Robust optimization is based on the assumption that uncertain data has a convex set as well finite termed uncertainty. The discussion starts with determining robust counterpart, which accomplished by assuming indeterminate in form of boxes, intervals, box-intervals, ellipses, or polyhedra. In this study, counterpart characterized box-interval uncertainty set. formulation also associated master ...

This paper presents a multi-objective model for location-transportation problem under uncertainty that has been developed to respond to crisis. In the proposed model, humanitarian aid distribution centers (HADC), the number and location of them, the amount of relief goods stored in distribution centers, the amount of relief goods sent to the disaster zone, the number of injured people transferr...

Abstract. We consider a conic-quadratic (and in particular a quadratically constrained) optimization problem with uncertain data, known only to reside in some uncertainty set U . The robust counterpart of such a problem leads usually to an NP-hard semidefinite problem; this is the case, for example, when U is given as the intersection of ellipsoids or as an n-dimensional box. For these cases we...

We consider linear programs with uncertain parameters, lying in some prescribed uncertainty set, where part of the variables must be determined before the realization of the uncertain parameters (”non-adjustable variables”), while the other part are variables that can be chosen after the realization (”adjustable variables”). We extend the Robust Optimization methodology ([1, 3, 4, 5, 6, 9, 13, ...

Optimization models for the production scheduling of power-intensive processes such as air separation can help realizing significant economical savings. However, if the electricity is procured in the dayahead or real-time market, the forecast for the hourly electricity prices contains a significant amount of uncertainty. In this work, we apply robust optimization to the uncertain electricity pr...

this paper proposes a family of robust counterpart for uncertain linear programs (lp) which is obtained for a general definition of the uncertainty region. the relationship between uncertainty sets using norm bod-ies and their corresponding robust counterparts defined by dual norms is presented. those properties lead us to characterize primal and dual robust counterparts. the researchers show t...

Robust optimization is an important technique to immunize optimization problems against data uncertainty. In the case of a linear program and an ellipsoidal uncertainty set, the robust counterpart turns into a second-order cone program. In this work, we investigate the efficiency of linearizing the second-order cone constraints of the latter. This is done using the optimal linear outer-approxim...

Multi-objective integer optimization model that contain uncertain parameter can be handled using the Adjustable Robust Counterpart (ARC) methodology with Polyhedral Uncertainty Set. The ARC method has two stages of completion, so completing second stage assisted by Benders Decomposition. This paper discusses systematic review on this topic Preferred Reporting Items for Systematic Reviews and Me...

In this paper, we examine the duality gap between the robust counterpart of a primal uncertain convex optimization problem and the optimistic counterpart of its uncertain Lagrangian dual and identify the classes of uncertain problems which do not have a duality gap. The absence of a duality gap (or equivalently zero duality gap) means that the primal worst value equals the dual best value. We f...