141 courses with the subject ORIE, each shown exactly as we captured it from the college's catalog, with every element we hold. Where the wording looks broken, that is our reading of the catalog, not the college's text.
ORIE 1380Data Science for All4
This course provides an introduction to data science using the statistical programming language R. We focus on building skills in inferential thinking and computational thinking, guided by the practical questions we seek to answer from data sets arising in medicine, economics and other social sciences. The course starts with essential R programming principles, and how to use R for data manipulation, visualization, and sampling. These techniques are then used to summarize and visualize real data sets, draw meaningful conclusions from those data, and assess the uncertainty surrounding those conclusions. Throughout the process, students will learn to develop hypotheses about their data, and use simulations and statistical techniques to test these hypotheses. The course also covers how to use the Tidyverse open-source R packages to clean and organize complex data sets, and create high quality graphics for data visualization.
ORIE 3120Practical Tools for Operations Research, Machine Learning and Data Science4
The practical use of software tools and mathematical methods from operations research, machine learning, statistics and data science. Software tools include structured query language (SQL), geographical information systems (GIS), Excel and Visual Basic programming (VBA), and programming in a scripting language (either R or Python). Operations research methods include inventory management, discrete event simulation, and an introduction to the analysis of queuing systems. Machine learning and statistical methods include multiple linear regression, classification, logistic regression, clustering, time-series forecasting, and the design and analysis of A/B tests. These topics will be presented in the context of business applications from transportation, manufacturing, retail, and e-commerce.
Covers principles of accounting, financial reports, financial-transactions analysis, financial-statement analysis, budgeting, job order and process-cost systems, standard costing and variance analysis, and economic analysis of short-term decisions.
Formulation of linear programming problems and solutions by the simplex method. Related topics such as sensitivity analysis, duality, and network programming. Applications include such models as resource allocation and production planning. Introduction to interior-point methods for linear programming.
A variety of optimization methods stressing extensions of linear programming and its applications but also including topics drawn from integer programming, dynamic programming, and network optimization. Formulation and modeling are stressed as well as numerous applications.
This course introduces the theory, algorithms, and applications of nonlinear optimization, which is at the core of many fundamental algorithmic challenges in AI, such as the training of models like deep neural nets and transformers, and is used at massive scales. We will study unconstrained and constrained optimization problems, focusing on convex and nonconvex settings. Topics include optimality conditions, convexity, gradient-based and Proximal-type methods, second-order methods, line-search strategies, and duality theory. Emphasis will be placed on both the mathematical foundations and the practical implementation of algorithms.
ORIE 3500Eng Probability and Statistics: Modeling and Data Science II4
A rigorous foundation in theory combined with the methods for modeling, analyzing, and controlling randomness in engineering problems. Probabilistic ideas are used to construct models for engineering problems, and statistical methods are used to test and estimate parameters for these models. Specific topics include: random variables, probability distributions, density functions, expectation and variance, multidimensional random variables, and important distributions including normal, Poisson, exponential, hypothesis testing, confidence intervals, and point estimation using maximum likelihood and the method of moments.
ORIE 3510Stochastic Processes for Decision-Making4
Uses basic concepts and techniques of random processes to construct models for a variety of problems of practical interest. Topics include: the Poisson process, Markov chains, renewal theory, models for queuing, and reliability.
Modern data sets, whether collected by scientists, engineers, medical researchers, government, financial firms, social networks, or software companies, are often big, messy, and extremely useful. This course addresses scalable robust methods for learning from big messy data. We'll cover techniques for learning with data that is messy - consisting of real numbers, integers, booleans, categoricals, ordinals, graphs, text, sets, and more, with missing entries and with outliers - and that is big - which means we can only use algorithms whose complexity scales linearly in the size of the data. We will cover techniques for cleaning data, supervised and unsupervised learning, finding similar items, model validation, and feature engineering.
ORIE 4100Manufacturing Systems Design: A Consulting Boot Camp4
This project-based course puts students in the roles of analysts and advisors to an industrial firm facing broad challenges in customer service, product quality, market share, and profitability. Students, working in teams, design a manufacturing logistics system and conduct capacity, material flow, and cost analyses of their design. By taking a view that integrates marketing, distribution, manufacturing, and engineering, students help the company transform into a world-class competitor.
ORIE 4120Inventory, Operations, and Supply Chain Management: Models and Optimization3
This course will provide a rigorous coverage of the (stochastic and deterministic) models commonly used in the study of inventory, operations, and supply chain management. This includes the multi-period newsvendor model and its many variants, as well as more sophisticated models which arise in supply chain management, logistics, and the study of operations more broadly. We will study tools for analyzing and optimizing such systems, as well as operational insights which can be extracted from such models. The course will in general have a fairly mathematical orientation, focusing on using tools from stochastic modeling, optimization, and dynamic programming/algorithms to formulate and analyze these models.
Supply chain management focuses on the flow of products, information, and money through organizations that constitute the supply chain. The course provides an overview of the key principles on which an effective supply chain should be constructed. These principles are presented and illustrated through a collection of cases. These cases are taught using an experiential learning model. Additionally, applications of analytic and simulation tools to the design and operation of supply chains are given.
Service systems arise primarily from the service sector of the economy. Examples are contact centers (also known as call centers), airlines, insurance and healthcare. This course describes techniques that are useful in the analysis and design of such systems. The class is structured around a number of cases. The emphasis is on modeling, solving the models, and interpreting the results. Both operational and strategic decisions are covered through appropriate examples.
This course develops the skills needed to use Operations Research modeling and data analysis skills in real applications, i.e., “for real.” The course teaches and uses general modeling principles in a selection of applications, e.g., epidemic interventions, emergency service deployments, community first responder systems, bike sharing, ride hailing, and other topics as time/interest allows.
ORIE 4154Revenue Optimization and Marketplace Design3
Application of modeling and optimization techniques in designing a company's interface with the market. We will cover a variety of topics (product pricing and capacity control; designing product assortments and customer segmentation; the use of customer data in modeling and optimization; the design of online platforms and markets), with examples from transportation, retail, hospitality and the sharing economy.
