Abstract
Known approaches to project team management typically rely on intuitive decisions of project managers, rather than regularities and laws of role interaction between project participants. To resolve this contradiction, it is necessary to generalize and develop applied aspects of the use of the Markov chains to represent and model the projects as a system of role communications in a project team. To construct a Markov chain, we used a well-known role model of a project team by R. Belbin, which represents the structure of project participants only qualitatively. We developed a graphical representation of the cognitive structure of the role model, which is similar to a directed graph with vertices – states of the project, and arcs that represent communication links between project participants. Construction of the graph enables us to create a matrix of transition probabilities for communications of a project. To finish the method of transformation of a role model, it is necessary to pass to the development of analytical stepwise method to solve the system of equations of the Markov chain with discrete states and time. It is shown that iterative solution of the system of equations of the Markov model forms a trajectory of development of virtual or actual projects based on the characteristics of role communications. The practical aspects of assessment of effectiveness of the trajectory of projects development were explored using the developed Markov model. Evaluation of results of change in the distribution of probabilities of states of a project in coordinates of probabilities of states of the system in steps revealed a significant effect on the progress and effectiveness of a project in the case of variation of competences of only one member of the team project. These results reflect the essential property of teamwork: effectiveness of projects depends on the coherence of roles of all project performers
Highlights
Three main entities of project systems: a team, a project and its environment, determine success of project implementation [1]
The main task of project teams is to find innovative solutions and methods for solving the problems posed by the environment and the project [4]
The second is focused on a competence provision of the project work and a role division in a team by the project manager [7]
Summary
Three main entities of project systems: a team, a project and its environment, determine success of project implementation [1]. The second is focused on a competence provision of the project work and a role division in a team by the project manager [7]. The task of these approaches is to increase professionalism and competence of a team through a combination of the roles of all participants and formation of conditions for rational interaction between members of the project team [8]. Contradictions between practical needs in the team organization of projects implementation and the lack of acceptable models for quantitative assessment of interaction between the members of a project team determines the relevance of research in terms of provision of teamwork effectiveness. Development of mathematical models that implement the role paradigm of a team activity will allow us to perform proactive (predicted) improvement of teams
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