Abstract
This study considers the task of planning the routes of multimodal transnational cargo transportation. Due to the extremely long length of such routes, delivery times and costs per cargo unit are extremely important. Delays in various types of transport and in the case of cargo transshipment are associated not only with the growth of cargo flows but also with the inconsistency of vehicle schedules. The purpose of this study is to improve the previously developed methodology for optimizing multimodal cargo transportation, taking into account the need for its application to transnational transport corridors. The content of the formulated network problem is reduced to a modification of the traveling salesman problem with an unknown number of transport points the route should pass through. Such a problem is NP-hard due to the time complexity of the algorithms. A modified algorithm has been developed, according to which the general problem with the number of N points is divided into several sub-problems. Transport points are grouped into consecutive subsets that are related by only one non-alternative way of transportation. This way can be any “bottleneck” of the transport network or an artificially created one. Such a decomposition of the problem gives a set of partial solutions, which were combined into the final optimal solution. The obtained solution to the routing problem of multimodal routes takes into account the cyclical schedules of the transport operation and gives a guaranteed exact optimum for calculations performed within the permissible time. In addition to determining the optimal route, the algorithm makes it possible to determine the required number of vehicles and their work schedules depending on the total cargo flow on the route.