A Primal Simplex Algorithm for Solving Linear Programming Problem with Grey Cost Coefficients

an extension of the classical linear programming problem to an inexact environment as well as fuzzy and stochastic environment. Hence, here a new approach for solving interval grey number linear programming problems is introduced without converting them to classical linear programming problems. The proposed method is established based on the primal simplex algorithm where the cost coefficient row includes grey numbers. As an essential tool in the solving process, a theoretical discussion on grey arithmetic and in particular an ordering role for grey numbers is necessary to evaluate the optimality conditions of a candidate feasible solution. It is also emphasized that the discussed model and the solution process is useful for real situations and practical cases, when a kind of the grey number linear programming is appeared, such as Water Resource Management and Planning, Economics, etc. Finally, the proposed approach is illustrated by a numerical example.