Optimization

Optimization theory and algorithms are foundational building blocks of Operations Research and Data Science. This is a major research area in the IEOR department, with significant emphasis on both discrete optimization (including integer and combinatorial optimization) and continuous optimization. Here, the main goal is to design efficient near-optimal algorithms for large-scale problems with provable performance bounds and advance the theoretical frontiers for such problems. Another important aspect especially from the perspective of practical applications is handling uncertainty in input data. This is a very active research area in IEOR with focus on various approaches including stochastic, robust, online and dynamic optimization. Optimization algorithms are central to most computational problems in data science including statistical estimation, machine learning, and business analytics, and find applications in most problems in practice. The research in IEOR in this area spans a broad spectrum of application areas including scheduling, matching markets, energy, health and financial and business analytics. Our faculty and students collaborate regularly with colleagues in Computer Science and other engineering departments and play an active role in the Data Science Institute.

Faculty
Daniel BienstockYuri FaenzaDonald GoldfarbVineet GoyalGarud N. Iyengar

Machine Learning

Machine learning and artificial intelligence are shaping the current and future practices in business management and decision making, thanks to the vast amount of available data, increase in computational power, and new optimization algorithms. The research at IEOR is at the forefront of this revolution, spanning a wide variety of topics within theoretical and applied machine learning, including learning from interactive data (e.g., multi-armed bandits and reinforcement learning), online learning, and topics related to interpretability and fairness of ML and AI. We are creating machine learning theory, algorithms, and systems for a broad spectrum of application areas, including financial technology, energy, recommendation systems, online advertising, business analytics, service systems, pricing and revenue management.  Our faculty and students regularly collaborate with cutting-edge AI technology companies as well as local businesses, e-commerce companies, media houses, government, and financial firms. We work closely with colleagues in computer science and other engineering departments, and play an active role in the Data Science Institute.

Faculty
Shipra AgrawalDaniel BienstockAgostino CapponiAdam ElmachtoubYuri FaenzaDonald GoldfarbVineet GoyalAli HirsaGarud N. IyengarHardeep JoharSoulaymane KachaniHenry LamVan-Anh TruongXunyu Zhou

 

Stochastic Modeling and Simulation

Stochastic modeling and its primary computational tool, simulation, are both essential components of Operations Research that are built upon probability, statistics, and stochastic processes to study complex physical systems. Such systems often take the form of a large-scale network of interconnected resources, such as the Internet, power/utility grids and other critical infrastructures, airline networks, global supply chains, hospitals and healthcare systems. Key problems of interest include: how to take measurement, evaluate system performance, and manage resources; how to assess risk and implement hedging and mitigation strategies; how to make decisions that are often required to be real-time, adaptive, and decentralized; and how to conduct analysis and optimization that are effective and robust, including wherever necessary using approximations and asymptotics. Basic tools and methodologies in this area closely interact and overlap with those in financial engineering, business analytics, machine learning, optimization, and computation. IEOR faculty with research/teaching interests in this area regularly collaborate with colleagues in other engineering and science departments and Columbia Business School, and play an active role in the Data Science Institute.

 

Financial engineering

Financial engineering (FE)  is a highly interdisciplinary field that makes use of the theoretical developments in financial economics, applied mathematics, operations research, statistics and computer science. The broad and extensive applications of FE have shaped up the entire landscape of financial practice especially in derivative pricing, portfolio management, and risk control. These applications in turn have inspired new problems in FE. In recent years, with an upsurge of developments in artificial intelligence, machine learning and data science, study and applications of financial technology (aka FinTech) have rapidly emerged and become an integral and important part of FE. IEOR offers a thriving research environment and a critical mass in FE rarely to be found in a single university in the country. Research problems include, to name just a few, reinforcement learning in stochastic control, mean-field games, systemic risk, quantitative behavioral finance and principal-agent problems. The department also takes full advantage of its New York location, drawing on expert practitioners for seminars, conference participation, research collaborations and internships for students. Indeed, collaborations with industry go beyond New York, exemplified by the establishment of the new ``FDT Center for Intelligent Asset Management" generously donated by a Hong Kong based FinTech company. 

 

Operations management and business analytics

The goal of operations management (OM) is to leverage mathematical models, algorithms, and analysis tools to understand and optimize key operations problems. Examples include the scheduling of appointments at a healthcare clinic, supply chain planning for an online retailer, energy management for an electrical grid, matching supply and demand in a sharing economy, designing a product assortment on an e-commerce website, and last-mile delivery for on-demand services. When data is readily available and used to address these types of problems, this is often referred to as business analytics (BA). Generally, OM and BA can rely on the use of many mathematical tools such as convex optimization, stochastic processes, mechanism design, machine learning, dynamic programming, and combinatorial optimization. The goal is to not only provide insightful and practical solutions, but to also provide a theoretical justification for their success. Our faculty students often collaborate with companies through the Data Science Institute and the Columbia Business Analytics Initiative. Doctoral students working in this area often go on to work as faculty at top business schools or at companies such as Amazon, Uber, and Airbnb.