Using the Simplex Method for a Type of Allocation Problems

• 作者: Yoshihiro Tanaka
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: ALLOCATION PROBLEMS Hall’s THEOREM Totally Unimodular MATRIX SIMPLEX Method
• 年，卷（期）: 2019,（2）
• 页码范围: 25-31
• 页数: 7页
• 分类号: O1

摘要

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.