The article presents a mathematical model that formalizes the process of managing the scientific activities of an organization. The model based on the theory of queuing. The principle of death - reproduction used in the construction. For a special case, a graph of states and a system of Kolmogorov differential equations are given. The intensity of the input and output streams are time-dependent non-stationary streams. The model allows us to consider various structures and schemes of interaction between scientific departments and various sce-narios for setting scientific tasks and the intensity of their solution by employees of the organization. A software package for decision-making has developed for the model for optimal management of the scientific activities of the department. The article presents one of the results of an experimental and model study of the influence of the motivational component and the level of competence of employees. Graphs of the system states given for the resulting solution. The research can used for comprehensive evaluation of results, planning, resource allocation and management of scientific activities.

Keywords: diversification of management, production diversification, financial and economic purposes of a diversification, technological purposes of ensuring flexibility of production

Effective communication between project managers and engineering teams is critical for the success of construction projects. This article develops a hierarchical (Stackelberg) game-theoretic model, where the manager acts as the leader and engineering teams act as followers. The model quantifies how both the leader and followers balance the benefits and costs associated with increasing communication efforts. We propose a two‐level (Stackelberg) model of strategic interaction between a project manager (leader) and engineering teams (followers) in construction projects. An efficient numerical algorithm is implemented in MATLAB to compute optimal strategies and analyze different project scenarios. Scenario analysis demonstrates how changes in project parameters affect the balance of efforts and profits, thereby guiding managerial recommendations for improving communication and reducing project risks. By considering aspects like risk, time delay, cost overruns, and resistance to change, we provide supervisors and agents communication efficiency functions. Using scenario analysis and numerical optimization, we determine the most efficient communication tactics to match the hierarchical structure of building projects.

Keywords: project efficiency, leader-follower dynamics, profit maximation, project management, communication efforts, time delay, cost overrun, risk, resistance to change

The purpose of this article is to analyze algorithms and models for conducting search and rescue operations in crowded areas during fires, as well as other man-made or natural emergencies. The chance of saving people's lives directly depends on the effectiveness of search and rescue operations. The article describes the brief essence of the Graph Model as a method of finding optimal solutions when building a route for conducting search operations in emergency situations, including fires at facilities with a mass presence of people.

Keywords: search and rescue operations, facilities with a mass presence of people, emergencies, rescue of people, fires, search for victims

The article addresses the challenges and proposes mathematical models for optimizing container freight transportation within complex logistics systems, emphasizing the growing importance of digital technologies and artificial intelligence in logistics by 2025. It highlights key industry issues such as decentralized global supply chains, environmental risks, infrastructure deficiencies, safety concerns, and notably, the costly problem of transporting empty containers, which accounts for a significant portion of operational expenses worldwide and in Russia. The core contribution is a modified three-dimensional transport optimization model that incorporates container types, cargo volumes, and transportation costs, including the cost variations due to partially filled or empty containers. The model extends classical transportation problem formulations by introducing a potentials method that accounts for the contributions of suppliers, recipients, and container costs to determine an optimal transport plan minimizing total costs. Constraints ensure that supply and demand conditions, container capacities, and route feasibility are respected. The model uniquely integrates the degree of container filling into cost calculations using a coefficient to adjust transportation costs accordingly. This approach enables more accurate and cost-effective freight planning. Additionally, the article discusses the development of a simulation model and a client-server application to automate the search for optimal transport plans, facilitating practical implementation. The proposed framework can be expanded to include various container types, cargo characteristics, and transport modes, offering a comprehensive tool for improving logistics efficiency in container freight transportation.

Keywords: diversification of management, production diversification, financial and economic purposes of a diversification, technological purposes of ensuring flexibility of production

The article examines the network model of district management within the subsidized region from the point of view of the upper level, taking into account the optimal response of the districts – the Stackelberg equilibrium is found. The results obtained are compared with the corresponding results in the creation of horizontal and integrated coalitions of districts and the region. The author examines the preference for creating coalitions for all participants in the system. It has been proven that cooperation is more profitable for weak and medium-sized districts, hierarchy is more profitable for a strong district, and independence is more profitable for the region as for the upper level. It is not profitable for the strong elements of the system to join a coalition, while it is more profitable for the weak elements to join a coalition.

