<![CDATA[Optimizing the use of train sets is an important problem in the management of rail transportation operations. From the naked eye, the equal number of trips in two directions does not necessarily reflect the minimum number of circuits required operationally. This research aims to model the Sawunggalih train travel schedule in the form of a Directed Acyclic Graph (DAG) and determine the minimum number of trains using the Minimum Path Cover (MPC) approach. DAG is built based on the possibility of continuing the journey without time and location conflicts. Next, the graph is transformed into a bipartite graph to obtain maximum matching using the Hopcroft–Karp algorithm. The research results show that from six daily trips, the maximum matching value obtained produces a Minimum Path Cover of two, so theoretically only two trains are needed to serve the entire schedule without conflict. This approach proves that graph modeling provides a more efficient mathematical solution than conventional estimation based on operational intuition.]]>
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