Mathematical Modeling of the Reliability of Mixed Cargo Transportation Under Dynamic Change of Conditions

Abstract

Topicality. Military threats determined the significant pace of changes in the risks of mixed cargoes transportation and proved the need for new methods of ensuring the reliability of transportation. First of all, there was the problem of assessing the levels of transportation reliability along individual routes and modeling a possible change of routes with the choice of safer options and ways of transportation. A particularly important function of such a model, due to the rapid pace of changes in risks, is the possibility of its practical application in real-time conditions.Aim and tasks. The purpose of the work is to develop a mathematical model of mixed cargo transportation in the conditions of dynamic changes in risks to increase the reliability of the transportation process, analyze alternative options for transportation, and identify opportunities for changing the route even in the process of cargo transportation. Achieving the goal of the study made it necessary to set and solve the following tasks: to implement the possibility of analyzing alternative transportation options and proposing route changes in real time; prove the capabilities of the developed model on the example of specific enterprises; to ensure reliability forecasting of the next cargo transportation stages; implement the possibility of optimizing multi-purpose tasks to ensure reliability, minimize the cost and time of transportation; to stratify the reliability of cargo transportation according to the level of threats probability.
 Materials and methods. Various general and special methods of knowledge were used in the work: the method of quantitative and qualitative comparison for the stratification of the cargo transportation reliability depending on the risks at individual stages; methods of vector analysis to take into account the probability of the cargo transportation risk at each stage of mixed transportation; the method of induction and deduction made it possible to consider the reliability of the transportation as the reciprocal of the transportation risk probability; the task fragmentation method allows to include probable stages of transportation in different transport routes; a method of mathematical formalization of the problem for the formation of a model of mixed cargo transportation using water transport in conditions of dynamic changes in risks.
 Research results. A mathematical model of mixed cargo transportation in conditions of dynamic changes in risks was developed to increase the reliability of transportation, analyze alternative transportation options, and identify opportunities for changing the route during cargo transportation. To solve this, the following tasks were developed: a mathematical model capable of analyzing alternative transportation options and proposing route changes in real life was developed; proven possibilities of the model on the example of specific enterprises; forecasting of the reliability the next cargo transportation stages is ensured; the possibility of optimizing multi-purpose tasks to ensure reliability, minimizing the cost and time of transportation has been implemented; stratification of the reliability cargo transportation by the level of probability threats was carried out.
 Conclusion. Using the model, the activities of enterprises that transported their products through the ports of the Sea of Azov were analyzed. Due to the decrease in the reliability of cargo transportation through the Kerch Strait, alternative routes for the transportation of mixed cargo are proposed, for the use of "river-sea" vessels at certain stages. Approbation of the model for increasing the efficiency of the transport and logistics process of enterprises proved its effectiveness. The use of the developed mathematical model for the analysis of enterprise activity indicated an implicit advantage of increasing the level of transportation reliability, in particular, in relation to identifying the possibility of reducing warehouse stocks with a significant saving of working capital at the same time. The presented results of the research make it possible to ensure the proper reliability of transportation of mixed cargoes, even in conditions of significant dynamic changes in the level of threats on transportation routes.