The method of finding the maximum possible carload with the minimum duration of its processing in a transport system represented by fuzzy triangular numbers is described. The transport system means a complex consisting of a marshalling yard, freight port station and seaport, operating in a single coordinated mode for processing the carriage traffic on the railway network. The actuality of this task lies in the fact that the existing methods of solution do not take into account possible changes in the operating conditions of transport facilities that may affect the duration of processing of the carriage traffic processing. The applied method takes into account the fuzzy nature of the duration of the execution of technological operations in the transport system, which makes it possible to take decisions that are more adapted to real conditions. The peculiarity of solving this problem is the application in the objective function of fuzzy coefficients of the duration of the execution of technological operations. For the first time, the work of the transport system has been considered, including not only objects for the promotion of freight railway cars within the railway network, but also their processing beyond its borders.