Title of Presentation: From Lotteries to Optimal Decision-making: Operations Research and the Theory of Moments

Abstract:

Lottery games, with their complex probabilistic structures and significant financial stakes, provide a fertile playground for Operations Research (O.R.) researchers. This talk explores the rich opportunities for applying advanced O.R. techniques to optimize various aspects of lottery operations, from ticket sales to payout management, and illustrates the broader implications for decision making in related fields. Through various real life case studies, we demonstrate how the study of lottery games can yield insights into human behavior, statistical anomalies, and effective risk management strategies. In particular, we show how mean-variance analysis, a core concept within the theory of moments, can be a powerful method in decision making within this sector. This method evaluates the trade-off between risk and return, providing a structured and quantitative approach to optimize decisions under uncertainty.

We also develop a general framework for the “picking winners” problem, aiming to select a small pool of candidate solutions to maximize the chances that one will perform exceedingly well in a combinatorial optimization problem, under a linear and additive random payoff function. This problem is formulated using a two-stage distributionally robust model with a mixed 0-1 semidefinite program, leveraging the Theory of Moments. This approach allows us to exploit the diversification effect to improve the chances of achieving a high ex-post payoff.

Applications of this framework in fields such as revenue management (offer construction) and fraud detection (credit rating) will be presented. Additionally, we demonstrate how this framework is connected to the field of explainable AI, enhancing transparency and trust in the decision-making process.

Bio

Chung Piaw Teo is the Provost’s Chair Professor at the NUS Business School and concurrently serves as the Executive Director of the Institute of Operations Research and Analytics (IORA) at the National University of Singapore. He is also the Co-Director of the SIA-NUS Digital Aviation Corp Lab and the Director of the Center on Modern Logistics at the Chongqing-NUS Research Institute.

Prior to his current appointments, he held several key positions at the NUS Business School, including Head of Department, Acting Deputy Dean, and Vice-Dean of the Research and Ph.D. Program. He has also been a fellow in the Singapore-MIT Alliance Program, an Eschbach Scholar at Northwestern University (US), a Professor at Sungkyunkwan Graduate School of Business (Korea), and a Distinguished Visiting Professor at YuanZe University (Taiwan).

In 2019, he was elected Fellow of INFORMS and was awarded the Public Administration Medal (Silver) by the Singapore Government in 2023. His research interests span service and manufacturing operations, supply chain management, discrete optimization, and machine learning. Currently, he is leading efforts at NUS to develop IORA as part of the University’s strategic initiatives in the Smart Nation Research Program. Additionally, he serves as a department editor for Management Science (Optimization, now Optimization and Analytics) and is a former area editor for Operations Research (Operations and Supply Chains).