Keywords: network model, Nash equilibrium, Stackelberg equilibrium, resource allocation, Lagrange multiplier method, cooperation, horizontal coalition, maximal coalition, complex coalition, independent behavior

A set of techniques for obtaining retrospective, statistical, expert information, data integration, competence deficit assessment and knowledge management to compensate for competence deficit in organisational systems is presented. For the purpose of practical implementation of an integrated approach to improving the management of organisational systems, a model and an algorithm for obtaining data by applying a set of techniques have been developed. In the future, the proposed methodological solutions will significantly improve the efficiency of organisational systems management through the rational application of automated management systems with components of trusted artificial intelligence.

Keywords: algorithm, critical events, integration, information resources, recommendations, systematisation, efficiency

The article focuses on the integration of digital educational technologies (EdTech) into the management of organizational systems in the context of digital transformation in education. Special attention is given to the analysis of the interconnection between technological, organizational, and market components of EdTech, as well as their impact on optimizing business processes and management strategies in educational institutions. The aim of the study is to develop a comprehensive definition of EdTech that reflects its evolution and role as a tool for management transformation. The research methodology includes a systematic analysis of the EdTech concept, modeling the interaction between technologies and educational organizations, and a critical evaluation of case studies on digital platform implementation. As a result, the paper proposes defining EdTech as a dynamic ecosystem that integrates digital management, personalized learning, and organizational culture adaptation. The conclusions emphasize the necessity of an ecosystem approach to EdTech management, considering infrastructure limitations, staff training, and regulatory aspects. The findings can be applied to the development of digital transformation strategies for educational institutions, resource planning optimization, and the formation of sustainable business models in the EdTech sector.

Keywords: EdTech, digital transformation, educational technologies, business processes, system analysis, management

This paper explores the content-based filtering approach in modern recommender systems, focusing on its key principles, implementation methods, and evaluation metrics. The study highlights the advantages of content-based systems in scenarios that require deep object analysis and user preference modeling, especially when there is a lack of data for collaborative filtering.

Keywords: сontent - oriented filtering, recommendation systems, feature extraction, similarity metrics, personalization

The article formulates the task of developing a fire safety management procedure based on a risk-based approach, taking into account the preferences of the decision maker in the multi–criteria system "result - cost – time". A multi-criteria mathematical model of the procedure under consideration has been developed, as well as an algorithm for its implementation with the development of information technology and a test case.

Keywords: risk-based approach, fire risk, decision support systems, Pareto-optimal solutions

Introduction: Mobile Gaming Addiction (MGA) has emerged as a significant public health concern, with the World Health Organization recognizing it as a gaming disorder. Russia, with its growing mobile gaming market, is no exception. Aims and Objectives: This study aims to explore the feasibility of using neural networks for early MGA detection and intervention, with a focus on the Russian context. The primary objective is to develop and evaluate a neural network-based model for identifying behavioral patterns associated with MGA. Methods: A proof of concept study was conducted, employing a simplified neural network architecture and a dataset of 101 observations. The model's performance was evaluated using standard metrics, including accuracy, precision, recall, F1-score, and AUC-ROC score. Results: The study demonstrated the potential of neural networks in detecting MGA, achieving an F1-score of 0.75. However, the relatively low AUC-ROC score (0.58) highlights the need for addressing dataset limitations. Conclusion: This study contributes to the growing body of literature on MGA, emphasizing the importance of considering regional nuances and addressing dataset limitations. The findings suggest promising avenues for future research, including dataset expansion, advanced neural architectures, and region-specific mobile applications.

Keywords: neural networks, neural network architectures, autoencoder, digital addiction, gaming addiction, digital technologies, machine learning, artificial intelligence, mobile game addiction, gaming disorder

The article analyzes the existing programs for training the population in actions and organization of actions in the field of civil defense, as well as in the field of protecting the population from natural and man-made emergencies. Conclusions are drawn about the relevance of existing programs, problems in this area are highlighted, and solutions are proposed to increase the effectiveness of these teaching methods.