Each year, the course will cover a different advanced topic at the intersection of data science and operations research, with the specific topic to be chosen by the instructor that year. The class will entail advanced reading, homework, and course project. Example semester-long topics include: Multi-arm bandit models in ML and OR, Statistical recovery in data science and OR, Graphical models in data science and OR, Causal inference in data science and OR, and Reinforcement learning in data science and OR.
Covers basic concepts of graphs, networks, and discrete optimization. Fundamental models and applications, and algorithmic techniques for their analysis. Specific optimization models studied include flows in networks, the traveling salesman problem, and network design.
ORIE 4340Applications of Optimization: Modeling and Computation4
This course will cover the use of optimization models in several industries. Covered industries will include manufacturing, process, distribution, retail, and transportation. We will not cover models used exclusively in the financial industry. In each covered industry we will start with simple text-book models, and then extend these models to reflect the realities of the industry, the existing business decisions processes and the available data. We expect to have lectures from experts in some of these industries, each of whom will also discuss Operations Research roles and careers.
Broad survey of the mathematical theory of games, including such topics as two-person matrix and bimatrix games; cooperative and noncooperative n-person games; and games in extensive, normal, and characteristic function form. Economic market games. Applications to weighted voting and cost allocation.
This course provides students with a rigorous perspective on, and a technical toolbox for, the design of democratic processes, treated through the lens of algorithmic analysis. The course exposes students to a range of such democratic algorithms and of algorithmic settings arising in democracy, including ranked choice voting, approval-based multi-winner elections, participatory budgeting, and apportionment. On a technical level, the course illustrates to students the richness of possible algorithmic approaches to a societal phenomenon, and it trains students in the rigorous application of techniques in this domain, including the axiomatic method, notions of fairness and proportionality, mathematical programming, social welfare functions, measures of power in weighted voting games, and measuring the quality of voting rules through competitive analysis (distortion). The course draws on classic and recent results in computational social choice.
ORIE 4390Optimization Models for Logistics, Networks, and Markets1.5
Hands-on experience with integer linear programming and dynamic programming: creating ILPs and DPs, implementing them, critiquing them, understanding solver output, and improving ILPs using better variables, constraints, symmetry breaking, etc. Examples of problems that we will study in this course are logistical problems like sequencing in production, scheduling problems with conflicts (vertex coloring), matching problems for markets and clustering problems in networks, but are not limited to these domains. In addition, a variety of general linear programming techniques such as Fourier-Motzkin elimination, Dantzig-Wolfe decomposition, Benders decomposition and extended formulations may be covered, as well as rounding techniques of LP solutions.
ORIE 4570Reinforcement Learning with Operations Research Applications3
The ongoing information revolution and the advent of the big data era make quantitative methods in the business context indispensable. This course introduces reinforcement learning, decision-making under uncertainty, and related algorithms through the lens of OR applications. Examples will be drawn from real-world problems in operations, revenue management, queuing, finance, transportation, healthcare, and other areas of interest. The course will cover modeling and applications, basic theory, and algorithms.
Introduction to Monte Carlo simulation and discrete-event simulation. Topics include: random variate and process generation; data-driven distribution modeling; input and output analysis; modeling, analysis and optimization of complex systems. Emphasizes tools and techniques needed in practice; in particular, modeling in simulation in Python, as well as commercial discrete-event simulation languages.
This is an introduction to the most important notions and ideas in modern financial engineering, such as arbitrage, pricing, derivatives, options, interest rate models, risk measures, equivalent martingale measures, complete and incomplete markets, etc. Most of the time the course deals with discrete time models. This course can serve as a preparation for a course on continuous time financial models such as ORIE 5600.
ORIE 4630Operations Research Tools for Financial Engineering4
Introduction to the applications of OR techniques, e.g., probability, statistics, and optimization, to finance and financial engineering. The course reviews probability and statistics and surveys assets returns, ARIMA time series models, portfolio selection using quadratic programming, regression, CAPM and factor models, option pricing, GARCH models, fixed-income securities, and resampling techniques. Covers the use of R for statistical calculations, simulation, and optimization.
In order to be able to assess the risk associated with future extreme values in financial returns, a practitioner must have an idea how heavy the tails of the returns are and how they cluster. The practitioner must also be able to understand the extremal risks associated with a portfolio of financial instruments, potentially of a large size. In this course the students will learn to work with extreme values, to understand the difference between light tails and heavy tails, and learn how the largest return and the total return grow for different types of tails. They will also learn statistical techniques (mostly through R packages) used to work with extreme values.
Examines the statistical aspects of data mining, the effective analysis of large datasets. Covers the process of building and interpreting various statistical models appropriate to such problems arising in scientific and business applications. Topics include naive Bayes, graphical models, multiple regression, logistic regression, clustering methods and principal component analysis. Assignments are done using one or more statistical computing packages.
ORIE 4742Info Theory, Probabilistic Modeling, and Deep Learning with Scientific and Financial Apps3
This course is about building and understanding machine learning models for scientific and financial applications. It will cover foundational aspects of information theory and probabilistic inference as they relate to model construction and deep learning. Topics include hamming codes, repetition codes, entropy, mutual information, Shannon information, channel capacity, likelihood functions, Bayesian inference, graphical models, and deep neural networks. The section on deep neural networks will consider fully connected, convolutional, recurrent, and LSTM networks, generative adversarial training, and variational autoencoders.
ORIE 4750Foundations of Causal Inference for Data-Driven Decisions4
This course provides a rigorous introduction to the theory and practice of causal inference for data-driven decision-making. Students will learn to identify and estimate causal effects using both experimental and observational data, combining statistical foundations with computational tools. Emphasis is placed on understanding causal assumptions, designing valid estimators, and analyzing the theoretical properties of each method. Attention will be given to unique challenges that arise in real-world operational and policy decisions. Example applications include online marketplaces, social networks, and inventory control. Topics include the potential outcomes framework, causal diagrams, randomized and quasi-experimental designs, matching and weighting methods, instrumental variables, difference-in-differences, and introductory causal machine learning.
ORIE 4820Data-Driven Decision Modeling and Analysis3
This course equips students with essential data-driven decision-making skills, integrating structured and unstructured data. It bridges classical modeling techniques with modern computational tools, emphasizing critical thinking, automation, and problem-solving. The curriculum prepares students for operations research, supply chain analytics, finance, and engineering management careers.
