Application of mathematical methods in logistics: using the traveling salesman problem and the auction method from game theory to optimize the selection of transport companies and cargo consolidation points

Abstract
This article discusses the application of mathematical methods in logistics to optimize the selection of transport companies and cargo consolidation points. Focusing on the Traveling Salesman Problem (TSP) as a core model, the authors demonstrate how to minimize transportation costs and time by finding efficient routes. Furthermore, the study introduces the Auction Method from game theory to allocate tasks and resources among multiple carriers, ensuring fair competition and optimal pricing. The proposed framework combines combinatorial optimization and strategic bidding, thereby enhancing decision-making in supply chain management. Our findings underscore the value of advanced mathematical models for streamlining logistic operations and reducing operational risks in complex multi-agent environments.