This article considers the use of the entropy method in the optimization and forecasting of multimodal transport under conditions of risks that can be determined simultaneously by deterministic, stochastic and fuzzy quantities. This will allow to change the route of transportation in real time in an optimal way with an unacceptable increase in the risk at one of its next stages and predict the redistribution of the load of transport nodes. The aim of this study is to develop a mathematical model for the optimal choice of an alternative route, the best for one or more objective functions in real time. In addition, it is proposed to use this mathematical model to estimate the dynamic change in turnover through intermediate transport nodes, forecasting their loading over time under different conditions that also include long-term risks which are significant in magnitude. To substantiate the feasibility of the proposed mathematical model, the analysis and forecast of cargo turnover through the seaports of Ukraine are presented, taking into account and analysing the existing risks.

中文翻译：

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熵作为优化多式联运的目标函数

本文考虑在风险可以由确定性、随机和模糊量同时确定的条件下，熵方法在多式联运的优化和预测中的应用。这将允许以最佳方式实时改变运输路线，在下一阶段的风险增加不可接受的情况下，并预测运输节点负载的重新分配。本研究的目的是为替代路线的最佳选择开发一个数学模型，实时选择一个或多个目标函数的最佳选择。此外，建议使用该数学模型来估计通过中间运输节点的周转量的动态变化，预测它们在不同条件下随时间推移的负载，这些条件还包括具有重大意义的长期风险。为了证实所提出的数学模型的可行性，我们对通过乌克兰海港的货物周转进行了分析和预测，同时考虑并分析了现有风险。