In line with the fundamental reform of the Russia administrative legislation, this article discusses the synthesis of a geoinformation system for preventive management of the full cycle of production on affairs about administrative offenses. According to the Anokhin - Sudakov's theory of functional systems, the tasks of forming a structural image and synthesizing a mathematical model to manage the administrative process stages, as well as the tasks of substantiating the mathematical criterion and its structural and functional implementation to prevent violations of a reasonable time in production on affairs about administrative offenses, were set. According to the law of management object integrity preservation, it is obtained that the opposing side of the administrative conflict counteracts by the joint use of protective (geoinformation), target (enforcement) and providing (geolocation) management subsystems, each of which generates a different contribution to efficiency at the next stage of the administrative process. To create a mathematical model for making a managerial decision, adequately formalized for each stage of the administrative process, a natural-scientific approach to the synthesis of management in conditions of limited resources was used. An analytical dependence is determined, that integrates the functioning regularities of law enforcement, geoinformation and geolocation components of the management system at the stage of administrative practice. When concretizing it, the possibility of representing administrative production by Poisson transitions of the affairs flow about administrative offenses between the states of the administrative process stages in a continuous Markov chain is used. Through modeling a Markov chain by the Kolmogorov - Chapman's equations system the criterion of preemptive management existence of the administrative process stages complex is revealed, allowing under proper efficiency of administrative production to optimize the intensity of identification and neutralization of threats to ensure a reasonable time in the target, protective or providing subsystems of management. The structure and functionality of probabilistic transitions of the affairs flow about administrative offenses, including management procedures, in a Markov chain of administrative production are established by their network modelling based on accumulated observations of administrative statistics. Numerical studies of a synthesized model of preemptive management of administrative production have clarified the effects of disruption of transition processes between states of administrative practice on its efficiency.

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ГЕОИНФОРМАЦИОННЫЕ ТЕХНОЛОГИИ decision making in affairs about administrative offenses involves establishing a formal analytical relationship between the technological components. The authors have developed a mathematical aggregate of the conditions for the existence of guaranteed management of the revealing and proving administrative offenses. It takes into account the parameters of offence case, parameters of involves application of a geoinformation system a final decision. Using a geoinformation system, the decision-maker is able to identify and neutralize the Poisson flow of production violations within a reasonable time period. The relationship between the time characteristics of the target process, its disruption, emergence, identification, and neutralization of violations and the indicators of the effectiveness of revealing and proving administrative offenses procedures is concretized by the system of Kolmogorov-Chapman equations. The intensities of the interacting processes are estimated by the structural-functional method through the critical paths of the corresponding network models.

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