Students engage in a mentored investigation or inquiry that aims to make a scholarly contribution to the field of operations research and information engineering. All students are mentored by Cornell faculty in ORIE and may also have additional mentors from the field.
Involves working as a TA in an ORIE course. The instructor assigns credits (the guideline is 1 credit per four hours per week of work with a limit of 3 credits).
Project-type work, under faculty supervision, on a real problem existing in some firm or institution. Opportunities in the course may be discussed with the associate director.
ORIE 5100Manufacturing Systems Design: A Consulting Boot Camp4
This project-based course puts students in the roles of analysts and advisors to an industrial firm facing broad challenges in customer service, product quality, market share, and profitability. Students, working in teams, design a manufacturing logistics system and conduct capacity, material flow, and cost analyses of their design. By taking a view that integrates marketing, distribution, manufacturing, and engineering, students help the company transform into a world-class competitor.
ORIE 5110Engineering Economics and Strategic Decision-Making1
Students learn to make sound financial decisions in engineering contexts using tools such as time value of money, discounted cash flow, and capital budgeting. The course covers tax implications and financial statement analysis. Emphasis is placed on evaluating real-world projects, sustainability, and developing persuasive business cases using Excel and Python.
ORIE 5120Inventory, Operations, and Supply Chain Management: Models and Optimization3
This course will provide a rigorous coverage of the (stochastic and deterministic) models commonly used in the study of inventory, operations, and supply chain management. This includes the multi-period newsvendor model and its many variants, as well as more sophisticated models which arise in supply chain management, logistics, and the study of operations more broadly. We will study tools for analyzing and optimizing such systems, as well as operational insights which can be extracted from such models. The course will in general have a fairly mathematical orientation, focusing on using tools from stochastic modeling, optimization, and dynamic programming/algorithms to formulate and analyze these models.
Supply chain management focuses on the flow of products, information, and money through organizations that constitute the supply chain. The course provides an overview of the key principles on which an effective supply chain should be constructed. These principles are presented and illustrated through a collection of cases. These cases are taught using an experiential learning model. Additionally, applications of analytic and simulation tools to the design and operation of supply chains are given.
ORIE 5129Data Science for e-Retail and the Sharing Economy3
Many online and tech businesses face logistics challenges that require optimal management of physical resources. These challenges may take the form of opening fulfillment centers at the right locations, stocking the right amount of inventory, running optimal number of servers to satisfy computing needs, repositioning bikes in urban bike-sharing systems, and dispatching and repositioning vehicles in online ride-sharing systems. Addressing these challenges often requires building and deploying large-scale optimization models that can make decisions on the fly. We will cover logistics models that allow firms to optimally use its physical resources. From an application perspective, our models will cover the inventory and supply chain theory, network design and transportation logistics. From a methodology perspective, we will use linear and integer programming, stochastic programming, and Markov decision processes. The course will include a number of large case studies that focus on practical implementations.
Service systems arise primarily from the service sector of the economy. Examples are contact centers (also known as call centers), airlines, insurance and healthcare. This course describes techniques that are useful in the analysis and design of such systems. The class is structured around a number of cases. The emphasis is on modeling, solving the models, and interpreting the results. Both operational and strategic decisions are covered through appropriate examples.
ORIE 5132Pricing Analytics and Revenue Management3
The field of Revenue Management (RM) deals with selling a product at the right price, at the right time to the right person. Many industries use revenue management tools to maximize the return on their limited supply of products including e-retail, manufacturing, transportation, entertainment, advertising, etc. For example, e-retailers use RM to decide what assortment of products to show to the customers. Airlines use RM to decide what fare classes should remain open and what fare classes should be closed. Hotels use Revenue management to choose the room rates and to decide how much to overbook. The course will cover different quantitative models in pricing analytics and revenue management including newsvendor models, demand forecasting, network revenue management, choice modeling, assortment optimization, service operations and auctions. We will present ideas and models in the context of different application settings.
This course develops the skills needed to use Operations Research modeling and data analysis skills in real applications, i.e., “for real.” The course teaches and uses general modeling principles in a selection of applications, e.g., epidemic interventions, emergency service deployments, community first responder systems, bike sharing, ride hailing, and other topics as time/interest allows.
This course in Discrete Optimization is focused on Nondeterministic Polynomial-hard problems but with a very strong focus on the use of Mixed-Integer Linear Programming, general-purpose solvers to attack them.
The course examines how the computing, economic and sociological worlds are connected and how these connections affects these worlds. Tools from computer science, game theory and mathematics are introduced and then used to analyze network structures present in everyday life. Topics covered include social networks, web search, auctions, markets, voting, and crypto-currencies (e.g. bitcoin).
Fundamental ideas of systems engineering, and their application to design and development of various types of engineered systems. Defining system requirements, creating effective project teams, mathematical tools for system analysis and control, testing and evaluation, economic considerations, and the system life cycle.Content utilizes model-based systems engineering, which is the integration of systems modeling tools, such as SysML, with tools for systems analysis, such as Matlab and Modelica. The vision for this integration is the ability to create and analyze complete parametric representations of complex products and systems. These systems make it possible to investigate the impact of changing one aspect of a design on all other aspects of design and performance. This course will familiarize students with these modeling languages. Off-campus students must provide their own Windows 7, internet-connected, computer with administrator access in order to install the commercial software used in this course.
ORIE 5142Systems Analysis Behavior and Optimization3
This is an advanced course in the application of analytical methodologies and tools to the analysis and optimization of complex systems. On completion of this course, students should be able to use probability and statistics as a modeling and analysis tool for systems exhibiting uncertainty; be able to use algorithms and dynamic programming to model and optimize systems with a recursive structure; be able to use optimization tools to optimize complex systems and tune parameters.
ORIE 5154Revenue Optimization and Marketplace Design3
Application of modeling and optimization techniques in designing a company's interface with the market. We will cover a variety of topics (product pricing and capacity control; designing product assortments and customer segmentation; the use of customer data in modeling and optimization; the design of online platforms and markets), with examples from transportation, retail, hospitality, and the sharing economy.
Each year, the course will cover a different advanced topic at the intersection of data science and operations research, with the specific topic to be chosen by the instructor that year. The class will entail advanced reading, homework, and course project. Example semester-long topics include: Multi-arm bandit models in ML and OR, Statistical recovery in data science and OR, Graphical models in data science and OR, Causal inference in data science and OR, and Reinforcement learning in data science and OR.
