A Stochastic Programming Framework for Multi-Stakeholder Decision-Making and Conflict Resolution

Victor Zavala

Chemical and Biological Engineering

University of Wisconsin-Madison

College of Engineering

Madison, WI 53706

We use conditional value at risk (CVaR) to create a general multi-stakeholder decision-making framework. In this setting, we consider conflicting priorities of a population of stakeholders on multiple performance objectives. We observe that stakeholder dissatisfactions (distance to their individual ideal solutions) can be interpreted as random variables. We thus shape the dissatisfaction distribution and find an optimal compromise solution by solving a risk minimization problem parameterized in the probability level. This enables us to generalize multi-stakeholder settings previously proposed in the literature that minimize average and worst-case dissatisfactions. We use the concept of the CVaR norm to give a geometric interpretation to this problem and use the properties of this norm to prove that the CVaR minimization problem yields Pareto optimal solutions for any choice of the probability level. We discuss a broad range of potential applications of the framework. We demonstrate the developments using a design case study of a combined heat and power system that seeks to simultaneously minimize cost, water, and emissions.