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

Abstract

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