Goal Driven Optimization

Achieving a targeted objective, goal or aspiration level are relevant aspects of decision making under uncertainties. We develop a goal driven stochastic optimization model that takes into account an aspiration level. Our model maximizes the shortfall aspiration level criterion}, which encompasses the probability of success in achieving the goal and an expected level of under-performance … Read more

A Tractable Approximation of Stochastic Programming via Robust Optimization

Stochastic programming, despite its immense modeling capabilities, is well known to be computationally excruciating. In this paper, we introduce a unified framework of approximating multiperiod stochastic programming from the perspective of robust optimization. Specifically, we propose a framework that integrates multistage modeling with safeguarding constraints. The framework is computationally tractable in the form of second … Read more

A Robust Optimization Framework for Analyzing Distribution Systems with Transshipment

This paper studies a distribution system consisting of multiple retail locations with transshipment operations among the retailers. Due to the difficulty in computing the optimal solution imposed by the transshipment operations and in estimating shortage cost from a practical perspective, we propose a robust optimization framework for analyzing the impact of transshipment operations on such … Read more

Constructing Risk Measures from Uncertainty Sets

We propose a unified theory that links uncertainty sets in robust optimization to risk measures in portfolio optimization. We illustrate the correspondence between uncertainty sets and some popular risk measures in finance, and show how robust optimization can be used to generalize the concepts of these measures. We also show that by using properly defined … Read more

A Robust Optimization Perspective of Stochastic Programming

In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for bounded random variables known as the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. We also propose a tractable robust optimization approach for obtaining robust solutions … Read more