TITLE:
Using the Simplex Method for a Type of Allocation Problems
AUTHORS:
Yoshihiro Tanaka
KEYWORDS:
Allocation Problems, Hall’s Theorem, Totally Unimodular Matrix, Simplex Method
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.9 No.2,
April
8,
2019
ABSTRACT: In this study we discuss the use of the simplex method to solve allocation problems whose flow matrices are doubly stochastic. Although these problems can be solved via a 0 - 1 integer programming method, H. W. Kuhn [1] suggested the use of linear programming in addition to the Hungarian method. Specifically, we use the existence theorem of the solution along with partially total unimodularity and nonnegativeness of the incidence matrix to prove that the simplex method facilitates solving these problems. We also provide insights as to how a partition including a particular unit may be obtained.