Mathematical Programming and Solution Approaches for Transportation Optimisation in Supply Network

The problem of transport is a special type of mathematical programming designed to search for the optimal distribution network, taking into account the set of suppliers and the set of recipients. This article proposes an innovative approach to solving the transportation problem and devises source codes in GNU Octave (version 3.4.3) to avoid the necessity of carrying out enormous calculations in traditional methods and to minimize transportation costs, fuel consumption, and CO${}_2$ emission. The paper presents a numerical example of a solution to the transportation problem using: the northwest corner, the least cost in the matrix, the row minimum, and Vogel’s Approximation Methods (VAM). The joint use of mathematical programming and optimization was applicable to real conditions. The transport was carried out with medium load trucks. Both suppliers and recipients of materials were located geographically within the territory of the Republic of Poland. The presented model was supported by a numerical example with interpretation and visualization of the obtained results. The implementation of the proposed solution enables the user to develop an optimal transport plan for individually defined criteria.