Victor
Zavala
Chemical
and Biological Engineering
University
of Wisconsin-Madison
College
of Engineering
Madison,
WI 53706
zavalatejeda@wisc.edu
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.