Implementation of an Algorithm for Scaling Matrices and Other Programs Useful in Linear Programming

Makowski, M. ORCID: https://orcid.org/0000-0002-6107-0972 & Sosnowski, J.S. (1981). Implementation of an Algorithm for Scaling Matrices and Other Programs Useful in Linear Programming. IIASA Collaborative Paper. IIASA, Laxenburg, Austria: CP-81-037

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Abstract

Matrix scaling is an operation in which the rows and columns of a matrix are multiplied by positive scalars such that the elements of the scaled matrix are similar in absolute magnitude. This can be very important when dealing with models in which matrix elements can take a wide range of values, especially since certain mathematical codes, such as MINOS, require that the absolute values of all non-zero elements should be "reasonably" close to one.

This paper describes the implementation of an optimal scaling method proposed by Curtis and Reid. The algorithm is outlined and a users' guide to the program implemented on the VAX at IIASA is given. (The scaling algorithm has been linked to the MINOS package at IIASA by Zenon Fortuna, who has also developed a rescaling routine linked to this package.)

Two other programs useful in linear programming are also described: the first is designed to print out a matrix by rows, and also gives diagnostic aid; the second makes it possible to merge up to five LP models into one, generating a resultant MPSX file that may be used to solve multicriteria problems.

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