A multi‐objective programming approach to solve grey linear programming

Abstract

Purpose The purpose of this paper is to extend an approach to solve linear programming problems with grey data and variables, based on a developed multi‐objective programming approach. Design/methodology/approach The proposed approach to generally solve the grey linear programming problems is based on the notion of order relation between interval grey numbers. This notion is applied to cascade the grey objective function to a bi‐objective problem based on the objective function of the original problem. The same approach is taken to transform grey constraints to a set of corresponding linear constraints. Finally, the obtained multi‐objective model can be solved by any existing methods in the literature. Findings One of the shortcomings of previous approaches to solve grey linear programming problems was that they required the grey coefficients of objective function to be both side negative or positive. The approach proposed here does not have such a requirement and guarantees the feasibility of solutions. Originality/value A different approach is developed in the paper that can be used to solve grey linear programming problems in general form. The method relaxes the limitation of existing approaches.