This course introduces careers in quantitative finance through senior industry speakers across trading, portfolio management, quantitative research, risk management, and FinTech. Sessions focus on career paths, required skills, and student-led discussion. In addition to guest lectures, the course offers students an opportunity to gain practical industry experience through an internship or industry-sponsored project.
ORIE 5213Discrete Optimization for Urban Planning and Mobility3
The course is organized around five major case studies on the use of discrete optimization and data (AI at large) for smart cities. Namely, 1) bike sharing, 2) bus transportation planning, 3) fairness in ambulance allocation (and police patrol), 4) downed tree reporting (NYC Department of Parks and Recreation), and 5) parcel delivery.The teaching is structured to provide three levels of understanding: a first level in which the problem is presented with its importance, impact, and characteristics. The need of a tech-based quantitative approach is claimed and justified. A second level in which, a high-level version of the algorithmic approach used to solve the problem is presented. A third level, dependent on students' interest and knowledge, in which the algorithmic approach is detailed.
A professional development course designed specifically for MEng students in ORIE concentrating in Financial Engineering. Through a series of panels and hands-on workshops, students will develop effective job search materials and participate in active exercises covering topics such as networking, interviewing for specific career paths, and other communication skills for today's professional environments.
ORIE 5217Designing and Running Personalized Health Experiments3
Traditionally, treatment guidelines and health recommendations are based on large cohort studies or randomized controlled trials (RCTs), which provide only average effect estimates. This limits their ability to predict whether an intervention will benefit an individual. With the rise of digital solutions, personalized approaches like N-of-1 trials are gaining traction. These modern designs allow for individual treatment effects and improve population-level effect estimates. This seminar covers N-of-1 trials and other modern study designs such as micro-randomized trials. First, we will get an overview of different study types and their characteristics, then we will give an introduction of the practical aspects for performing N-of-1 trials, and then the main focus of the class will be on methodological approaches for planning and analyzing N-of-1 trials.
This course covers numerical techniques for quantitative trading in Finance. The main computational tool is Python. The computational techniques draw from interpolation, linear algebra, optimization, stochastic control, Monte Carlo simulation, queuing theory, finite difference methods, binomial trees, as well as statistical techniques such as regression, co-integration and principal components analysis. The applications include pricing, market microstructure, hedging and asset allocation for bonds, futures, equities and options. The focus is on theories that can be implemented in trading situations and the Interactive Brokers platform is used extensively for trading assignments.
ORIE 5235Sustainable Urban and Energy Delivery Systems3
The course focuses on how to transition from legacy energy delivery infrastructures dependent on fossil fuel to a sustainable decarbonized grid that harnesses distributed renewable energy resources and responsive demand from buildings, electrified transportation systems, and industrial loads. The content includes models and abstractions for the architecture of the cyber-physical energy system, its economics, and future evolution, and numerical optimization and learning methods in support of the infrastructure's safety critical operations in the legacy system and in the future architecture. At the MSc level the students will focus on learning how to use tools and data while at the graduate level the students will be asked to also solve problems, formulate novel solutions, interpret results. Similarly, to differentiate the MSc from PhD level and course outcomes, the final project will require the MSc students to pick one out of a set of predefined problems while the PhD students will have to define an original problem and solution.
ORIE 5240Bond Mathematics and Mortgage-Backed Securities2
A transaction-oriented course covering U.S. Bond markets. The course covers valuation, trading strategies, and risk profiles of bonds, with a special emphasis on mortgage-backed securities.
This course is taught by a seasoned finance professional and focuses on the tools and techniques used by quantitative traders. The topics covered include risk measurement and management, alpha forecasting methods, and the development and application of trade execution cost models. The emphasis of the course is to enable students to apply quantitative financial models within a real-life trading environment.
ORIE 5253Special Topics in Financial Engineering II2
This course is taught by a seasoned finance professional and provides an overview of the current challenges in the asset management industry and proposes practical solutions to overcome these challenges.
ORIE 5254Special Topics in Financial Engineering III2
This course is taught by a seasoned finance professional and is designed to familiarize students with the most recent developments in the equity derivatives marketplace. The emphasis will be on practical side of trading and analyzing attractive strategies in the equity derivatives markets.
ORIE 5255Special Topics in Financial Engineering IV2
Artificial intelligence is rapidly transforming financial services, introducing new forms of models such as machine learning systems, foundation models, and large language models that operate very differently from traditional financial models. This course provides a rigorous treatment of AI model risk management in financial institutions, combining traditional model governance principles with modern AI system design. Students will study how AI models are developed, evaluated, monitored, and governed in regulated financial environments.
ORIE 5256Special Topics in Financial Engineering V2
This course is taught by a seasoned finance professional. Machine learning (ML) is changing virtually every aspect of our lives. As it relates to finance, this is the most exciting time to adopt a disruptive technology that will transform how everyone invests for generations. Students will learn scientifically sound ML tools used in the financial industry.
ORIE 5257Special Topics in Financial Engineering VI2
Algorithmic trading and ML-powered tools have impacted all asset classes: beyond the most liquid (and well-studied) equity markets, we have observed a growing number of assets (such as bonds, foreign exchange, crypto, on-line adverts, etc.) that are now primarily traded electronically, yet not necessarily via a classical exchange. In this course, we will cover the tools required to compete in FX, Rates and Crypto markets, covering the main protocols (price-streams, second-price auctions, etc.) with particular emphasis on how to apply the latest ML techniques to gain a competitive edge.
Python is rapidly becoming a golden standard for quantitative finance. In this course students will be exposed to the powerful and fast open-source data science libraries and specific applications of analyzing financial data sets.
ORIE 5259Market Microstructure and Algorithmic Trading: Theory and Practice1.5
Modern financial markets have evolved to offer a variety of methods to trade and interact withother participants. Seemingly simple, the different microstructures can create opportunities for improved execution. Alongside the rise of complex market structures, algorithmic trading has become more sophisticated and increasingly reliant on AI & ML models: we introduce the core concepts of algorithmic execution, spanning the full spectrum of trading horizons, from High Frequency market-making to strategies that aim to efficiently execute large orders.
