The Value of Flexibility in Robust Location-Transportation Problems

This article studies a multi-period capacitated fixed-charge location-transportation problem in which, while the location and capacity of each facility need to be determined immediately, the determination of final production and distribution of products can be delayed until actual orders are received in each period. In contexts where little is known about future demand, robust optimization, … Read more

Multistage Robust Mixed Integer Optimization with Adaptive Partitions

We present a new partition-and-bound method for multistage adaptive mixed integer optimization (AMIO) problems that extends previous work on finite adaptability. The approach analyzes the optimal solution to a static (non-adaptive) version of an AMIO problem to gain insight into which regions of the uncertainty set are restricting the objective function value. We use this … Read more

Robust constrained shortest path problems under budgeted uncertainty

We study the robust constrained shortest path problem under resource uncertainty. After proving that the problem is \NPhard in the strong sense for arbitrary uncertainty sets, we focus on budgeted uncertainty sets introduced by Bertsimas and Sim (2003) and their extension to variable uncertainty by Poss (2013). We apply classical techniques to show that the … Read more

New Discoveries of Domination between Traffic Matrices

A traffic matrix $D_1$ dominates a traffic matrix $D_2$ if any capacity reservation supporting $D_1$ supports $D_2$ as well. We prove that $D_3$ dominates $D_3+ \lambda(D_2-D_1)$ for any $\lambda\geq 0$ if $D_1$ dominates $D_2$. By the property , it is pointed out that the domains supported by different traffic matrices are isomorphic on the extended … Read more

Efficient approaches for the robust network loading problem

We consider the Robust Network Loading problem with splittable flows and demands that belong to the budgeted uncertainty set. We compare the optimal solution cost and computational cost of the problem when using static routing, volume routing, affine routing, and dynamic routing. For the first three routing types, we compare the compact formulation with a … Read more

Data-driven learning in dynamic pricing using adaptive optimization

We consider the pricing problem faced by a retailer endowed with a finite inventory of a product offered over a finite planning horizon in an environment where customers are price-sensitive. The parameters of the product demand curve are fixed but unknown to the seller who only has at his disposal a history of sales data. … Read more

Multi-stage adjustable robust mixed-integer optimization via iterative splitting of the uncertainty set

In this paper we propose a methodology for constructing decision rules for integer and continuous decision variables in multiperiod robust linear optimization problems. This type of problems finds application in, for example, inventory management, lot sizing, and manpower management. We show that by iteratively splitting the uncertainty set into subsets one can differentiate the later-period … Read more

The Descriptor Continuous-Time Algebraic Riccati Equation. Numerical Solutions and Some Direct Applications

We investigate here the numerical solution of a special type of descriptor continuous-time Riccati equation which is involved in solving several key problems in robust control, formulated under very general hypotheses. We also give necessary and sufficient existence conditions together with computable formulas for both stabilizing and antistabilizing solutions in terms of the associated matrix … Read more

Adaptive Robust Optimization with Dynamic Uncertainty Sets for Multi-Period Economic Dispatch under Significant Wind

The exceptional benefits of wind power as an environmentally responsible renewable energy resource have led to an increasing penetration of wind energy in today’s power systems. This trend has started to reshape the paradigms of power system operations, as dealing with uncertainty caused by the highly intermittent and uncertain wind power becomes a significant issue. … Read more

The robust stabilization problem for discrete-time descriptor systems

We investigate here the robust stabilization problem for the descriptor discrete time systems and build an optimal solution in the case when both the nominal system and the perturbations are given in terms of left coprime factorizations. Moreover our formulas are given straight from the original data, using solely the stabilizing solutions of two Riccati … Read more