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. Whereas 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 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. Summary of Contribution: Our paper studies a fundamental problem in operations research: what criteria to optimize when uncertainties are involved. Extending from the classical chance constraint model, we propose a new decision criterion by an axiomatization approach. We then investigate the computing issue in the corresponding distributionally robust optimization problem. In particular, we provide solution methods for continuous and discrete optimization. After that, we apply it to a practical operations problem, surgery allocation decisions in healthcare management. The computational studies demonstrate the appealing performance of our proposed approach on this surgery allocation problem.