This course offers a broad overview of computational techniques and mathematical skills useful for data scientists. Topics include: unix shell, regular expressions, version control: (git), data structures and algorithms, working with databases, data analysis using Python and related libraries (Pandas, NumPy/Scipy, scikit-learn), parallel computing (Map-Reduce, Spark, Hadoop), basic finite-precision arithmetic, an overview of standard machine learning and optimization algorithms, and time-permitting, a guided tour of functional programming. Students are expected to be comfortable in at least one programming language; Python will be used for most of the course
ORIE 5290Distributed Optimization for Machine Learning and AI3
This is a graduate-level course about theory, algorithms and applications of distributed optimization and machine learning. The course covers the basics of distributed optimization and learning algorithms and their performance analyses when they are used to solve large-scale distributed problems arising in AI, machine learning, signal processing, communication networks, and power systems.
Formulation of linear programming problems and solutions by the simplex method. Related topics such as sensitivity analysis, duality, and network programming. Applications include such models as resource allocation and production planning. Introduction to interior-point methods for linear programming.
A variety of optimization methods stressing extensions of linear programming and its applications but also including topics drawn from integer programming, dynamic programming, and network optimization. Formulation and modeling are stressed as well as numerous applications.
From fitting regression models to training neural networks, many problems in artificial intelligence can be cast as optimization problems. This course studies the fundamentals of optimization as they apply to artificial intelligence. Much of the focus will be on convex optimization, covering topics such as convex analysis, gradient descent for constrained and unconstrained problems, proximal gradient descent, variants of Newton’s method, and the Frank-Wolfe algorithm. The treatment will be at a fairly sophisticated level, giving sound justifications for the algorithms studied.
Covers basic concepts of graphs, networks, and discrete optimization. Fundamental models and applications, and algorithmic techniques for their analysis. Specific optimization models studied include flows in networks, the traveling salesman problem, and network design.
ORIE 5340Applications of Optimization: Modeling and Computation4
This course will cover the use of optimization models in several industries. Covered industries will include manufacturing, process, distribution, retail, and transportation. We will not cover models used exclusively in the financial industry. In each covered industry we will start with simple text-book models, and then extend these models to reflect the realities of the industry, the existing business decisions processes and the available data. We expect to have lectures from experts in some of these industries, each of whom will also discuss Operations Research roles and careers.
Broad survey of the mathematical theory of games, including such topics as two-person matrix and bimatrix games; cooperative and noncooperative n-person games; and games in extensive, normal, and characteristic function form. Economic market games. Applications to weighted voting and cost allocation.
ORIE 5355Applied Data Science: Decision-Making Beyond Prediction3
This course considers the data science challenges beyond training an accurate predictive model, especially for systems about people (data of behavior), and for people (deployed models to influence behavior). Whether for online marketplaces, transportation, governmental, or urban systems, effective data science in such settings requires dealing with user incentives and strategic behavior, networked and decentralized decision-making, and privacy and ethics concerns. Primary evaluation will be through programming based assignments (in Python) and conceptual questions.
This course provides students with a rigorous perspective on, and a technical toolbox for, the design of democratic processes, treated through the lens of algorithmic analysis. The course exposes students to a range of such democratic algorithms and of algorithmic settings arising in democracy, including ranked choice voting, approval-based multi-winner elections, participatory budgeting, and apportionment. On a technical level, the course illustrates to students the richness of possible algorithmic approaches to a societal phenomenon, and it trains students in the rigorous application of techniques in this domain, including the axiomatic method, notions of fairness and proportionality, mathematical programming, social welfare functions, measures of power in weighted voting games, and measuring the quality of voting rules through competitive analysis (distortion). The course draws on classic and recent results in computational social choice.
Explores optimization in the context of finance, including methodologies beyond linear programming, such as second-order cone programming and semidefinite programming. Topics include Markowitz portfolio theory and modeling; factor models for portfolio selection and risk control; the Black-Litterman model (and related Bayesian topics); utility functions; coherent risk measures; stochastic programming; and optimal execution of portfolio transactions. Emphasis is on concepts that are directly implementable.
This course covers algorithmic and computational tools for solving optimization problems with the goal of providing decision-support for business intelligence. We will cover the fundamentals of linear, integer and nonlinear optimization. We will emphasize optimization as a large-scale computational tool, and show how to link programming languages with optimization software to develop industrial-strength decision-support systems. We will demonstrate how to incorporate uncertainty into optimization problems. Throughout the course, we will cover a variety of modern applications, including pricing and marketing for e-commerce, ad auctions on the web, and on-line ride-sharing.
ORIE 5390Optimization Models for Logistics, Networks, and Markets1.5
Hands-on experience with integer linear programming and dynamic programming: creating ILPs and DPs, implementing them, critiquing them, understanding solver output, and improving ILPs using better variables, constraints, symmetry breaking, etc. Examples of problems that we will study in this course are logistical problems like sequencing in production, scheduling problems with conflicts (vertex coloring), matching problems for markets and clustering problems in networks, but are not limited to these domains. In addition, a variety of general linear programming techniques such as Fourier-Motzkin elimination, Dantzig-Wolfe decomposition, Benders decomposition and extended formulations may be covered, as well as rounding techniques of LP solutions.
ORIE 5500Eng Probability and Statistics: Modeling and Data Science II4
A rigorous foundation in theory combined with the methods for modeling, analyzing, and controlling randomness in engineering problems. Probabilistic ideas are used to construct models for engineering problems, and statistical methods are used to test and estimate parameters for these models. Specific topics include: random variables, probability distributions, density functions, expectation and variance, multidimensional random variables, and important distributions including normal, Poisson, exponential, hypothesis testing, confidence intervals, and point estimation using maximum likelihood and the method of moments.
ORIE 5510Introduction to Engineering Stochastic Processes I4
Uses basic concepts and techniques of random processes to construct models for a variety of problems of practical interest. Topics include: the Poisson process, Markov chains, renewal theory, models for queuing, and reliability.
