A New Integer Linear Programming Model of Transportation Problem

The transportation problem has been a central focus in operational research, to determine the most cost-effective routes for moving goods or people. With the continuous development of modern logistics and the increasing complexity of supply chain management, optimizing transportation systems has become more crucial than ever. This paper introduces a novel approach that combines classical transportation problems with Minimum Spanning Tree (MST) techniques, enabling a more efficient way to address real-world logistics issues. Our model incorporates a topological graph that includes not only factories and retail stores but also intermediate warehouses to balance the flow of goods. To solve this problem efficiently, we propose a new Intger linear programming (ILP) model with flow balance constraints and using a CPLEX solver to get the numerical results. Through numerical experiments based on Chinas automobile transportation industry, we demonstrate the practical applicability of our approach in minimizing transportation costs. Additionally, we discuss future research directions,including the integration of dynamic demand and production capabilities.