The consideration and study of the process of functioning of the offices of the company were the following objectives. Determine the quantitative dependencies of the input flow of patients and unserved requests (refusals). To conduct the sensitivity analysis. Build a basic model of a dental company as a simulation model (input model) that provides targeted variation of input parameters, and a linear programming model (output model) that processes simulation results and provides data on the degree of sensitivity of the model to changes in its parameters. Compare two simulation models of a dental company with different numbers of doctors. Determine the most effective model. Determine a combination of management variables in the optimization model that takes into account the amount of estimated lost profits due to rejection of applications, and based on this, make a conclusion about the need to hire additional employees, thereby increasing the profitability of the dental company. To achieve these goals, the following tasks were solved. A simulation model of a dental company as a Queuing system in the GPSS language was developed and studied. It is determined under which parameters the model is most effective. An analysis of the sensitivity of the model to changes in its parameters is performed. Numerical Monte Carlo methods were used to investigate this issue. We have developed a custom application in the VBA object-oriented programming language that allows you to determine for a certain period of time, starting with how many failures, you should hire an additional doctor, so that the company's profit is maximized. The practical value of the proposed model lies in its flexibility, complex nature, and consistency in the organization and technological regulation of the company's main systems and business processes. The model of a dental company has a sufficient degree of universality, as it can be used in any branch of the service sector. more complicated when you add players. The term "truel" we understand the rivalry three players. They are assigned some values of accuracy the probabilities of eliminating the opponent in one shot. At each stage of the game is chosen by the active player (the selection rule active player either randomly or by prior agreement between the players about their participation). The active player chooses an opponent to eliminate or passes the course. Developed mathematical models for different formulations of the conditions of the game (random or fixed choice of the active player). For each model are analyzed based on the probability of winning in the "truly" of accuracy, based on randomly generated program values. Comparing analytical solution and simulation, we see that they have the same answers. For large dimensions similar games analytical method requires complex calculations, so an acceptable alternative is the simulation method. Data research nahegelegenen in political and judicial practices, as well as analytical tools for the study of the theory of evolution.

Keywords: simulation model, Queuing systems, GPSS World, linear programming model, Monte Carlo numerical methods, VBA

In general, games like duels, in which each of two players has the goal to eliminate the enemy, are quite a popular problem from game theory. The problem becomes much more complicated when you add players. The term ""truel"" we understand the rivalry three players. They are assigned some values of accuracy the probabilities of eliminating the opponent in one shot. At each stage of the game is chosen by the active player (the selection rule active player either randomly or by prior agreement between the players about their participation). The active player chooses an opponent to eliminate or passes the course. Developed mathematical models for different formulations of the conditions of the game (random or fixed choice of the active player). For each model are analyzed based on the probability of winning in the ""truly"" of accuracy, based on randomly generated program values. Comparing analytical solution and simulation, we see that they have the same answers. For large dimensions similar games analytical method requires complex calculations, so an acceptable alternative is the simulation method. Data research nahegelegenen in political and judicial practices, as well as analytical tools for the study of the theory of evolution.

Keywords: truel, simulation, game duel three persons,Markov chain, variance of natural selection, the matrix of transition probabilities, fundamental matrix, stochastic process, the three prisoners dilemma, game theory, coalition games