We will learn how to model randomness, analyze its impact, and make optimal decisions when it is present. We will cover stochastic modeling techniques, statistical principles, simulation, and decision-making under uncertainty. Using applications, we will demonstrate how we can use statistical principles to gain insight from data generated by systems with randomness. We will use simulation models to assess the performance of such systems and gauge how it changes in response to our decisions. We will introduce and use stochastic modeling techniques, such as Markov chains and Poisson processes, to build models of random phenomena and use these to gain understanding and guide decisions. As well as covering theoretical concepts, the course will put substantial emphasis in computational implementation of both simulation and decision-making problems.
Introduces statistical tools for the analysis of time-dependent data. Data analysis and application will be an integral part of this course. Topics include linear, nonlinear, seasonal, multivariate modeling, and financial time series.
ORIE 5570Reinforcement Learning with Operations Research Applications3
The ongoing information revolution and the advent of the big data era make quantitative methods in the business context indispensable. This course introduces reinforcement learning, decision-making under uncertainty, and related algorithms through the lens of OR applications. Examples will be drawn from real-world problems in operations, revenue management, queuing, finance, transportation, healthcare, and other areas of interest. The course will cover modeling and applications, basic theory, and algorithms.
Introduction to Monte Carlo simulation and discrete-event simulation. Topics include: random variate and process generation; data-driven distribution modeling; input and output analysis; modeling, analysis and optimization of complex systems. Emphasizes tools and techniques needed in practice; in particular, modeling and simulation in Python, as well as commercial discrete-event simulation languages.
Introduction to Monte Carlo simulation. Topics include: random variate and process generation; data-driven distribution modeling; input and output analysis. Emphasizes modeling and simulation in Python.
ORIE 5582Monte Carlo Methods in Financial Engineering2
An overview of Monte Carlo methods as they apply in financial engineering. Generating sample paths. Variance reduction (including quasi random number), discretization, and sensitivities. Applications to derivative pricing and risk management.
ORIE 5600Financial Engineering with Stochastic Calculus I4
Introduction to continuous-time models of financial engineering and the mathematical tools required to use them, starting with the Black-Scholes model. Driven by the problem of derivative security pricing and hedging in this model, the course develops a practical knowledge of stochastic calculus from an elementary standpoint, covering topics including Brownian motion, martingales, the Ito formula, the Feynman-Kac formula, and Girsanov transformations.
ORIE 5610Financial Engineering with Stochastic Calculus II4
Building upon the foundation established in ORIE 5600, this course presents advanced models for pricing and hedging financial derivatives, along with essential computational methods. The curriculum focuses on models for equities, foreign exchange, and fixed-income securities, utilizing local and stochastic volatility frameworks, the Heston model, partial differential equation (PDE) methods, change of numeraire techniques, stopping times, and the Heath-Jarrow-Morton (HJM) model.
ORIE 5630Operations Research Tools for Financial Engineering4
Introduction to the applications of OR techniques, e.g., probability, statistics, and optimization, to finance and financial engineering. The course reviews probability and statistics and surveys assets returns, ARIMA time series models, portfolio selection using quadratic programming, regression, CAPM and factor models, option pricing, GARCH models, fixed-income securities, and resampling techniques. Covers the use of R for statistical calculations, simulation, and optimization.
Regression, ARIMA, GARCH, stochastic volatility, and factor models. Calibration of financial engineering models, estimation of diffusion models, estimation of risk measures, multivariate models and copulas, bayesian statistics. Students are instructed in the use of R software.
ORIE 5650Quantitative Methods of Financial Risk Management3
A historical perspective of market risk measurement including the Markowitz, CAPM and APT models and of insurance risk management, a description of the Value-at-Risk approach and an overview of VaR variants and extensions such as delta-VaR, CVaR and more generally distorsion risk measures, and a description of the qualitative approach of risk management by different companies. The course surveys methods for evaluating risk and consider multivariate methods for evaluating portfolios requiring copula tools which have become popular. Topics in credit risk: methods for determining default probabilities and company ratings based on financial ratios, and approaches to measuring credit risk which can be roughly divided into structural models and reduced-form models; first to default products and impact of correlation. Topics in insurance: pensions and life insurance, property and casualty insurance. Topics in finance: correlation of extremes, Herd index and systemic risk. Topics for environmental risks: flood risk, hurricane risk, weather derivatives and cat-bonds. Topics in energy: extremes and nuclear risk, energy supply issues, river network dam management. Regulations aspects (Basel II-III for banks and Solvency II for the insurance industry) and internal risk models for banks and insurance companies. Issues about concrete implementation of extreme value theory for regulation. Introduction to economic capital and economic capital allocation, and to competition issues in insurance and between old and new energies. Case studies and concrete examples of quantitative risk management issues and applications to financial, insurance, energy and environmental sectors. Participation of Chief Risk Officers of some companies to one or two sessions.
In order to be able to assess the risk associated with future extreme values in financial returns, a practitioner must have an idea how heavy the tails of the returns are and how they cluster. The practitioner must also be able to understand the extremal risks associated with a portfolio of financial instruments, potentially of a large size. In this course the students will learn to work with extreme values, to understand the difference between light tails and heavy tails, and learn how the largest return and the total return grow for different types of tails. They will also learn statistical techniques (mostly through R packages) used to work with extreme values.
ORIE 5735Graph-based Data Science and AI Models for Networked Systems3
The goal of this course is to introduce data structural and computational models that are indexed by the irregular support of a graph. The graph represents the network that couples the dynamics of many agents, or it can be a more abstract Bayesian graphical model that explains how observations are conditionally dependent. The course will start from introducing basic concepts in graph theory followed by an introduction to random graphs models. This part will be followed by network dynamical models that model the observations from these processes. Bayesian graphical models will be briefly covered as a more general statistical abstraction and computational framework to perform inferences. The course will then introduce the students to the emerging field of graph signal processing, a theory that generalizes digital and image processing to graph signals.
Examines the statistical aspects of data mining, the effective analysis of large datasets. Covers the process of building and interpreting various statistical models appropriate to such problems arising in scientific and business applications. Topics include naive Bayes, graphical models, multiple regression, logistic regression, clustering methods and principal component analysis. Assignments are done using one or more statistical computing packages.
