The article deals with the problem of estimating the rational number and utilization rate of the vehicles' fleet. According to the analysis results of the state-of-the-art literature it has been revealed that the issue of substantiating the rational fleet size and the rate of its utilization were not fully solved. The purpose of the study was to increase the efficiency of servicing transportation orders by determining the required number of vehicles. The goal of the research was the influence of the transportation process parameters on the truck utilization rate. Originating from the probabilistic nature of the transportation process, it has been proposed to use the AnyLogic software product to develop a simulation model for vehicle orders' servicing. From the processing of the experimental results by the regression analysis methods, it has been found that the dependence of changes in the vehicle utilization rate is of a linear form.