The problem of the optimal arrangement of the auxiliary fleet of a small shipping company that transports supply cargoes in the regions of the Eastern Arctic is discussed in the paper. The «small shipping company» term in the framework of the study means that the transport company has a small number of vessels (from two to three) under its management and carries out cargo transportation in one single direction. Since mathematical modeling and model experiment make it possible to speed up the process of making a managerial decision and bring it to a higher quality level, it is proposed, within the framework of the developed methodological support for the planning and management of the fleet of a small shipping company, to use one of the mathematical models of production planning of maritime transport and adapt it to the investigated technological process. It is known that one of the conditions for the successful development of the sea freight transport system and infrastructure modernization is the optimal use of the port fleet resources. For this reason, the object of optimization for the mathematical model is the process of performing offshore transshipment operations using the resources of the port fleet. The result of the study is a mathematical model for the arrangement of barges for the carriage of goods on a raid, which allows, among other things, to determine the optimal need for each type of available floating craft for handling ships arriving for unloading. When distributing the tug fleet, the option of attaching the thrust to the tonnage was considered, in which the tug changes the vessel in each port of the line, thereby achieving the maximum degree of utilization and the minimum costs for the maintenance of the tug per ton of cargo.