MODEL OF THE TRANSPORT PROBLEM IN THE CASE OF CARGO DELIVERY BY TWO DIFFERENT TYPES OF VEHICLES
https://doi.org/10.33815/2313-4763.2025.2.31.178-186
Abstract
The article considers the features of modeling the transport problem in the case when the cargo can be delivered by two different types of vehicles. The classical transport model does not take into account the variability of transportation costs by type of transport, which requires the construction of special mathematical models and methods for reducing them to a standard form. The aim of the work is to construct special types of models of the transport problem in the case of cargo delivery by the number of types of vehicles, more than two, and to propose algorithms for solving such transport problems by reducing them using appropriate procedures to the classical model. Three approaches to the formalization of multimodal transportation have been developed. The first approach is based on the sequential transportation of cargo by both types of transport, which involves the formation of a final cost matrix as the sum of the corresponding elements of a three-dimensional matrix. The second approach involves the choice of the type of transport that provides the lowest delivery cost for each individual “supplier–consumer” connection. The third approach is based on the introduction of a probability matrix or partial cargo shares, which determine what part of the cargo should be transported by each mode of transport. For each of the models, procedures are proposed for reducing the three-dimensional cost structure to a two-dimensional form, which allows the application of the potential method to find the optimal transportation plan. The numerical examples presented confirm the correctness and practical applicability of the proposed models. The results obtained can be used to optimize logistics schemes, manage multimodal transportation, and also to develop software tools to support decision-making in transport systems.
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