Keywords: natural emergencies, civil defense, emergency situations, civil defense, training program, population training, avalanches, life safety, railway

The article explores a model in which it is possible to predict the timing of obsolescence of a construction site. The purpose of the described techniques is to ensure stable operation and reliable operation of facilities. The presented methodological approaches make it possible to improve the accuracy of the assessment of degradation processes, covering both technical elements and structural parts of buildings and infrastructure systems. The article focuses on effective tools and methods used to survey the current state of real estate, as well as to anticipate changes in their performance over time. The paper considers the application of a generalized computational wear scheme that demonstrates changes in the organization and destruction of building elements throughout the service life. This scheme takes into account the continuous influence of external conditions on the structure of the structure. The universal formula proposed for the analysis serves as a research tool and displays the course of changes in the state of technical systems under the influence of prolonged loads.

Keywords: organizational and technological solutions, reliability, quality control, monitoring of compliance with standards, efficiency, production costs

This study is devoted to the analysis of decision-making models in ensuring the protection of public order. The results obtained will allow us to formulate a new mathematical model of decision-making, which will allow us to obtain objective management decisions to ensure the protection of public order in the territory of the Republic of Tajikistan with the possibility of simulation. The object of the study is the process of ensuring the protection of public order. In the scientific literature and in open sources of information, there is a large number of works describing models and algorithms developed on the basis of various mathematical tools. The analysis of a number of papers on this topic will allow us to formulate a new mathematical model of decision-making, which will optimize and improve the quality of prepared decision-making projects while ensuring the protection of public order. The study revealed that the basis for improving the effectiveness of ensuring the safety of citizens during mass events is an effective management decision. 1) Based on this, an analysis of decision-making models is presented, the purpose of which is to determine the need to create a decision-making model while ensuring the protection of public order in the Republic of Tajikistan. 2) A model of decision-making in ensuring the protection of public order in the Republic of Tajikistan is proposed. The model is implemented based on the synthesis of mathematical modeling methods, including cluster analysis, pairwise comparison method and Petri nets. The model allows you to divide committed events, i.e. crimes into clusters according to previously defined criteria. At the final stage, the model allows you to simulate each event, thereby predicting the possible development of the event under study. The presented results of the analysis of decision-making models made it possible to formulate a new mathematical model of decision-making in ensuring the protection of public order in the interests of the Republic of Tajikistan.

Keywords: public order protection, mathematical model, cluster analysis, pairwise comparison method, expert assessments, Petri nets

A two-level mathematical model of optimal management of investment and construction projects is proposed. The Customer acts as the upper-level or leading control entity in the model. The General Contractor is the lower-level control entity. It is assumed that both control entities strive to maximize their gain. The target function of the leader takes into account the estimated fixed income from apartment sales, profit from the velocity of money circulation, and the average estimated payment for work. The target function of the follower takes into account the payment for work from the Customer, additional payment or a fine, and payment for workers. The information regulations of the Stackelberg game are used in the study of the model. An algorithm for constructing a solution is given. In the general case, the problem is solved numerically by means of simulation modeling. The results of numerical experiments are given. A number of conclusions are made.

Keywords: two-level hierarchical model, Stackelberg equilibrium, customer, general contractor, leader, follower

This article reveals the features of the operation of information and measuring systems during gas transportation. The issues reflected in the article are particularly relevant in the context of the need to achieve the efficiency of information and measuring systems in the oil and gas industry. The purpose of the scientific research is to develop an approach to information and measuring systems in oil and gas organizations based on the digital twin model. To achieve this goal, the article analyzes practical cases of information and measuring systems in oil and gas organizations, reflects the features of certification of information and measuring systems used in oil and gas organizations, and presents the results of developing an approach to information and measuring systems in oil and gas organizations based on the digital twin model.

