Some consequences on the planar three-index transportation problem

Abstract

In this study, some algebraic characterizations of the coefficient matrix A of the planar three-index transportation problem are derived and the equivalent formulation of this problem is obtained using the Kronecker product. It is shown that eigenvectors of the matrix G ⁺ G are characterized in terms of eigenvectors of the matrix A ⁺ A , where G ⁺ is the Moore–Penrose inverse of the coefficient matrix G of the equivalent problem.

Keywords:

• linear programming
• transportation problem
• equality constrained optimization problem
• generalized inverses

2000 AMS Subject Classifications :

• 90C08
• 15A09