Matrix balancing : a comparative study /

Abstract

The problem of "balancing" a matrix is not new, but there have been many changes in the methods used to find a balanced matrix. This paper will introduce several different methods and present the various algorithms using a uniform notation. The algorithms will be derived, detailed, and finally applied to the same sample problem in order to compare the results. Although the first three algorithms are undoubtedly faster, the Modified Transportation Model offers more flexibility. It returns a fmal matrix that is often in a more usable form, in light of the various applications. The software package "EXCEL" by Microsoft was chosen for testing these methods for a variety of reasons. Although code is readily available for similar algorithms in various programming languages, the applications of matrix balancing problems are seldom taken into consideration; these applications are in the fields of business and industry, where this particular software is already being used and is easy to access.