Algorithms for Transportation Logistics Problems

At the present time almost every city faces traffic jams problem. Obviously, it is a source of traffic accidents, discomfort for residents and economic problems, connected with waste of employee time and etc. The problem has been researched since the fifties years of twenties century. Since then, several effective approaches to solving the problem of traffic jams have appeared which have been successfully implemented in large cities and urban agglomeration around the world, including Moscow, New York and others. But this algorithms need to be regular updated because of city-network growth and increase in the number of participants. Consequently, this issue became more significant and attractive for researches. Therefore, the traffic flows distribution problem is considered in this paper. Modern researchers consider the opportunity of applying various algorithms to solve this problem including heuristics algorithms. The purpose of this paper is to investigate a mathematical model of the transport network of a large city or urban agglomeration, designed for transport flows prediction. An essential feature of the model is: current version does not take into account the time of day, the concept of “generalized price” movement as a criterion for estimation of the routes and inter-district “transport” distances. The article contains description and result of software implementation of a three-stage Beckmann model with the Franke-Wulff algorithm established using the python programming language Key words: traffic jam, mathematical model, transport network, flows prediction, generalized price, three-stage Beckmann model, Franke-Wulff algorithm, Python.