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Linear programming under ϵ‐contamination uncertainty

Journal Contribution - Journal Article

This paper considers a constrained optimisation problem with at least one element modelled as an ε-contamination uncertainty. The uncertainty is expressed in the coefficient matrices of constraints and/or coefficients of goal function. In our previous work, such problems were studied under interval, fuzzy sets, and probability-box uncertainty models. Our aim here is to give theoretical solutions to the problem under another advanced (and informative) ε-contamination uncertainty model and generalise the approach to calculate the theoretical solutions for linear cases. The approach is to convert the linear optimisation problem under uncertainty to a decision problem using imprecise decision theory where the uncertainty is eliminated. We investigate what theoretical results can be obtained for ε-contamination type of uncertainty model and compare them to classical case for two different optimality criteria: maximinity and maximality. A numerical example is considered for illustration of the results.
Journal: Computational and Mathematical Methods
ISSN: 2577-7408
Issue: 2
Volume: 2
Pages: 1 - 15