Systems Evaluation and Repricing Theorems

When a system is described in terms of a linear programming problem max c^Tx with Ax ≦ b, x ≧ 0, study of its properties, e.g., sensitivity analyses, etc., focuses on effects of alterations in the triple (A, b, c) on the properties of the system. These effects are non-linear and generally lead one away from a model with convenient special structure to much more complex systems. In this paper, methods (“repricing-reprocessing” theorems) are developed which (under certain assumptions about real world behavior) permit one to assess these effects exactly by means of a model of the same structure which can be prescribed in advance. The proofs of these theorems are accomplished by the “chained construction” methods of Charnes and Cooper. Approximation techniques and exact characterization of the non-linearities are also presented.