Timetable design for a helicopter maintenance process using timed event petri nets and max-plus algebra

In this paper an algorithm for computing a generalized eigenmode of reducible regular matrices over the max-plus algebra is applied to a helicopter maintenance process. A timed event Petri net model is constructed from the state transition dynamics table that characterizes the transport system. A max-plus recurrence equation, with a reducible and regular matrix, is associated to the timed event Petri net. Next, given the reducible and regular matrix, the problem consists in giving an algorithm which will tell us how to compute its generalized eigenmode over the max plus algebra. The solution to the problem is achieved by studying some type of recurrence equations. In fact, by transforming the reducible regular matrix into its normal form, and considering a very specific recurrence equation, an explicit mathematical characterization is obtained, upon which the algorithm is constructed. The generalized eigenmode obtained sets a timetable for the helicopter maintenance process.