Optimizing unbalanced freight deliveries in transportation networks

Abstract

This paper reports a comparative analysis of the known methods for reducing open transportation problems to a balanced form in order to further optimize freight traffic based on them. A series of significant shortcomings have been revealed that largely narrow the scope of their application. A new method has been proposed, termed the method of proportional redistribution of cargo transportation volumes among participants in the transportation process, devoid of the identified shortcomings. The transportation problem is a special case of the general linear programming problem, to which one of the methods for solving it, namely the simplex one, can be applied. A procedure to construct a simplex table based on the data from the transport table has been described, as well as the algorithm of subsequent simplex transformations. A transportation problem is often stated in the form of a map of the location of transport hubs of cargo dispatch and destination. A matrix-network model has been proposed, which makes it possible to reduce the network representation to a matrix form with the subsequent finding of the optimal plan for cargo transportation. In order to identify the priority of methods for reducing open transportation problems to a balanced form, 100 transportation problems that are unbalanced in terms of the volume of cargo transportation were solved. That was done with the help of a designed decision support system for the management of freight transport. As a criterion, the best freight transportation plan was chosen. As a result, the simplex method proved the best in 48 cases, the coefficient method ‒ in 27, the dummy node method ‒ in 16, and the difference method ‒ in 9 cases. The use of a decision support system for the management of freight transport has increased its efficiency by an average of 25 %