In the situation of rapidly developing e-commerce, there is a need to expand the possibilities of cargo delivery. Of course, there is the problem of optimizing transport routes. The problem of probabilistic mathematical modeling of the carriers preferences of and their clients is considered. Patterns of preferences are formulated based on the solution of a multicriteria problem. Choosing a route by a random carrier is considered as an optimization problem with a random preference function. We investigate the case of a random delivery time. The results of this study can also be useful for mathematical modeling of transport networks.