A fresh view on the tolerance approach to sensitivity analysis in linear programming

A fresh view on the tolerance approach to sensitivity analysis in linear programming The tolerance approach to sensitivity analysis in linear programming aims at finding a unique numerical value (tolerance) representing the maximum absolute perturbation which can be applied simultaneously and independently on each right-hand-side or objective coefficient without affecting the optimality of the given basis. Some extensions have been proposed in the literature, which allow for individual tolerances for each coefficient, thus enlarging the tolerance region. In this paper we review the main results concerning the approach, giving new and simpler proofs, and we propose an efficient geometric algorithm returning a tolerance region that is maximal with respect to inclusion. We compare our method with the existing ones on two examples, showing how a priori information can be naturally exploited by our algorithm to further enlarge individual tolerances. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png European Journal of Operational Research Elsevier

A fresh view on the tolerance approach to sensitivity analysis in linear programming

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Abstract

The tolerance approach to sensitivity analysis in linear programming aims at finding a unique numerical value (tolerance) representing the maximum absolute perturbation which can be applied simultaneously and independently on each right-hand-side or objective coefficient without affecting the optimality of the given basis. Some extensions have been proposed in the literature, which allow for individual tolerances for each coefficient, thus enlarging the tolerance region. In this paper we review the main results concerning the approach, giving new and simpler proofs, and we propose an efficient geometric algorithm returning a tolerance region that is maximal with respect to inclusion. We compare our method with the existing ones on two examples, showing how a priori information can be naturally exploited by our algorithm to further enlarge individual tolerances.

Journal

European Journal of Operational ResearchElsevier

Published: Nov 16, 2005

References

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