Spectral Properties of Structured Matrices in Transportation Problems
Abstract
The Hitchcock-Koopmans transportation problem is a well-known and fundamental optimization problem which focuses on minimization of the objective function which is basically the transportation cost from multiple sources to multiple destinations. In this article, we present some novel results on the spectral properties of structured matrices appearing in Hitchcock-Koopmanstransportation problems. The results on the computation of singular values are presented with usage of tools from linear algebra and matrix analysis. The new results are derived on interconnection between structured singular values of pseudo-inverse and D-stable matrices of Hitchcock-Koopmans transportation models. The numerical experimentation shows the behavior of singular values. The Matlab EigTool is used for the computation of pseudo-spectrum of pseudo-inverse matrix corresponding to the transportation model.