Abstract
This study investigates the integration of the Minimum Cost Flow (MCF) method with the Traveling Salesman Problem (TSP) to optimize distribution within supply chain networks, addressing inefficiencies in delivery routing. The primary contribution lies in demonstrating how combining MCF with TSM can significantly reduce travel distances and the number of trips required to meet demand. The study employs a hybrid optimization approach, where MCF is used to allocate supplies efficiently to demand nodes, and TSP is applied to optimize the sequence of deliveries, ensuring minimal travel distance. A case study is conducted to compare the performance of using MCF alone versus the combined MCF+TSP approach in a real-world distribution scenario. The results show that the MCF-only method covered a total distance of 289.18 km and required 22 trips to fulfill demand. In contrast, integrating TSP reduced the total distance to 63 km—a 78.21% improvement—and cut the number of trips to just 3. These findings underscore the effectiveness of the combined approach in reducing transportation costs and streamlining logistics operations. The study concludes that while MCF is valuable for balancing supply and demand, its integration with TSM provides a more holistic solution that optimizes both cost and route efficiency. The results highlight the practical implications for supply chain managers seeking to enhance efficiency and sustainability in their operations. Future research is recommended to explore real-time data integration and the scalability of the combined method in larger and more complex logistics networks.

Key words: Supply Chain Optimization; Minimum Cost Flow (MCF); Traveling Salesman Problem (TSP); Route Optimization; Logistics Efficiency.