<![CDATA[Efficient distribution route planning is a key factor in reducing logistics costs. This study compares the effectiveness of the Minimum Spanning Tree (MST) using the Kruskal and Floyd–Warshall algorithms against the Ant Colony Optimization (ACO) approach combined with the Travelling Salesman Problem (TSP) for optimizing mineral water distribution routes in Manado City, Indonesia. Distance data between six distribution points (one depot and five Indomaret outlets) were obtained from digital maps and modeled as a weighted graph. MST was analyzed using the Kruskal and Floyd–Warshall algorithms manually, then validated using POM-QM for Windows 5 software. The results show that MST with the Kruskal algorithm produces the shortest total distance of 9.14 km, consistent with software validation. In contrast, the ACO-TSP approach yields a longer distance of 18.14 km, or 98.5% longer. Computational complexity analysis reveals the superiority of Kruskal with O(E log E) compared to Floyd–Warshall with O(V³) and ACO with O(n²·t). In conclusion, for small-scale distribution networks with simple topology, the deterministic MST method outperforms the ACO metaheuristic. The optimal route generated is A→B→C→F→E→D with a total distance of 9.14 km.]]>
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