Keywords: information and measuring systems; oil and gas industry; certification; digital twin model; gas transportation; approach; work efficiency

The article analyzes modern methods of planning and rescheduling schedules for software development projects in conditions of dynamically changing requirements and limited resources. The scientific task of optimizing the management processes of the development team through the dynamic allocation of tasks is formulated, which is relevant due to the need to quickly respond to changes in the production calendar and project input data. The proposed solution is based on the use of a genetic algorithm to automate schedule rescheduling, which allows taking into account key performance criteria such as minimizing downtime, optimal load distribution among employees, and compliance with technological dependencies between tasks. The analysis showed that the dynamic rescheduling technique is able to quickly adjust the initial schedule when new requirements appear or working conditions change, which significantly improves the quality of planning and increases the system's resilience to external changes. The results of the study confirmed that the developed approach allows achieving an optimal balance between the usefulness of the work performed and the cost of adjusting the plan. The data obtained indicate that the use of genetic algorithms for dynamic schedule management in software development projects is highly promising, which opens up opportunities for further research in the field of flexible management methods and adaptive resource allocation in conditions of uncertainty.

Keywords: genetic algorithms, optimization problems, schedule theory, project management, the problem of ordering projects with limited resources

Concepts of organizational queueing system and organizational queuing system of the type "ralway - marine port" are introduced. We prove an activity of the main components of these queuing systems and present their characteristics. Relative to this class of organizational systems we specify the control problems and formulate the viability conditions which are required to provide sustainability.

Keywords: control in organizatioal systems,interaction between railway and marine ports, sustainable development

The purpose of developing the model and algorithms is to improve the management of public training in the field of public protection and civil defense of the Republic of Tajikistan as an integrated system that combines a set of interconnected elements that form its emergence and are determined by a set of functional properties, hierarchy and multiplicity of descriptions, as a complex organizational system [1]. The research uses methods of analysis and systematization. In particular, John Cotter's model of change is used, which allows structuring the process of managing the training of the population at different levels. Algorithms have been developed that take into account different social groups and their specific needs. This makes public education programs more adaptable and accessible to everyone. The obtained training algorithms can serve as a basis for improving public training management in the field of public protection and civil defense by integrating them into functional and infological models. The mathematical model of assessing the readiness of the population makes it possible to identify weaknesses in the training of the population and develop specific measures to eliminate them. The developed training management model and algorithms contribute to the formation of a structured system focused on the real needs of citizens. This includes their active participation in ensuring security, which, in turn, contributes to the creation of a more secure and secure environment in the country. The results of the study can be the basis for further development of the civil defense system in Tajikistan and improvement of training in the field of public protection and civil defense in emergency situations.

Keywords: civil defense, public training system, public training model, public training management, Republic of Tajikistan

In this work, an approach is considered, which makes it possible to obtain scientific-based management decisions on the development of organizational systems. The purpose of the work is to show in a particular example the development of a fuzzy cognitive model development process, to analyze the model for sustainability, to determine the activation vertex complexes. The toolkit for describing and analyzing a fuzzy cognitive model is based on the basic concepts of fuzzy graph theory. Simulation results are given, directed to the development of possible scenarios for the development of situations of a socio-economic system of the Rostov region. The results are clearly illustrated by examples of fourteen scenarios, the matching of which to the main factors made it possible to determine a plurality of pessimistic and optimistic and to give recommendations to the face receiving the decision.

Keywords: control, organizational system, cognitive model, simulation modeling, fuzzy graph, sustainability

Rapid urbanization in developing countries, particularly Iran and Turkey, has increased environmental challenges that require systemic and engineering-based strategies for managing sustainable development projects. This study presents a structured approach to engineering modeling and managing urban environmental projects using five metropolitan areas: Tehran, Mashhad, Isfahan, Shiraz, and Istanbul. Particular attention is paid to the socio-economic impacts of implementing sustainable initiatives, including job creation, cost reduction, and improved urban quality. Istanbul’s successful experience in integrating waste-to-energy systems and switching to electric public transport is compared with less effective and disparate practices in Iranian cities. Based on the analysis, policy recommendations are developed to promote interregional cooperation and form a coherent sustainable development framework for policymakers and urban planners.

