DEVELOPMENT OF THE MARKOV MODEL OF A PROJECT AS A SYSTEM OF ROLE COMMUNICATIONS IN A TEAM

Abstract

Розроблено метод трансформації в ланцюг Маркова відомої рольової моделі команди проекту Р. Белбіна. Запропоновано описати взаємодію між виконавцями проекту у формі орієнтованого графа рольової моделі. Показано, що орієн-тований граф становить основу для побудови ланцюга Маркова. Розроблено метод ітераційного рішення системи рівнянь, що описують ланцюг Маркова. Досліджено практичні аспекти діяльності команд на основі рольових комунікацій при реалізації проектів

Разработан метод трансформации в цепь Маркова известной ролевой модели команды проекта Р. Белбина. Предложено описать взаимодействие между исполнителями проекта в форме ориентиро-ванного графа ролевой модели. Показано, что ориентированный граф составляет основу для построения цепи Маркова. Разработан метод итерационного решения системы уравнений, описывающих цепь Маркова. Исследованы практические аспекты деятельности команд на основе ролевых коммуникаций при реализации проектов

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