Solving the Problem of Linear Programming with Cost Coefficients and Grey Resources Using the Primal Simplex Algorithm

In most real-world issues, we are dealing with situations where accurate data and complete information are not available. One way to deal with these uncertainties in real life is to use Grey System Theory (GST). In this paper, a linear programing problem in a grey environment with interval Grey Numbers (GN) is considered. Most of the proposed methods for solving grey linear programing problems are done by using GN whitening and turning the problem into a common linear programing problem. However, in this paper we seek to solve the grey linear programing problem directly without turning it into a regular linear programing problem in order to maintain uncertainty in the original problem data in the final answer. For this purpose, by proving the desired theorems, we propose a method based on the initial simplex algorithm to solve grey linear programing problems. This method is simpler than the previous methods. We emphasize that the proposed concept is useful for real and practical situations. To illustrate the efficiency of the method, we solve an example of Grey Linear Programming (GLP).

کلیدواژه ها:

Uncertainty ، Grey interval numbers ، Grey linear programming