A new initial basis for the simplex method combined with the nonfeasible basis method

Abstract

The simplex method is a popular method to solve a linear programming problem. It starts by choosing an initial basis associated with the origin point which is far from the optimal point in some problems. In this paper, we introduce a construction of an initial basis for starting the simplex method associated with an extreme point which is close to the optimal solution. This construction involves the angle between the coefficient vector of the objective function and the coefficient vector of each constraint. The small angles will be considered to construct a basis. If the proposed initial basis gives the infeasible solutions, then the nonfeasible basis method is performed to avoid the use of artificial variables. Not only the starting point is close to the optimal point, but also the artificial variable is needless. The results in the computational aspect show that the number of iterations and the running time of our method are less than other methods.