MATHEMATICAL MODELS OF ROAD CONSTRUCTION, RECONSTRUCTION AND REPAIR UNDER CONDITIONS OF UNCERTAINTY

The article highlights the importance of mathematical modeling in road construction, reconstruction, and repair in Ukraine. We can outline the importance of this research by taking into account such factors as financial instability and financial uncertainty, as well as the importance to comply with safety standards during any road-related maintenance work. We would also like to point out that there is an increasing need for new tools for optimization and improvement of construction operations. This need exists both due to factors of uncertainty, such as climatic anomalies, dynamics of road traffic, and technological progress in construction, as well as due to numerous social challenges that result in an increase in traffic load, for instance, an ongoing military conflict. The main goal of our research is to implement mathematical modeling into different phases of any road-related maintenance work, from planning to executing, under conditions of limited finances. Achieving the aforementioned goal will allow to improve assessing and repairing the critical areas and will also improve the choice of optimal nondestructive inspection methods for identifying any damage in road coating and infrastructure. To achieve this goal, we use methods of statistical and system analysis, multi-criteria optimization, and decision-making theory. The main emphasis is on the development of strategic management decisions and their effectiveness. We have managed to prove that the use of mathematical modeling during the planning phase of any road works allows us to effectively distribute the available financial resources even if they are limited. This practice also makes it possible to dynamically alter the volumes of funding depending on expert analysis of the importance or project completion status. Upon completion of the initial planning stage, which includes repairing all critical areas of the road in order to minimize the risk of road traffic accidents and using methods of increased safety, we have managed to develop a plan with concrete steps. Following the aforementioned steps allows us to reduce a total number of road traffic accidents occurring in critical areas by 1.4-1.6 times. These results are possible to achieve without going over the established financial restrictions. We have also developed criteria for assessing the quality of damage identification on the road coating. These criteria are based on the defect detection rate. We have provided a detailed explanation of how this rate can increase from 0,891 to 0,967. Further scientific research conducted by the author of this paper will focus on a detailed analysis of the results of the implementation of illustrated mathematical models, especially as mathematical support of the analytical and information system for monitoring the state of road infrastructure.