SOLUSI MASALAH EIGEN DALAM ALJABAR MAX-PLUS DENGAN MENGGUNAKAN PROGRAM LINEAR; ( EIGENPROBLEMS SOLUTION IN MAX-PLUS ALGEBRA USING LINEAR PROGRAMMING )

Trioni Indahsah Anggraini, Ari Suparwanto

2015 | Disertasi | FMIPA

One example of dynamic event system is the transportation system. In operational issues, there are two interesting questions on the transportation system, ”how to set the system in order to ensure that it moves forward in regular steps, i.e. so that for a given constant ?, the interval between the beginnings of consecutive cycles on every crossroad is ?? In addition, suppose that there is a given schedule for the system, and the time interval between two consecutive starts of all jobs should not exceed a certain value ?, is it possible to start the system in such a way that the schedule will be kept? The first problem is closely related to eigenproblems, and the second problem related to the sub-vector eigen. This paper gives an overview of eigen problem (eigenvalues and eigenvectors) in max-plus algebra related to finitely soluble eigenproblem. It discusses about criteria for existence of finite eigenvectors and description of all finite eigenvector for any square matrix. Furthermore, this paper will be also discussed about sub-eigenvectors problem, that if it is related to linear programming problem, it will obtain a method of finding eigenproblem solution.

Kata Kunci : N