Menu

TutORials

The TutORials in Operations Research series is published annually by INFORMS as an introduction to emerging and classical subfields of operations research and management science. These chapters are designed to be accessible for all constituents of the INFORMS community, including current students, practitioners, faculty, and researchers. The publication allows readers to keep pace with new developments in the field and serves as augmenting material for a selection of the tutorial presentations offered at the INFORMS Annual Meeting.

Large-Scale Optimization via Monotone Operators

This tutorial presents a unified analysis of convex optimization algorithms through
the abstraction of monotone operators. Through this streamlined approach, we derive
and analyze a wide variety of classical and modern algorithms, including: Gradient
Descent, Dual Ascent, Proximal Point Method, Proximal Gradient Method, Projected
Gradient Method, Forward-Backward Splitting, Peaceman–Rachford Splitting,
Douglas–Rachford Splitting, Davis–Yin Splitting, Method of Multipliers, Proximal
Method of Multipliers, Alternating Direction Method of Multipliers, Alternating Minimization Algorithm, Primal-dual hybrid gradient (PDHG), PDLP, and Condat–Vũ.
 

Speakers: Ernest Ryu and Wotao Yin

Turning the Tide: Data Analytics and Optimization Approaches for Mitigating the University Mental Health Crisis

In this TutORial, we address the growing mental health crisis affecting university
campuses across the nation. Specifically, we provide a comprehensive overview of the
challenges faced by Counseling and Psychological Services (CAPS) centers and present
a range of data analytics and Operations Research tools aimed at mitigating these
issues. By posing key unresolved questions, we offer a holistic analysis that spans the
spectrum from individual patient outcomes to system-level operational performance,
highlighting the complex interdependencies between clinical effectiveness and operational efficiency. Through this lens, we present a structured and accessible framework that both summarizes and contextualizes the primary operational and clinical challenges in university mental health services. In doing so, we also showcase a variety of data-driven methodologies designed to address these challenges, offering insight into the strengths and limitations of current approaches.

Speaker:Hrayer Aprahamian

Modeling with Attack Graphs for Securing Cyber-physical Systems

Modern critical infrastructures consist of increasingly complex and interdependent cyber-physical systems (CPS). Securing cyber-physical infrastructure requires understanding how components interact with one another across physical, cyber, and human dimensions, as well as how threat modeling affects system components and operations. This tutorial reviews modeling techniques for CPS security, focusing on network models, threat modeling techniques, and prescriptive decision-making. Attack graphs offer a structured and systematic approach to modeling threats to a system and are crucial in cybersecurity risk management.We review three applications of operations research modeling techniques that leverage attack graphs for CPS security: allocating a security budget for cybersecurity planning, developing vulnerability metrics for securing
cyber-physical energy systems, and performing risk assessments for administrating
election systems. Through these applications, we demonstrate the potential for using
attack graphs for prescriptive decision-making and proactive planning to secure CPS.

Speaker: Laura A. Albert and Carmen Haseltine

The Gittins Index: A Design Principle for Decision-Making Under Uncertainty

The Gittins index is a tool that optimally solves a variety of decision-making problems involving uncertainty, including multi-armed bandit problems, minimizing mean latency in queues, and search problems like the Pandora’s box model.
However, despite the above examples and later extensions thereof, the space of problems that the Gittins index can solve perfectly optimally is limited, and its definition is rather subtle compared to those of other multi-armed bandit algorithms.
As a result, the Gittins index is often regarded as being primarily a concept of theoretical importance, rather than a practical tool for solving decision-making problems.
 
The aim of this tutorial is to demonstrate that the Gittins index can be fruitfully applied to practical problems.
We start by giving an example-driven introduction to the Gittins index, then walk through several examples of problems it solves—some optimally, some suboptimally but still with excellent performance.
Two practical highlights in the latter category are applying the Gittins index to Bayesian optimization, and applying the Gittins index to minimizing tail latency in queues.
 

Speaker: Ziv Scully and Alexander Terenin

Five Starter Problems: Solving Quadratic Unconstrained Binary Optimization Models on Quantum Computers

This tutorial offers a quick, hands-on introduction to solving Quadratic Unconstrained Binary Optimization (QUBO) models on currently available quantum computers and their simulators. We cover both IBM and D-Wave machines: IBM utilizes a gate-circuit architecture, and D-Wave is quantum annealer. We provide examples of three canonical problems and two models from practical applications. The tutorial is structured to bridge the gap between theory and practice: we begin with an overview of
QUBOs, explain their relevance and connection to quantum algorithms, introduce key quantum computing concepts, provide the foundations for two quantum heuristics, and provide detailed implementation guides. An associated GitHub repository provides the
codes in five companion notebooks. In addition to reaching undergraduate and graduate students in computationally intensive disciplines, this article aims to reach working industry professionals seeking to explore the potential of near-term quantum applications.
As our title indicates, this tutorial is intended to be a starting point in a journey towards solving more complex QUBOs on quantum computers.
 

