A geometric approach for solving fuzzy linear programming problems

Abstract

In this paper we first recall some definitions and results of fuzzy plane geometry, and then introduce some definitions in the geometry of two-dimensional fuzzy linear programming (FLP). After defining the optimal solution based on these definitions, we use the geometric approach for obtaining optimal solution(s) and show that the algebraic solutions obtained by Zimmermann method (ZM) and our geometric solutions are the same. Finally, numerical examples are solved by these two methods.

An integrated fuzzy-stochastic model for revenue management

“…Among the approaches for solving FLP, the method proposed by Zimmermann is the most often used when the objective function and/or the right-hand sides of the constraints are fuzzy. Indeed, as several literature (Lai and Hwang, 1992; Zimmermann, 2001) has pointed out, the Zimmermann’s approach has the advantage of few assumptions and easy computation compared with alternative fuzzy methods (Safi et al, 2007).…”

Parametric linear programming for a materials requirement planning problem solution with uncertainty

“…Al resolver el modelo (5) por técnicas de programación paramétrica (Hillier, 2002) se obtiene el conjunto de soluciones que maximizan la función objetivo dependiendo del parámetro θ (Safi et al, 2007). Esto es, para todo valor de θ se obtiene una solución óptima x*(θ) con el respectivo valor óptimo Z*(θ) que satisfaga conjuntamente las restricciones en el grado 1θ.…”

“…. When solving the parametrical programming model (5) (see Hillier, 2002), a set of solutions is obtained maximising the objective function, depending on parameter θ (Safi et al, 2007). This is, for every θ, an optimal solution x*(θ) is obtained with respective Z*(θ) value that jointly satisfies constraints in degree 1θ.…”