Managing Distributional Ambiguity in Stochastic Optimization through a Statistical Upper Bound Framework

Stochastic optimization is often hampered by distributional ambiguity, where critical probability distributions are poorly characterized or unknown. Addressing this challenge, we introduce a new framework that targets the minimization of a statistical upper bound for the expected value of uncertain objectives, facilitating more statistically robust decision-making. Central to our approach is the Average Percentile Upper … Read more

Data-Driven Distributionally Preference Robust Optimization Models Based on Random Utility Representation in Multi-Attribute Decision Making

Preference robust optimization (PRO) has recently been studied to deal with utility based decision making problems under ambiguity in the characterization of the decision maker’s (DM) preference. In this paper, we propose a novel PRO modeling paradigm which combines the stochastic utility theory with distributionally robust optimization technique. Based on the stochastic utility theory, our … Read more

A Data Driven Functionally Robust Approach for Coordinating Pricing and Order Quantity Decisions with Unknown Demand Function

We consider a retailer’s problem of optimal pricing and inventory stocking decisions for a product. We assume that the price-demand curve is unknown, but data is available that loosely specifies the price-demand relationship. We propose a conceptually new framework that simultaneously considers pricing and inventory decisions without a priori fitting a function to the price-demand … Read more

A Robust Additive Multiattribute Preference Model using a Nonparametric Shape-Preserving Perturbation

This paper develops a multiattribute preference ranking rule in the context of utility robustness. A nonparametric perturbation of a given additive reference utility function is specified to solve the problem of ambiguity and inconsistency in utility assessments, while preserving the additive structure and the decision maker’s risk preference under each criterion. A concept of robust … Read more

Decision Making Based on a Nonparametric Shape-Preserving Perturbation of a Reference Utility Function

This paper develops a robust optimization based decision-making framework using a nonparametric perturbation of a reference utility function. The perturbation preserves the risk-aversion property but solves the problem of ambiguity and inconsistency in eliciting the reference utility function. We study the topology of the perturbation, and show that in the decision-making framework the price of … Read more

Robust Decision Making using a General Utility Set

We develop the concept of utility robustness to address the problem of ambiguity and inconsistency in utility assessments. A robust decision-making framework is built on a utility set which characterizes a decision maker’s risk attitude described by boundary and auxiliary conditions. This framework is studied using the Sample Average Approximation (SAA) approach. We show the … Read more

Robust Decision Making using a Risk-Averse Utility Set

Eliciting the utility of a decision maker is difficult. In this paper, we develop a flexible decision making framework, which uses the concept of utility robustness to address the problem of ambiguity and inconsistency in utility assessments. The ideas are developed by giving a probabilistic interpretation to utility and marginal utility functions. Boundary and additional … Read more

Concepts and Applications of Stochastically Weighted Stochastic Dominance

Stochastic dominance theory provides tools to compare random entities. When comparing random vectors (say X and Y ), the problem can be viewed as one of multi-criterion decision making under uncertainty. One approach is to compare weighted sums of the components of these random vectors using univariate dominance. In this paper we propose new concepts … Read more

Robust and Stochastically Weighted Multi-Objective Optimization Models and Reformulations

In this paper we introduce robust and stochastically weighted sum approaches to deterministic and stochastic multi-objective optimization. The robust weighted sum approach minimizes the worst case weighted sum of objectives over a given weight region. We study the reformulations of the robust weighted sum problem under different definitions of deterministic weight regions. We next introduce … Read more

Risk Adjusted Budget Allocation Models with Application in Homeland Security

This paper presents and studies several models for multi-criterion budget allocation problems under uncertainty. We start by introducing a robust weighted objective model, which is developed further using the concept of stochastic dominance to incorporate risk averseness of the decision maker. A budget minimization variant of this model is also presented. We use a Sample … Read more