M. Andy, Rudhito and D. Arif Budi, Prasetyo (2014) SYSTEMS OF INTERVAL MIN-PLUS LINEAR EQUATIONS AND ITS APPLICATION ON SHORTEST PATH PROBLEM WITH INTERVAL TRAVEL TIMES. Proceeding of International Conference On Research, Implementation And Education Of Mathematics And Sciences 2014. (Submitted)
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Abstract
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.
| Item Type: | Article |
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| Uncontrolled Keywords: | Min-Plus Algebra, Linear System, Shortest Path, Interval. |
| Subjects: | Prosiding > ICRIEMS 2014 > MATHEMATICS & MATHEMATICS EDUCATION |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Pendidikan Matematika > Matematika |
| Depositing User: | Eprints |
| Date Deposited: | 07 Nov 2014 04:28 |
| Last Modified: | 07 Nov 2014 04:28 |
| URI: | http://eprints.uny.ac.id/id/eprint/11494 |
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