Modern data sets, whether collected by scientists, engineers, medical researchers, government, financial firms, social networks, or software companies, are often big, messy, and extremely useful. This course addresses scalable robust methods for learning from big messy data. We'll cover techniques for learning with data that is messy --- consisting of real numbers, integers, booleans, categoricals, ordinals, graphs, text, sets, and more, with missing entries and with outliers --- and that is big --- which means we can only use algorithms whose complexity scales linearly in the size of the data. We will cover techniques for cleaning data, supervised and unsupervised learning, finding similar items, model validation, and feature engineering.
ORIE 5742Info Theory, Probabilistic Modeling, and Deep Learning with Scientific and Financial Apps3
This course is about building and understanding machine learning models for scientific and financial applications. It will cover foundational aspects of information theory and probabilistic inference as they relate to model construction and deep learning. Topics include hamming codes, repetition codes, entropy, mutual information, Shannon information, channel capacity, likelihood functions, Bayesian inference, graphical models, and deep neural networks. The section on deep neural networks will consider fully connected, convolutional, recurrent, and LSTM networks, generative adversarial training, and variational autoencoders.
Learn and apply key concepts of modeling, analysis and validation from machine learning, data mining and signal processing to analyze and extract meaning from data. Implement algorithms and perform experiments on images, text, audio and mobile sensor measurements. Gain working knowledge of supervised and unsupervised techniques including classification, regression, clustering, feature selection, and dimensionality reduction.
ORIE 5751Applied Causal Inference using Machine Learning3
Provides an applied treatment of modern causal inference using machine learning to handle high-dimensionality and nonparametric estimation. Formulates key causal questions in the languages of structural equation modeling and potential outcomes. Presents methods for estimating and constructing confidence intervals on causal and structural parameters using machine learning, including de-biased machine learning, and for learning how to predict heterogeneous treatment effects. Introduces tools from machine learning and deep learning developed for prediction purposes and discusses how to adapt them to causal inference. Emphasizes the applied and practical perspectives with real-world-data examples and assignments. Requires basic knowledge of statistics and machine learning and programming experience in R or Python.
ORIE 5752Foundations of Causal Inference for Data-Driven Decisions4
This course provides a rigorous introduction to the theory and practice of causal inference for data-driven decision-making. Students will learn to identify and estimate causal effects using both experimental and observational data, combining statistical foundations with computational tools. Emphasis is placed on understanding causal assumptions, designing valid estimators, and analyzing the theoretical properties of each method. Attention will be given to unique challenges that arise in real-world operational and policy decisions. Example applications include online marketplaces, social networks, and inventory control. Topics include the potential outcomes framework, causal diagrams, randomized and quasi-experimental designs, matching and weighting methods, instrumental variables, difference-in-differences, and introductory causal machine learning.
ORIE 5820Data-Driven Decision Modeling and Analysis3
This course equips students with essential data-driven decision-making skills, integrating structured and unstructured data. It bridges classical modeling techniques with modern computational tools, emphasizing critical thinking, automation, and problem-solving. The curriculum prepares students for operations research, supply chain analytics, finance, and engineering management careers.
A professional development course designed specifically for MEng students in ORIE. Through a series of panels and hands-on workshops, you will develop effective job search materials and participate in active exercises covering topics such as networking, interviewing for specific career paths, and other communication skills for today's professional environments.
Weekly meeting for master of engineering students. Discussion with industry speakers and faculty members on the uses of engineering in the effective and efficient design, manufacturing, marketing, distribution, sustainment, and retirement of goods and services.
Substantial, group-based design project that has a strong systems design component. The project must be approved by an ASE 1 instructor before the student enrolls in the course. (The following projects are preapproved: FSAE, HEV, Robocup, Brain.) A formal report is required.
Initial segment of the Master of Engineering project experience, culminating in a project charter that details the problem statement, the data and resources to be used, and a work plan for the spring semester.
Faculty-supervised project work that may involve independent readings, scholarly research, or an applied project in collaboration with a Cornell entity or an external partner organization. Students must submit a proposal detailing the project goals, statement of work, deliverables, and learning outcomes. The proposal must be approved by the supervising faculty member and the student's program director.
ORIE 6125Computational Methods in Operations Research3
A suite of tools and techniques that enable computation in operations research. Structured and efficient programming, code optimization, code review, version management systems, building a user interface, exploring and manipulating large-scale datasets.
Students will learn about theoretical approaches from across computer science, economics, and operations research to group decision settings, in particular in voting and the fair allocation of resources. This course will mainly focus on theoretical approaches to these topics. We will study key solution concepts from computational social choice theory, cooperative and non-cooperative game theory, and fair division: approaching them with tools from optimization, algorithms, and probability. The course will cover the foundations of these concepts, as well as cutting-edge research results based on these concepts. As part of the course, students will read, present, and discuss research papers, and perform a research project.
This class will explore topics in the intersection of computer science, economics, and operations - on the application of algorithms, data science/machine learning, and mechanism design to the study of democracy, markets, and societal systems at large.
ORIE 6180Online Decision-Making and Market Design3
This course focuses on studying optimization problems faced with two sources of uncertainty: Online decision-making: Settings involving multiple decisions over time, with uncertainty about future events, and where actions affect current and future outcomes. Market design: Settings involving multiple decision-making agents, with uncertainty about agents’ types, and where agents’ actions affect each other as well as overall outcomes. Our aim is to develop mathematical foundations for these problems – how to formulate them (and why they are related); common algorithmic tools for solving them; analyzing the performance and limits of these algorithms; comparing different models of knowledge in terms of their effect on decision-making; and understanding how to handle different objectives in these settings. Our approach will be primarily theoretical, focusing on mathematical techniques for designing and analyzing algorithms with formal guarantees. However, the problems we consider have significant practical motivation, and we will see lots of examples throughout the course.
ORIE 6217Applied Bayesian Analysis for Computational Research3
Bayesian modeling and data analysis is a powerful tool for computational research. It consists of writing a probability model and then fitting it with observed data, while handling uncertainty. The model can be flexible, encompassing hierarchy, spatio-temporal dynamics, graphs, and high-dimensionality. This course is a graduate, hands-on introduction to Bayesian analysis in Stan and/or Pyro. The focus will be on writing and fitting models in practice for computational research, including the applied Bayesian statistics workflow: model building, checking, and evaluation. The course will also discuss research papers that use such methods.
