THE SIMPLIFYING OF THE SOLUTION OF LINEAR OPTIMIZATION PROBLEMS IN PROJECT MANAGEMENT

Abstract

Modern mathematic models of project management processes description can be use in many cases to linear optimization problems. Simplification algorithms provide an efficient method of searching for solution of an optimization problem. If we project a multidimensional process onto a two-dimensional plane, this method will enable graphic visualization of the problem solution matrixes. A significant simplification of the algorithms for preparing the linear optimization problem in computer calculations can be achieved using the concept of duality in linear optimization problems. The linear optimization problem forms are equivalent. This can be achieved provided that transformation techniques are used to move from one form of tasks to another. To simplify the transformation of linear optimization problems, the transition from maximizing to minimizing the objective function is used. This research has proposed a method of simplifying the combinatorial solution of a discrete optimization problem. It is based on decomposition of the system representing a system of constraints of a five-dimensional initial problem into the two-dimensional coordinate plane. There was a model example considered for solving a five-dimensional linear optimization problem based on such projecting of a multidimensional space onto the two-dimensional one. The paper is concerned with construction of a chain of efficient algorithms to simplify the primary mathematic model of problem and realization its computer-aided calculation. Applied value of the proposed approach consists in using the scientific result for enabling the possibility to improve canonical methods of optimization problem solution and, respectively, for simplification of computer-assisted calculation.