Symmetry-Based Route Optimization for International Land Logistics Using an Extended Traveling Salesman Problem with Distance–Time Constraints and Real-Time Google Maps Data

This study develops novel mathematical models to capture the complexities of international land logistics by extending the classical Traveling Salesman Problem (TSP) within a symmetry-aware optimization framework. A focused review of literature provides the theoretical basis for model formulation and highlights the limitations of conventional distance-only approaches. In international transport, shorter routes are often assumed to reduce energy use; however, this assumption overlooks the decisive influence of travel time and traffic variability. In this context, symmetry offers a useful analytical lens, as balanced relationships among distance, time, and fuel consumption can reveal more efficient logistics structures. Accordingly, two models are proposed: the Traditional Traveling Salesman Problem in terms of Distance Concentration (TTSPD), which minimizes route length, and the Extended Traveling Salesman Problem in terms of Distance and Time Concentration (ETSPDT), which jointly considers distance, travel time, and fuel consumption. Furthermore, TTSPD was employed to validate ETSPDT, since it is based on the traditional TSP. Both models are solved exactly using the Solver Add-in in Microsoft Excel 2024 with data derived from Google Maps. The results show that ETSPDT achieves superior energy efficiency and average speed, demonstrating the practical value of multidimensional, symmetry-informed optimization for sustainable supply chain and logistics management.