Rigorous treatment of the theory and computational techniques of linear programming and its extensions, including formulation, duality theory, algorithms; sensitivity analysis; network flow problems and algorithms; theory of polyhedral convex sets, systems of linear equations and inequalities, Farkas' Lemma; and exploiting special structure in the simplex method and computational implementation.
Continuation of ORIE 6300. Introduces optimization problems over mixed-integer sets and studies the mathematical foundations of such problems. The algebraic and geometric properties of polyhedral formulations of mixed-integer programming problems are studied. Key topics include: formulations, relaxations, polyhedral theory, cutting planes, column generation, decomposition and enumeration. Some homework assignments would include computational tasks that require using optimization software.
Discrete Optimization problems are generally formulated through Mixed-Integer Linear and Nonlinear Programming (MIP) and solved, to a large extent, by both commercial and noncommercial MIP solvers. Solving the formulated models to proven optimality is generally not necessary on the application side and often out of reach. However, computing high quality feasible solutions is a strong requirement in applications. The course covers the methodology behind the development of effective heuristic methods within MIP solvers and presents recent hybridization mechanisms based on data and Machine Learning.
ORIE 6360Optimization Under Uncertainty: Robust and Online Models3
In most sequential decision problems, uncertainty evolves over time and we need to make decisions in the face of uncertainty. This is a fundamental problem arising in almost every business application where real-time decisions are based on the information revealed thus far. The uncertainty in the problem can be modeled in a number of ways (e.g., a probability distribution over some parameters or an uncertainty set for some variables) and the selection of an appropriate framework is purely a choice of the decision-maker. Such a selection depends on various considerations ranging from the availability of historical data to the tractability of the resulting optimization problem and the robustness of resulting solutions. In the first part of the class, we primarily focus on robust optimization which is a widely used paradigm to handle adversarial models of uncertainty. We also contrast robust optimization with various other paradigms such as stochastic optimization and distributionally robust optimization. In the second part of the class, we focus on discrete optimization problems under uncertainty such as two-stage facility location and sequential matching problems. We will discuss these classes of discrete problems under both the paradigm of robust optimization (worst-case scenario analysis) as well as online optimization (competitive ratio analysis).
ORIE 6365Continuous Optimization: Algorithms and Complexity3
Graduate course on the theory and algorithms of continuous optimization. Prepares students for research in optimization theory and for developing advanced methods for applications in operations research, machine learning, and related domains. Topics: convexity, smooth and non-smooth problems, duality. Ellipsoid and subgradient methods. Mirror descent and the geometry of optimization problems. Accelerated optimal methods, lower complexity bounds and resisting oracles. Composite problems. Stochastic and large-scale optimization, variance reduction techniques. Second-order algorithms: Newton, quasi-Newton, and interior-point methods. Applications will be drawn from machine learning, semidefinite programming, and large-scale graph optimization.
ORIE 6367Advanced Algorithms in Continuous Optimization3
The field of continuous optimization lies at the intersection of applied mathematics, operations research, and a wide range of scientific and engineering applications. In recent years, the rapid growth of data-driven technologies and large-scale computational models has led to intense research activity in the development and analysis of efficient optimization algorithms. Significant progress has been made in convex optimization, with mature theory and scalable algorithms now available. However, many modern applications arising in machine learning, signal and image processing, data science, and engineering design lead to inherently nonconvex optimization problems. For such problems, algorithmic design is considerably more challenging, and theoretical understanding is far less complete. This course focuses on algorithms for continuous optimization, with an emphasis on both convex and nonconvex settings. We will study a mixture of classical foundational methods and recent algorithmic developments that are widely used in contemporary applications.
Introduction to stochastic processes that presents the basic theory together with a variety of applications. Topics include Markov processes, renewal theory, random walks, branching processes, Brownian motion, stationary processes, martingales, and point processes.
Covers sample spaces, events, sigma fields, probability measures, set induction, independence, random variables, expectation, review of important distributions and transformation techniques, convergence concepts, laws of large numbers and asymptotic normality, and conditioning. In the last part of the course, we will cover applications to epidemic modeling.
Introduction to Monte Carlo and discrete-event simulation. Emphasizes underlying theory. Random variate generation, input and output analysis, variance reduction, selection of current research topics.
ORIE 6640Martingale Theory and Applications in Finance3
This course introduces Martingale Theory with a view towards applications to pricing and hedging of financial derivatives. We discuss both complete and incomplete markets as well as risk measure-based pricing and hedging approaches. Further topics include market models for financial derivatives and recent machine-learning developments in finance such as deep hedging.
Topics include review of distribution theory of special interest in statistics: normal, chi-square, binomial, Poisson, t, and F; introduction to statistical decision theory; sufficient statistics; theory of minimum variance unbiased point estimation; maximum likelihood and Bayes estimation; basic principles of hypothesis testing, including Neyman-Pearson Lemma and likelihood ratio principle; confidence interval construction; and introduction to linear models.
Empirical observation of deep neural networks shows surprising phenomena that classical statistical theory fails to fully describe. For example, bounds on generalization error from classical statistics grow with the flexibility of the model class but neural networks often exhibit low generalization error despite being extremely flexible. Also, training deep neural networks with stochastic gradient descent produces accurate models despite non-convexity of the loss landscape. A recently emerged literature is developing new theory to explain these and other mysteries. After presenting relevant theoretical results from classical statistics and a brief refresher on deep learning, the course will present theoretical results from recent research articles, complementing them with empirical evidence, emphasizing what is unknown along with what is known.
Priors, posteriors, Bayes estimators, decision theory, asymptotic theory, Bayes factors, credible regions, hierarchical models, nonparametric Bayes, computational methods, Bayesian robustness, and applications. This is a theory-oriented course intended for PhD students. For a more applied introduction to Bayesian statistics, students should take STSCI 4780, Bayesian Data Analysis: Principles and Practice, which is offered in the spring.
Properties of the multivariate normal distribution. Distribution theory for quadratic forms. Properties of least squares and maximum likelihood estimates. Methods for fixed-effect models of less than full rank. Analysis of balanced and unbalanced mixed-effects models. Restricted maximum likelihood estimation. Some use of software packages and illustrative examples.
Weekly one and one-half hour meeting devoted to presentations by distinguished visitors, by faculty members, and by advanced graduate students on topics of current research in the field of operations research.
