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:
[1] 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.