Data-driven Stochastic Vehicle Routing Problems with Deadlines

Vehicle routing problems (VRPs) with deadlines have received significant attention around the world. Motivated by a real-world food delivery problem, we assume that the travel time depends on the routing decisions, and study a data-driven stochastic VRP with deadlines and endogenous uncertainty. We use the non-parametric approaches, including k-nearest neighbor (kNN) and kernel density estimation … Read more

A Double-oracle, Logic-based Benders decomposition approach to solve the K-adaptability problem

We propose a novel approach to solve K-adaptability problems with convex objective and constraints and integer first-stage decisions. A logic-based Benders decomposition is applied to handle the first-stage decisions in a master problem, thus the sub-problem becomes a min-max-min robust combinatorial optimization problem that is solved via a double-oracle algorithm that iteratively generates adverse scenarios … Read more

Distributional robustness and inequity mitigation in disaster preparedness of humanitarian operations

We study a predisaster relief network design problem with uncertain demands. The aim is to determine the prepositioning and reallocation of relief supplies. Motivated by the call of the International Federation of Red Cross and Red Crescent Societies (IFRC) to leave no one behind, we consider three important practical aspects of humanitarian operations: shortages, equity, … Read more

Risk-averse Regret Minimization in Multi-stage Stochastic Programs

Within the context of optimization under uncertainty, a well-known alternative to minimizing expected value or the worst-case scenario consists in minimizing regret. In a multi-stage stochastic programming setting with a discrete probability distribution, we explore the idea of risk-averse regret minimization, where the benchmark policy can only benefit from foreseeing Delta steps into the future. … Read more

A Column Generation Scheme for Distributionally Robust Multi-Item Newsvendor Problems

In this paper, we study a distributionally robust multi-item newsvendor problem, where the demand distribution is unknown but specified with a general event-wise ambiguity set. Using the event-wise affine decision rules, we can obtain a conservative approximation formulation of the problem, which can typically be further reformulated as a linear program. In order to efficiently … Read more

Robust Integration of Electric Vehicles Charging Load in Smart Grid’s Capacity Expansion Planning

Battery charging of electric vehicles (EVs) needs to be properly coordinated by electricity producers to maintain network reliability. In this paper, we propose a robust approach to model the interaction between a large fleet of EV users and utilities in a long-term generation expansion planning problem. In doing so, we employ a robust multi-period adjustable … Read more

Data-Driven Optimization with Distributionally Robust Second-Order Stochastic Dominance Constraints

Optimization with stochastic dominance constraints has recently received an increasing amount of attention in the quantitative risk management literature. Instead of requiring that the probabilistic description of the uncertain parameters be exactly known, this paper presents the first comprehensive study of a data-driven formulation of the distributionally robust second-order stochastic dominance constrained problem (DRSSDCP) that … Read more

Affine Decision Rule Approximation to Immunize against Demand Response Uncertainty in Smart Grids’ Capacity Planning

Generation expansion planning (GEP) is a classical problem that determines an optimal investment plan for existing and future electricity generation technologies. GEP is a computationally challenging problem, as it typically corresponds to a very large-scale problem that contains several sources of uncertainties. With the advent of demand response (DR) as a reserved capacity in modern … Read more

The Value of Randomized Strategies in Distributionally Robust Risk Averse Network Interdiction Games

Conditional Value at Risk (CVaR) is widely used to account for the preferences of a risk-averse agent in the extreme loss scenarios. To study the effectiveness of randomization in interdiction games with an interdictor that is both risk and ambiguity averse, we introduce a distributionally robust network interdiction game where the interdictor randomizes over the … Read more

Equal Risk Pricing and Hedging of Financial Derivatives with Convex Risk Measures

In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where risk is measured according to convex risk measures, we … Read more