In max-plus algebra, some algorithms for determining the eigenvector of irreducible matrices are the power algorithm and the Kleene star algorithm. In this research, a modified Kleene star algorithm will be discussed to compensate for the disadvantages of the Kleene star algorithm. The Kleene star algorithm’s time complexity is O(n(n!)), and the new Kleene star algorithm’s time complexity is O(n4), while the power algorithm’s time complexity cannot be calculated. This research also applies max-plus algebra in a railroad network scheduling problem, constructing a graphical user interface to perform schedule calculations quickly and easily.
