This article reviews the basic methodological approaches to the arrangement of the logistics supply of manufacturing, research or tourism facilities based in the Arctic. The main purpose of this article was to optimize the processes of supply the Arctic territories with the use of high-tech approach, which integrates the concept of “green” logistics technology (reverse logistics, in particular) and methods of economic and mathematical modeling for inventory management and planning the purchase of resources necessary to ensure the proper functioning of the Arctic facilities. Taking into account the fact that the Arctic holds interests of many countries and corporations, as well as taking into account the fact that further development of the Arctic must be environmentally responsible, the integration of traditional and new approaches to the arrangement of supply of the Arctic facilities through the use of reverse logistic technologies of economic and mathematical modeling using the correlation-regression analysis were proposed. © 2016, Econjournals. All rights reserved.