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Extended local stability radii for post-optimality analysis of linear multi-objective integer optimization problems
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AI
DOI：10.1080/0305215x.2026.2653667.png)
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Abstract
En 中文
Post-optimality analysis in linear programming is done through either the stability of the optimal solution (discrete decision variables) or the stability of a given optimal basis with respect to perturbations of the input data (continuous decision variables). Both approaches have been well studied in the literature. In this article, a post-optimality analysis technique is presented that is more general than the tolerance approach and less computationally expensive. Namely, this article extends the notion of local quasi-stability radii in order to allow perturbations into the input data. The present result is applied to ore production problems. As the input data might be of different magnitude, the advantage of this extension is to incorporate information provided by the decision maker into the computation of the local quasi-stability radii. Then, better individual tolerances of the input data of linear multi-objective optimization problems are obtained. The extension is based on the introduction of weighted norms in the formulation of the post-optimality analysis. The weighted norms account for the information provided by the decision maker.
Keywords:
Post-optimality analysis
prior information
individual tolerances
multi-objective optimization
ore production