Linear programming under p-box uncertainty model

Abstract

This paper considers a constrained optimisation problem under uncertainty with at least one element modelled as a probability box 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 ε-contamination uncertainty models. Our aim here is to give theoretical solutions to the problem under more advanced and informative (p-box) uncertainty model and generalise the approach to calculate the theoretical solutions for linear programming problems. The approach is to convert the 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 probability box type of uncertainty model and compare them to classical cases for two different optimality criteria: maximinity and maximality.