Anton Braverman

Asymptotic Methods in Operations (OPNS-530-0)

This course introduces the mathematical foundations and modeling principles behind fluid and diffusion limits, with an emphasis on their use as approximation tools in operations. Fluid limits often capture first-order, law-of-large-numbers behavior; diffusion limits capture second-order stochastic fluctuations. These approximations are not merely technical devices: they explain congestion, delay, variability, resource pooling, heavy traffic behavior, and the qualitative structure of good controls. The course is intended for PhD students who want to develop a rigorous and reusable toolkit for stochastic modeling. While many examples will come from queues and stochastic processing systems, the methods are broadly relevant across operations, applied probability, revenue management, marketplace design, service operations, healthcare operations, and data-driven decision making. Students who take the course should leave with both a conceptual understanding of why fluid and diffusion approximations work and a technical foundation for using these methods in their own research.

Queueing Networks: Models, Algorithms and Emerging Applications (OPNS-522-0)

This course aims to expose students to advanced methods in stochastic analysis and develop a toolbox of probabilistic analytical techniques. To focus the discussion, the course will be centered around queueing networks, which serve as building blocks in many modeling applications. Topics covered include fundamental queueing models, fluid and diffusion processes, limit theorems and approximations, and stochastic control. To discuss the algorithmic/computational elements of stochastic control, we will touch on approximate dynamic programming and explore how it is used in the control of queueing networks.

Stochastic Processes I (OPNS-516-1)

The course prepares the student with an understanding of Stochastic Processes. This course covers the following topics: Poisson Processes, discrete-time Markov chains, and continuous time Markov chains. It applies these concepts to queuing systems. Students are expected to have some background in probability.

Supply Chain Management (OPNS-455-0)

What are the key capabilities a supply chain must develop to support the business strategy of a firm? What is the relationship between the desired capabilities and the structure of a supply chain? This course provides a framework to answer these questions. We define supply chain structure in terms of the following drivers of performance: facilities, information, inventory and transportation. The relationship between structure and performance is analyzed using various case studies that require students to develop analytical spreadsheet models to support their decision making. Students are taught the strategic role of the supply chain. The course also discusses methodologies for designing and planning a supply chain.

Decision Models & Prescriptive Analytics (OPNS-450-0)

The value of analytics and artificial intelligence (AI) in today's business landscape cannot be overstated. These tools have become integral to the decision-making process for many organizations across a variety of industries, including services, marketing, transportation, online platforms, and finance. AI systems often utilize a range of analytics techniques to make data-driven, evidence-based decisions. The analytics tools can be broadly classified to three types:

• Descriptive (What happened?): The interpretation of historical data to identify trends and patterns
• Predictive (What will happen?): The use of statistical and machine learning techniques to forecast future outcomes
• Prescriptive (What should be done?): The use of data-driven models to prescribe the best action plan.

Prescriptive analytics, in particular, plays a key role in the functionality of AI systems. This type of analytics involves the use of data-driven models to determine the best course of action in a given situation, based on data and analysis of past outcomes and trends. By utilizing prescriptive analytics, organizations can make informed, strategic decisions that optimize outcomes and drive business success. For example, an AI system might use prescriptive analytics to determine the best way to match drivers with riders, recommend the best portfolio of stocks, or to recommend the most effective marketing campaign for a new product. By leveraging the power of advanced analytics techniques, organizations can gain a competitive edge and make more informed, strategic decisions that can drive growth and success.

This course focuses on developing a holistic understanding of prescriptive analytics by introducing the basic principles and techniques of applied mathematical modeling for managerial decision-making. You will learn to use important analytic methods, such as spreadsheet modeling, optimization, and Monte Carlo simulation, to recognize their assumptions and limitations, and to employ them in decision-making. The emphasis will be on model formulation and interpretation of results, rather than on mathematical theory or coding. We will cover a wide range of prescriptive analytics models that are widely used in diverse industries and functional areas, including finance, operations, and marketing.