Speaker: Prof. Melvyn Sim
National University of Singapore
Title: Distributionally Robust Optimization
Date and time: Monday 23 January 2017, 3:00pm.
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus
Abstract: We develop a modular and tractable framework for solving an adaptive distributionally robust linear optimization problem, where we minimize the worst-case expected cost over an ambiguity set of probability distributions. The adaptive distributionally robust optimization framework caters for dynamic decision making, where decisions can adapt to the uncertain outcomes as they unfold in stages. For tractability considerations, we focus on a class of second-order conic (SOC) representable ambiguity set, though our results can easily be extended to more general conic representations. We show that the adaptive distributionally robust linear optimization problem can be formulated as a classical robust optimization problem. To obtain tractable formulation, we approximate the adaptive distributionally robust optimization problem using linear decision rule (LDR) techniques. More interestingly, by incorporating the primary and auxiliary random variables of the lifted ambiguity set in the LDR approximation, we can significantly improve the solutions and for a class of adaptive distributionally robust optimization problems, exact solutions can also be obtained. Using the new LDR approximation, we can transform the distributionally adaptive robust optimization problem to a classical robust optimization problem with an SOC representable uncertainty set. Hence, depending on the ambiguity set, the resulting framework is either a linear optimization problem or a second-order conic optimization problem (SOCP), which can be solved efficiently by general purpose commercial grade solvers. Finally, to demonstrate the potential for solving management decision problems, we develop an algebraic modeling package and illustrate how it can be used to facilitate modeling and obtain high quality solutions for addressing a medical appointment scheduling problem and a multiperiod inventory control problem.
Bio: Prof. Melvyn Sim is the Head of Department and Provost’s Chair Professor at the Department of Decisions Sciences, 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 serves as an associate editor for Operations Research, Management Science and Mathematical Programming Computations.