On scaling linear programming problems

The scaling of linear programming problems remains a rather poorly understood subject (as indeed it does for linear equations). Although many scaling techniques have been proposed, the rationale behind them is not always evident and very few numerical results are available. This paper considers a number of these techniques and gives numerical results for several real problems. Particular attention is given to two “optimal” scaling methods, giving results on their speed and effectiveness (in terms of their optimality criteria) as well as well as their influence on the numerical behavior of the problem.