Multi‐objective linear programming with interval coefficients: A fuzzy set based approach

Abstract

Purpose

The purpose of this paper is to extend a methodology for solving multi‐objective linear programming (MOLP) problems, when the objective functions and constraints coefficients are stated as interval numbers.

Design/methodology/approach

The approach proposed in this paper for the considered problem is based on the maximization of the sum of membership degrees which are defined for each objective of multi objective problem. These membership degrees are constructed based on the deviation from optimal solutions of individual objectives. Then, the final model based on membership degrees is itself an interval linear programming which can be solved by current methods.

Findings

The efficiency of the solutions obtained by the proposed method is proved. It is shown that the obtained solution by the proposed method for an interval multi objective problem is Pareto optimal.

Research limitations/implications

The proposed method can be used in modeling and analyzing of uncertain systems which are modeled in the context of multi objective problems and in which required information is ill defined.

Originality/value

The paper proposed a novel and well‐defined algorithm to solve the considered problem.

Citation

Hossein Razavi Hajiagha, S., Amoozad Mahdiraji, H. and Sadat Hashemi, S. (2013), "Multi‐objective linear programming with interval coefficients: A fuzzy set based approach", Kybernetes, Vol. 42 No. 3, pp. 482-496. https://doi.org/10.1108/03684921311323707