CMMSE: Linear programming under ϵ‐contamination uncertainty

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.