Max-plus Algebra and Application to Matrix Operations

Abstract

This paper study mathematical theory, called the max-plus algebra, which have the wherewithal for a uniform treatment of most problems that arise in the area of Operations Research. The basic properties of max-plus algebra is also explained including how to solve systems of max-plus equations. In this paper, the discrepancy method of max-plus is used to solve n×n and m×n system of linear equations where m ≤ n. From the examples presented, it is clear that an n × n system of linear equations in (max, ⊕,⊗) and (,+, ·) either had One solution, an In nite number of solutions or No solution. Also, both m × n system of linear equations (where m < n) in (max,⊕,⊗) and (,+, ·) have either an in nite number of solutions or no solution. It is therefore clear that many charateristics of the max-plus algebraic structure can be likened to the conventional mathematical structures. Max-plus is used to solve di erent types of matrix operations. We also applied max-plus algebra in solving linear programming problem involving linear equations and inequalities.