Target Oriented Distributionally Robust Optimization and Its Applications to Surgery Allocation

In this paper, we propose a decision criterion that characterizes an enveloping bound on monetary risk measures and is computationally friendly. We start by extending the classical Value at Risk (VaR) measure. While VaR evaluates the threshold loss value such that the loss from the risk position exceeding that threshold is at a given probability level, it fails to indicate a performance guarantee at other probability levels. We define the Probabilistic Enveloping Measure (PEM) to establish the bound information for the tail probability of the loss at all levels. Using a set of normative properties, we then generalize the PEM to the Risk Enveloping Measure (REM) such that the bound on the general monetary risk measures at all levels of risk aversion are captured. The coherent version of the REM (CREM) is also investigated. We demonstrate its applicability by showing how the coherent REM can be incorporated in distributionally robust optimization. Specifically, we apply the CREM criterion in the surgery block allocation problems and provide a formulation that can be efficiently solved. Based on this application, we report favorable computational results from optimizing over the CREM criterion