Mathematical experiment in logistics research of multimodal freight transportation with time and cost indicators

Aim: Development of a new approach to optimizing the process of cargo flows distribution at the transport loop. Construction of a mathematical model of the freight transportation process, which equally takes into account the interests of various participants in the transportation process. Materials and Methods: A mathematical model of the freight transportation process is built, which is based on the infrastructure indicators of the considered part of the railway loop and is a multicriteria optimization problem of integer programming. The algorithm for solving the problem is common for land transport and is implemented in the environment of a computer algebra system. As a project, which is an example of the application of the developed transport and logistics method, a part of the North-Caucasian railway, adjacent to the main cargo ports of the Azov-Black Sea basin, is considered. The considered railway loop is a transit component, actively exploited for Russian exports, in particular, grain cargoes. Results: The issues of organizing rail freight transportation in multimodal transport and technological systems are researched on the basis of egalitarian and utilitarian approaches in welfare theory. These approaches are considered in relation to the participants in the transportation process (agents) within the framework of the time and cost indicators of this process. Computational procedures for finding optimal distributions of cargo flows have been brought to concrete results. Conclusion: A mathematical experiment used as a simulation modeling tool allows versatile and purposeful manipulation of the indicators of the transportation process and the restrictions imposed on transportation plans. The cargo flows distributions to port unloading stations obtained as a result of Pareto optimization are analyzed from the point of view of their rationality and usefulness in relation to agents.