Max-plus Algebra and Application to Matrix Operations

This paper study mathematical theory, called the max-plus algebra, which have the wherewithalfor a uniform treatment of most problems that arise in the area of Operations Research. Thebasic properties of max-plus algebra is also explained including how to solve systems of max-plusequations.In this paper, the discrepancy method of max-plus is used to solven×nandm×nsystem of linearequations wherem≤n. From the examples presented, it is clear that ann×nsystem of linearequations in (Rmax,⊕,⊗) and (R,+,·) either had One solution, an In nite number of solutionsor No solution. Also, bothm×nsystem of linear equations (wherem < n) in (Rmax,⊕,⊗) and(R,+,·) have either an in nite number of solutions or no solution. It is therefore clear that manycharateristics of the max-plus algebraic structure can be likened to the conventional mathematicalstructures. Max-plus is used to solve di erent types of matrix operations.We also applied max-plus algebra in solving linear programming problem involving linearequations and inequalities.