Solving the matrix balancing problem An algorithm based on a modification of the transportation problem

Abstract

The classical matrix balancing problem has many applications in areas such as economics and statistics. Generally, solutions to instances of this problem are found by minimizing either a squared or entropy objective function. This paper introduces a new procedure for solving the problem derived from a weighted least absolute value objective function. An efficient algorithm, incorporating the ideas of piecewise linear programming with the traditional transportation algorithm, is developed and presented. A simple example is illustrated and a computer program, written in FORTRAN, is given. Finally, special features of the program are discussed.