One of the most remarkable theories in probability and statistics is the law of large numbers. Law of large numbers describes the behavior of random phenomena when they are reiterated infinitely or in very large trials. Apart from the mathematical exposition of the law of large numbers, its theory and applications have been widely used in gambling houses, financial sectors, and healthcare insurance where uncertainties deteriorate prediction and financial strength. However, the applications of the law of large numbers are not confined to the referred sectors and could be widely applied to industrial organizations and service provider companies in which large number of stochastic phenomena incorporate in their planning. In this thesis, the applications of the law of large numbers are studied in relation to logistics and transportation under conditions of operating in large networks. The results of this study assert that transportation companies can benefit from operating in large networks to increase the filling performance of their vehicles, fleet, etc. Equivalently, according to the law of large numbers the inferior capacity utilization in unit loads, containers, etc. converges to 0 with probability 1 as the size of the network grows. / Uppsatsnivå: D