Target-Oriented Distributionally Robust Optimization and Its Applications to Surgery Allocation
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AbstractIn 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.
Acceptance Date19/10/2021
All Author(s) ListVincent Tsz Fai Chow, Zheng Cui, Daniel Zhuoyu Long
Journal nameINFORMS Journal on Computing
Year2022
Month7
Volume Number34
Issue Number4
PublisherINFORMS
Pages2058 - 2072
ISSN1091-9856
eISSN1526-5528
LanguagesEnglish-United States
Keywordsrisk measure, enveloping bound, distributionally robust optimization, surgery block allocation
