Scalings in Linear Programming: Necessary and Sufficient Conditions for Invariance

Abstract

We analyze invariance of the conclusion of optimality for the linear
programming problem under scalings (linear, affine, . . . ) of various
problem parameters such as: the coefficients of the objective function,
the coefficients of the constraint vector, the coefficients of one or more
rows (columns) of the constraint matrix. Measurement theory concepts
play a central role in our presentation and we explain why such
approach is a natural one.

Keywords: Sensitivity Analysis, Scaling, Measurement