By Harvey J. Greenberg, Richard P. O'Neill
Communications of the ACM,
July 1981,
Vol. 24 No. 7, Pages 451-456
10.1145/358699.358712
Comments
This paper describes a form of purposeful data perturbation in a linear programming model which pertains to uncertainties in the magnitudes of the matrix coefficients. A problem in value pool construction is described first, then a resolution based on a new concept, “covering lattices.” Computer representations of real values, limited by finite precision, is an example of a covering lattice. After presenting the strategy and tactical variations, the effects of resident distortion are analyzed. Several theorems are presented that measure bias under a variety of assumptions. An appendix is included that contains mathematical proofs.
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