# MODELLING GAME TASK OF ASSIGNING STAFF TO PERFORM IT-PROJECTS BASED ON ONTOLOG IES

## Authors

• P. Kravets Lviv Polytechnic National University, Lviv, Ukraine, Ukraine
• V. Lytvyn Lviv Polytechnic National University, Lviv, Ukraine, Ukraine
• V. Vysotska Lviv Polytechnic National University, Lviv, Ukraine, Ukraine

## Keywords:

project, agent, ontology, staff assigning, coloring of random graph, stochastic game, Markovian recursive method, adaptation, self-learning

## Abstract

Context. This article describes how to solve the game problem of assigning staff to work on projects based on an ontological approach. The essence of the problem is this. There is a need to create teams to carry out several projects. Each project is defined by a set of necessary ontological knowledge. To implement projects, managers invite qualified specialists (agents), whose abilities are also defined by sets of ontologies. The composition of the teams should be such that the combined ontologies of their agents cover the set of ontologies of the respective projects. Each agent with a certain probability can take part in the implementation of several projects. Simultaneous work of the agent on different projects is not allowed. It is necessary to determine the order of project implementation and the corresponding order of personnel appointment.

Objective of the study is to develop a mathematical model of stochastic game, recurrent Markov methods for its solution, algorithmic and software, computer experiment, analysis of results and development of recommendations for their practical application.

Method. A stochastic game algorithm for coloring an undirected random graph was used to plan project execution. To do this, the number of vertices of the graph is taken equal to the number of projects. The edges of the project graph for which the same agent is invited are connected by edges. Due to the recovery failures of agents, the connections between the vertices of the graph change dynamically. It is necessary to achieve the correct coloring of the random graph. Then projects with the same colored vertices of the graph can be executed in parallel, and projects with different colors of vertices – in series.

Results. The article builds a mathematical model of a stochastic game and a self-learning Markov method for its solution. Each vertex of the graph is controlled by the player. The player’s pure strategies are the elements of the color palette. After selecting the color of their own top, each player calculates the current loss as a relative number of identical colors in the local set of neighboring players. The goal of the players is to minimize the functions of average losses. The Markov recurrent method provides an adaptive choice of colors for the vertices of a random graph based on dynamic vectors of mixed strategies, the values of which depend on the current losses of players. The result of a stochastic game is an asymptotically correctly colored random graph, when each edge of the initial deterministic graph will correspond on average to different colors of vertices.

Conclusions. A computer experiment was performed, which confirmed the convergence of the stochastic game for the problem of coloring a random graph. This made it possible to determine the procedure for appointing staff to implement projects.

## Author Biographies

### P. Kravets, Lviv Polytechnic National University, Lviv, Ukraine

PhD, Associate Professor of Information Systems and Networks Department

### V. Lytvyn, Lviv Polytechnic National University, Lviv, Ukraine

Dr. Sc., Professor, Head of Information Systems and Networks Department

### V. Vysotska, Lviv Polytechnic National University, Lviv, Ukraine

PhD, Associate Professor of Information Systems and Networks Department

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2022-04-12

## How to Cite

Kravets, P., Lytvyn, V., & Vysotska, V. (2022). MODELLING GAME TASK OF ASSIGNING STAFF TO PERFORM IT-PROJECTS BASED ON ONTOLOG IES . Radio Electronics, Computer Science, Control, (1), 130. https://doi.org/10.15588/1607-3274-2022-1-14

## Section

Progressive information technologies