 ### Journals Information

Mathematics and Statistics Vol. 9(2), pp. 81 - 92
DOI: 10.13189/ms.2021.090201
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## On Application of Max-Plus Algebra to Synchronized Discrete Event System

A. A. Aminu 1, S. E. Olowo 1, I. M. Sulaiman 2,*, N. Abu Bakar 3, M. Mamat 2
1 Department of Mathematics, Faculty of Mathematics and Computing, Kano University of Science and Technology Wudil, Nigeria
2 Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Besut Campus, 22200, Malaysia
3 Faculty of Applied Social Sciences, University Sultan Zainal Abidin, Terengganu, Malaysia

ABSTRACT

Max-plus algebra is a discrete algebraic system developed on the operations max ( ) and plus ( ), where the max and plus operations are defined as addition and multiplication in conventional algebra. This algebraic structure is a semi-ring with its elements being real numbers along with ε=-∞ and e=0. On the other hand, the synchronized discrete event problem is a problem in which an event is scheduled to meet a deadline. There are two aspects of this problem. They include the events running simultaneously and the completion of the lengthiest event at the deadline. A recent survey on max-plus linear algebra shows that the operations max ( ) and plus ( ) play a significant role in modeling of human activities. However, numerous studies have shown that there are very limited literatures on the application of the max-plus algebra to real-life problems. This idea motivates the basic algebraic results and techniques of this research. This paper proposed the discrepancy method of max-plus for solving n×n system of linear equations with n≤n, and further show that an nxn linear system of equations will have either a unique solution, an infinitely many solutions or no solution whiles nxn linear system of equations has either an infinitely many solutions or no solution in ( ). Also, the proposed concept was extended to the job-shop problem in a synchronized event. The results obtained have shown that the method is very efficient for solving n×n system of linear equations and is also applicable to job-shop problems.

KEYWORDS
Max Plus Algebra, Matrix Operations, Job-Shop Problem

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
 A. A. Aminu , S. E. Olowo , I. M. Sulaiman , N. Abu Bakar , M. Mamat , "On Application of Max-Plus Algebra to Synchronized Discrete Event System," Mathematics and Statistics, Vol. 9, No. 2, pp. 81 - 92, 2021. DOI: 10.13189/ms.2021.090201.

(b). APA Format:
A. A. Aminu , S. E. Olowo , I. M. Sulaiman , N. Abu Bakar , M. Mamat (2021). On Application of Max-Plus Algebra to Synchronized Discrete Event System. Mathematics and Statistics, 9(2), 81 - 92. DOI: 10.13189/ms.2021.090201.