Keywords: sustainable development, environmental project management, socio-economic effects, renewable energy, circular economy, waste-to-energy, urban infrastructure, Tehran, Mashhad, Isfahan, Shiraz, Istanbul

The article analyzes traditional and flexible project management methodologies, their key features, advantages and limitations. Traditional methodologies such as the waterfall model and the critical path method rely on sequential planning that is suitable for projects with fixed requirements. Agile methodologies (Agile, Scrum) are highly adaptable, which is important for projects with frequent changes. The authors compare the conditions of application of both approaches and describe the criteria for choosing a methodology depending on the type and dynamics of the project. The article will be useful for both practitioners and researchers in the field of project management.

Keywords: project management, project management methodology, cascade model, critical path method, program evaluation and review technique, agile software development, critical path method

In the article the sustainability of the network model of districts within the subsidized region is investigated both in terms of each of their dynamic parameters: fixed assets, labor population and its efficiency; and in their combination. In addition, the problem of the lower level in the hierarchical system is solved in the form of a Nash equilibrium – optimal district strategies are found for a given known distribution of subsidies by the region between them. It has been revealed that if there are subsidies to the district, agents do not care how much money is allocated to the development of the district, since all consumption of the district is provided by subsidies, and there are no subsidies to the district, it has to spend 90% of gross product to invest in production.

Keywords: continuous dynamic model, discrete dynamic model, subsidized region, target functions, share of investments, relationships between districts, fertility rate, mortality rate, fixed assets, labor population, Nash equilibrium

Distributed data storage systems (DSS) are multi-parameter, complexly configurable systems. Fault tolerance and reliability of DSS data storage are ensured by a set of different methods. To assess the efficiency of new methods, it is convenient to use software tools that simulate the operation of DSS. The purpose of this work is to study the existing software simulators of DSS to assess the potential of their use. The study is based on the analysis of several software simulators that model the operation of DSS. The analysis took into account such parameters as the choice of the redundancy introduction method, the data placement method, the data recovery algorithm after failure, and the choice of storage architecture. The results of the study show that simulators offer a wide range of options for modeling fault tolerance, but some of them demonstrate greater efficiency in some scenarios. A generalized structural diagram of the simulators is built, revealing the features of the architecture and principles of operation. The CR-SIM simulator has the greatest functionality, but its source codes and executable file are not available. Simulators with open source code do not have a flexible architecture for their expansion with new methods. The сonclusion is made about the need to develop a new simulator in the form of an open source software tool, the architecture of which is designed for its expansion. Such a simulator will allow testing new developments in the field of fault tolerance enhancement technologies.

Keywords: data storage system, fault tolerance, erasure codes, software simulator, dependability, simulation model

The study is devoted to the development of electronic and distance learning tools for mastering the skills of applying mathematical methods by specialists in the field of automated systems development. The concept (structure) of an automated information system (AIS) for managing the life cycle of exercises to study optimization methods has been developed and schematically presented. An important element of decision support in the AIS is software simulators (training and training components) that generate exercise options and automatically check them based on the properties of mathematical models of optimization problems. An algorithmic and prototype software for the training subsystem for monitoring the skills of solving optimization problems have been developed. Variations in the interfaces for constructing a mathematical model for an optimization problem by a student when performing an exercise in the AIS are demonstrated. Building a model in the interface and, accordingly, the complexity of the exercise depends on the number of model parameters that can be changed by the student. The simulator provides an integral assessment of the student's actions when performing the task. The introduction of the simulator into the digital educational environment of the university will automate and simplify the implementation of current and intermediate control of knowledge and skills in the disciplines studied.

Keywords: optimization problems, mathematical programming, decision support, software simulator, mathematical modeling of systems and processes, visual modeling

An optimization model has been developed for the minimum required number of employees carrying out transport security measures included in transport security units, taking into account the algorithm for distributing employees, including various groups according to individual functions performed at different security levels, as well as the likelihood of various threats to transport security.

Keywords: transport strategy, digitalization of transport security, cost optimization, transport security units, requirements for ensuring transport security