An integrated approach is proposed in the study of rational schemes for the distribution of cargo flows at a regional transport loop for multimodal transportation, considered within the framework of an oligopolistic market. A technique has been developed for the parallel application of two approaches, differing in their mathematical nature, to the issues of increasing the economic efficiency of these transportations. The results obtained by the previously developed method of economic and geographical delimitation of «influence areas» of loading stations serve as a justification for the correctness of the results obtained by using an algorithm based on the Pareto optimization of the freight transportation process. Rational variants for organizing the freight transportation, taking into account time and cost indicators, have been obtained. The system of analytical calculations is used as a software tool to obtain a mathematically sound and transport-logistic diversified model of a regional oligopolistic freight market.
The process of multimodal freight transportation on a railway loop is investigated, for which a multicriteria optimization model with time indicators is created, which is a nonlinear integer programming problem. The developed approach is based on egalitarian and utilitarian principles in the welfare theory and allows (along with Pareto optimal transportation plans) to find other plans that can be considered rational from the point of view of maintaining the balance of interests of the transportation process participants. A mathematical experiment is an effective heuristic tool in research. The algorithm for solving the optimization problem is implemented in the environment of a computer algebra system and brought to numerical results.
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