Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Le Thanh Hue
Pages: [9] - [19]
Received Date: August 11, 2017
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121865
The paper studies the linear programming problem with non-negative input data and applies the station cone algorithm to find the solution. From the non-negative input data and station cone algorithm’s properties, the author has shown how to derive the feasible solution in a simple way. This significantly reduces the computational time, because it skips the feasible solution study phase without having to use the phase I of the simplex algorithm to search. The paper also points out how an interior point is the center of a convex polyhedron in the feasible domain. This is the point in order to connect with the vertex of the station cone which serves to identify the variables in and out of the simplex pivot. Another important part of this paper is the experimental calculation of the station cone algorithm for the above problem class. Tests have shown that the station cone algorithm has fewer iterations than the dual simplex method.
linear program, station cone algorithm, dual simplex method.
