Robust Decision Making: Addressing Uncertainties in Distributions

Abstract

This paper develops a general approach to risk management in military applications involving uncertainties in information and distributions. The risk of loss, damage, or failure is measured by the Conditional Value-at-Risk (CVaR) measure. Loosely speaking, CVaR with the confidence level α estimates the risk of loss by averaging the possible losses over the (1 - α) · 100% worst cases (e.g., 10%). As a function of decision variables, CVaR is convex and therefore can be efficiently controlled/optimized using convex or (under quite general assumptions) linear programming. The general methodology was tested on two Weapon-Target Assignment (WTA) problems. It is assumed that the distributions of random variables in the WTA formulations are not known with certainty. The total cost of a mission (including weapon attrition) was minimized, while satisfying operational constraints and ensuring destruction of all targets with high probabilities. The risk of failure of the mission (e.g., targets are not destroyed) is controlled by CVaR constraints. The case studies conducted show that there are significant qualitative and quantitative differences in solutions of deterministic WTA and stochastic WTA problems.

This work was partially supported by the Air Force grant F49620-01-1-0338.