TY  - JOUR
UR  - http://fmipa.uny.ac.id
AV  - public
TI  - SYSTEMS OF INTERVAL MIN-PLUS LINEAR EQUATIONS  AND ITS APPLICATION ON SHORTEST PATH PROBLEM  WITH INTERVAL TRAVEL TIMES
KW  - Min-Plus Algebra
KW  -  Linear System
KW  -  Shortest Path
KW  -  Interval.
ID  - UNY11494
A1  - M. Andy, Rudhito
A1  - D. Arif Budi, Prasetyo
PB  - Yogyakarta State University
N2  - The travel times in a network are seldom precisely known, and then could be represented into the interval of real number, that is called interval travel times. This paper discusses the solution of the iterative systems of interval min-plus linear equations its application on shortest path problem with interval travel times. The finding shows that the iterative systems of interval min-plus linear equations, with coefficient matrix is semi-definite, has a maximum interval solution. Moreover, if coefficient matrix is definite, then the interval solution is unique. The networks with interval travel time can be represented as a matrix over interval min-plus algebra. The networks dynamics can be represented as an iterative system of interval min- plus linear equations. From the solution of the system, can be deter-mined interval earliest starting times for each point can be traversed. Furthermore, we can determine the interval fastest time to traverse the network. Finally, we can determine the shortest path interval with interval travel times by determining the shortest path with crisp travel times.
Y1  - 2014/05//
JF  - Proceeding of  International Conference On Research, Implementation And Education  Of Mathematics And Sciences 2014
ER  -