Methods of Optimizing the Supply Based on the Distribution Network with Implications for Sustainable Transport

This work explores the organization of a supply system within a military transportation network. The nodes of the studied network, comprising suppliers and recipients of supplies (representing delivery and collection points), were geographically identified, as well as the volume of cargo transported in each connection. The idea was to improve the efficiency of supply within the network, understood as minimizing total transportation costs. Calculations were performed using three methods: North–West Corner Method (N-WCM), least cost in the matrix method (LCMM), and Vogel’s Approximation Method (VAM). As a result of the calculations, basic feasible solutions (BFS) were obtained for each method, satisfying the constraint conditions. Each BFS was degenerate, because each contained m + n − 1 basic (non-zero) elements. In accordance with the calculation methodology, optimization was performed for each BFS using the potential method. For N-WCM and LCMM, up to five iterations were required, while for VAM, only one iteration was sufficient, confirming the best performance for this method. In addition to the total transport costs, additional criteria such as total distance, fuel consumption and CO2 emissions were considered.