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  suggested the use of linear programming in addition to the Hungarian method. Specifically, we use the Birkhoff’s theorem to prove that the simplex method enables solving these problems. We also provide insights how to obtain a partition that includes a particular unit.
Discussion Paper Series (Hokkaido University), Ser. A, No. 2018-331, October 2018