of Artificial Complex Systems Engineering, Graduate School of Engineering, Hiroshima University, Japan

Correspondence: [*] Corresponding author: Kosuke Kato, Miyake 2-1-1, Saeki-ku, Hiroshima, 731-5193, Japan. Tel.: +81 82 921 5394; Fax: +81 82 921 8971; E-mail: [email protected]

Abstract: In this paper, we focus on two-level linear programming problems involving random variable coefficients in objective functions and constraints. According to the concept of chance constrained programming, the two-level stochastic linear programming problems are transformed into deterministic ones through the expectation optimization model and the variance minimization model. After introducing fuzzy goals for objective functions, interactive fuzzy programming to derive a satisfactory solution for decision makers is presented as a fusion of stochastic approach and fuzzy one. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.

Keywords: Two-level linear programming, stochastic programming, interactive fuzzy programming, expectation optimization, variance minimization

DOI: 10.3233/KES-2009-0179

Journal: International Journal of Knowledge-based and Intelligent Engineering Systems, vol. 13, no. 3-4, pp. 111-118, 2009