<![CDATA[This study aims to analyze the existence of eigenvalues in the min-plus algebra matrix structure and to explain their relevance to shortest path problems in defense logistics systems. The method used is a literature study of sources discussing the theory of eigenvalues, eigenvectors, precedence graphs, minimum mean weight of elementary circuits, and the application of eigenvalues in the min-plus algebra matrix structure to shortest path determination. The results show that eigenvalues in the min-plus algebra matrix structure always exist due to the existence of the minimum mean weight of elementary circuits in the precedence graph of the min-plus algebra matrix structure. These eigenvalues have a mathematical interpretation as the minimum cycle time of a system, making them relevant for application in optimizing defense logistics distribution routes. The conclusion of this study shows that the existence of eigenvalues in the min-plus algebra matrix structure can serve as a mathematical basis for more efficient shortest path planning, particularly in minimizing delays in logistics distribution in the defense sector. Keywords: Min-plus Algebra, Precedence Graph, Defense Logistics, Eigenvalues, Shortest Path ]]>
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