We consider the problem of minimizing the overall cost of a supply chain, over a possibility long horizon, under demand uncertainly which is known only crudely. Under such circumstances, the method of choice is Robust Optimization, in particular the Affinely Adjustable Robust Counterpart (AARC) method which leads to tractable deterministic optimization problems. The latter is due to a recent re...

In recent years the robust counterpart approach, introduced and made popular by Ben-Tal, Nemirovski and El Ghaoui, gained more and more interest among both academics and practitioners. However, to the best of our knowledge, only very few results on the relationship between the original problem instance and the robust counterpart have been established. This exposition aims at closing this gap by...

In this paper we present a robust duality theory for generalized convex programming problems in the face of data uncertainty within the framework of robust optimization. We establish robust strong duality for an uncertain nonlinear programming primal problem and its uncertain Lagrangian dual by showing strong duality between the deterministic counterparts: robust counterpart of the primal model...

In this exposition the robust counterpart approach by Ben-Tal, El Ghaoui and Nemirovski is investigated with respect to its costs and benefits, with the focus on the costs of robustification. Although robust optimization has gained more and more interest among both academics and practitioners and although this certainly represents a well-established theory, it is to some extent unclear, if and ...

“The Price of Robustness” by Bertsimas and Sim [4] represented a breakthrough in the development of a tractable robust counterpart of Linear Programming Problems. However, the central modeling assumption that the deviation band of each uncertain parameter is single may be too limitative in practice: experience indeed suggests that the deviations distribute also internally to the single band, so...

This paper studies the vehicle routing problem with time windows and multiple deliverymen in which customer demands are uncertain and belong to a predetermined polytope. In addition to the routing decisions, this problem aims to define the number of deliverymen used to provide the service to the customers on each route. A new mathematical formulation is presented for the deterministic counterpa...

In the paper, we propose a tractable robust counterpart for solving the uncertain linear optimization problem with correlated uncertainties related to a causal ARMA(p, q) process. This explicit treatment of correlated uncertainties under a time series setting in robust optimization is in contrast to the independent or simple correlated uncertainties assumption in existing literature. under some...

In the paper, we develop, discuss and illustrate by simulated numerical results a new model of multi-stage asset allocation problem. The model is given by a new methodology for optimization under uncertainty – the Robust Counterpart approach.

In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It turns out that to do so on...

this paper proposes a robust portfolio optimization programming model with options. Under constrains of variance efficiency and shortfall preference structure, we derive optioned portfolios with the maximum expected return of robust counterpart. A numerical example using Monte Carlo illustrates some of the features and applications of this model.