Kusuoka Representations of Coherent Risk Measures in General Probability Spaces

Kusuoka representations provide an important and useful characterization of law invariant coherent risk measures in atomless probability spaces. However, the applicability of these results is limited by the fact that such representations do not always exist in probability spaces with atoms, such as finite probability spaces. We introduce the class of functionally coherent risk measures, … Read more

Stochastic Network Design for Disaster Preparedness

We propose a new stochastic modeling approach for a pre-disaster relief network design problem under uncertain demand and transportation capacities. We determine the size and the location of the response facilities and the inventory levels of relief supplies at each facility with the goal of guaranteeing a certain level of network reliability. The overall objective … Read more

Optimization with multivariate conditional value-at-risk constraints

For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers’ risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate … Read more

Single-Leg Airline Revenue Management with Overbooking

Airline revenue management is about identifying the maximum revenue seat allocation policies. Since a major loss in revenue results from cancellations and no-show passengers, over the years overbooking has received a significant attention in the literature. In this study, we propose new models for static and dynamic single-leg overbooking problems. In the static case, we … Read more

Mathematical Programming Approaches for Generating p-Efficient Points

Probabilistically constrained problems, in which the random variables are finitely distributed, are non-convex in general and hard to solve. The p-efficiency concept has been widely used to develop efficient methods to solve such problems. Those methods require the generation of p-efficient points (pLEPs) and use an enumeration scheme to identify pLEPs. In this paper, we … Read more

Two-Stage Stochastic Programming Involving CVaR with an Application to Disaster Management

Traditional two-stage stochastic programming is risk-neutral; that is, it considers the expectation as the preference criterion while comparing the random variables (e.g., total cost) to identify the best decisions. However, in the presence of variability risk measures should be incorporated into decision making problems in order to model its effects. In this study, we consider … Read more

Valid Inequalities and Restrictions for Stochastic Programming Problems with First Order Stochastic Dominance Constraints

Stochastic dominance relations are well-studied in statistics, decision theory and economics. Recently, there has been significant interest in introducing dominance relations into stochastic optimization problems as constraints. In the discrete case, stochastic optimization models involving second order stochastic dominance (SSD) constraints can be solved by linear programming (LP). However, problems involving first order stochastic dominance … Read more