Representation of project systems using the Markov chain

Abstract

The known approaches to project management are typically based on the intuitive decisions by project managers, not on theoretical foundations, patterns and laws of project management. In order to solve this contradiction, it is necessary to conduct the generalization and develop applied aspects for using the Markov chains to represent and model the weakly structured project management systems. To construct the Markov chain, we used a modified system of project management, which is represented in the standard of project management and defines the scheme of interaction between project participants. A method for the transformation of this scheme into a homogeneous Markov chain with discrete states and time is developed. It is demonstrated that iteration solution of the system of equations of the Markov model makes it possible to construct a trajectory of development of virtual or actual project systems. We examined practical aspects in measuring the effectiveness of trajectory of project development by using the devised Markov model. An evaluation of results of changing the probability distribution of project states in the coordinates of probabilities of the system states by steps revealed a significant effect on the progress and efficiency of a project only in the case of variation of terms of cooperation within a project team.