CMMSE: Linear programming under ϵ‐contamination uncertainty. Issue 2 (29th January 2020)

• Record Type: Journal Article
• Authors: Shariatmadar, Keivan; De Ryck, Matthias; Driesen, Kristof; Debrouwere, Frederik; Versteyhe, Mark
• Is Part Of: Computational and mathematical methods. Volume 2:Issue 2(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-01-29
• Subjects: decision theory -- maximality & maximinity -- uncertain linear programming -- ϵ‐contamination; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1077
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract : This paper considers a constrained optimization problem with at least one element modeled 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 generalize the approach to calculate the theoretical solutions for linear cases. The approach is to convert the linear optimization 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.