The Dao of Robustness Achieving Robustness in Prescriptive Analytics
Dr. Melvyn Sim
National University of Singapore
November 6, Friday
13:40 via Zoom
We present a model for optimization under uncertainty called robustness optimization that favors solutions for which the model’s constraint would be the most robust or least fragile under uncertainty. The decision maker does not have to size the uncertainty set, but specifies an acceptable target, or loss of optimality compared to the baseline model, as a tradeoff for the model’s ability to withstand greater uncertainty. We axiomatize the decision criterion associated with robustness optimization, termed as the fragility measure, which is a class of Brown and Sim (2009) satisficing measure, and it satisfies the properties of monotonicity, positive homogeneity, subadditivity, pro-robustness, and anti-fragility. We provide a representation theorem and connect it with known fragility measures including the decision criterion associated with the GRC-sum of Ben-Tal et al. (2017) and the riskiness index of Aumann and Serrano (2008). We present a suite of practicable robustness optimization models for prescriptive analytics including linear, adaptive linear, data driven adaptive linear, combinatorial and dynamic optimization problems. Similar to robust optimization, we show that robustness optimization via minimizing the fragility measure can also be done in a tractable way. We also provide numerical studies on static, adaptive, and data-driven adaptive problems and show that the solutions to the robustness optimization models can withstand greater impact of uncertainty compared to the corresponding robust optimization models without increasing the cost or incurring additional computational effort.
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Dr. Melvyn Sim is Professor and Provost's Chair at the Department of Analytics & Operations, NUS Business school. His research interests fall broadly under the categories of decision making and optimization under uncertainty with applications ranging from finance, supply chain management, healthcare to engineered systems. He is one of the active proponents of Robust Optimization and has given invited talks in this field at international conferences. Dr. Sim won second places in the 2002 and 2004 George Nicholson best student paper competition and first place in the 2007 Junior Faculty Interest Group (JFIG) best paper competition. He is also the recipient of the 2009 NUS outstanding young researcher award. Dr. Sim serves as an associate editor for Operations Research, Management Science and Mathematical Programming Computations