Speakers: Sridhar Tayur and Arul Rhik Mazumder

The Role of Optimization in the Decarbonized Energy Systems of the Future

Energy is a fundamental need of human activity. Electricity in particular is a critical
resource for society in the 21st century and its ubiquitous use in our houses and cities
makes it an essential part of our daily life. As we aim to reduce the environmental
impact of human activity, a historical energy transition is under way. This transition
raises several major challenges for electric power systems. We begin with an overview
of the general trends of change in power systems, followed by examples of real-world
success of mathematical optimization techniques in practice. We then introduce the
unit commitment problem and how to obtain commitment decisions that are robust in
the context of large-scale penetration of renewables. This is followed by an aggregatorbased
optimization model to support the participation of so-called prosumers in the
electricity markets and their potential to contribute flexibility to the power system.
Next we consider several of the recent research developments concerning charging
infrastructure for electric vehicles. We conclude with a summary of important future
research opportunities for the optimization community in electric energy systems.
 

Speakers: Miguel F. Anjos

Social Media Information Operations

The battlefield of information warfare has moved to online social networks, where
influence campaigns operate at unprecedented speed and scale. As with any strategic
domain, success requires understanding the terrain, modeling adversaries, and executing
interventions. This tutorial introduces a formal optimization framework for
social media information operations (IO), where the objective is to shape opinions
through targeted actions. This framework is parameterized by quantities such as network
structure, user opinions, and activity levels—all of which must be estimated
or inferred from data. We discuss analytic tools that support this process, including
centrality measures for identifying influential users, clustering algorithms for detecting
community structure, and sentiment analysis for gauging public opinion. These
tools either feed directly into the optimization pipeline or help analysts interpret the
information environment. With the landscape mapped, we highlight threats such as
coordinated bot networks, extremist recruitment, and viral misinformation. Countermeasures
range from content-level interventions to mathematically optimized influence
strategies. Finally, the emergence of generative AI transforms both offense and
defense, democratizing persuasive capabilities while enabling scalable defenses. This
shift calls for algorithmic innovation, policy reform, and ethical vigilance to protect
the integrity of our digital public sphere.
 

Speakers: Tauhid Zaman and Yen-Shao Chen

 

Mitigating the Impacts of Wildfires on Electric Power Systems through Stochastic Optimization

Dry and windy weather conditions significantly increase the risk of wildfires, whose
spread exacerbates the vulnerability of the grid and results in prolonged power outages.
This tutorial introduces and reviews recent streams of studies on addressing
this challenge through stochastic optimization approaches, including static, adaptive,
dynamic, and distributionally robust models. In particular, we account for random
failures of power lines, which depend not only on the ambient environment (such as
temperature, wind speed, and fire) but also on the power flowing through the line,
introducing decision-dependent uncertainty (DDU). We introduce the modeling of
wildfire, power systems operations, and their interactions, as well as how stochastic
optimization models can characterize DDU and mitigate the impacts of wildfires on
electric power systems. As examples, we mention three models, ranging from long-term
planning to short-term and dynamic reconfiguration of a power system amidst wildfireprone
conditions. For each model, we provide a numerical case study to demonstrate
the value of modeling (e.g., DDU and dynamic reconfiguration) in mitigating the
impacts of wildfires.

Speakers: Juan-Alberto Estrada-Garcia, Xinyi Zhao, Ruiwei Jiang, Alexandre Moreira,  and Chaoyue Zhao

Statistical and Algorithmic Foundations of Reinforcement Learning

As a paradigm for sequential decision making in unknown environments, reinforcement learning (RL) has received a flurry of attention in recent years. However, the explosion
of model complexity in emerging applications and the presence of nonconvexity exacerbate the challenge of achieving efficient RL in sample-starved situations, where
data collection is expensive, time-consuming, or even high-stakes (e.g., in clinical trials, autonomous systems, and online advertising). How to understand and enhance the sample and computational efficacies of RL algorithms is thus of great interest. In this tutorial, we aim to introduce several important algorithmic and theoretical developments in RL, highlighting the connections between new ideas and classical topics. Employing Markov Decision Processes as the central mathematical model, we cover
several distinctive RL scenarios (i.e., RL with a simulator, online RL, offline RL, robust RL, and RL with human feedback), and present several mainstream RL approaches
(i.e., model-based approach, value-based approach, and policy optimization). Our discussions gravitate around the issues of sample complexity, computational efficiency,
as well as algorithm-dependent and information-theoretic lower bounds from a nonasymptotic viewpoint.
 

Speakers: Yuejie Chi, Yuxin Chen, and Yuting Wei

Responsible Machine Learning via Mixed-Integer Optimization

In the last few decades, Machine Learning (ML) has achieved significant success across
domains ranging from healthcare, sustainability, and the social sciences, to criminal
justice and finance. But its deployment in increasingly sophisticated, critical, and
sensitive areas affecting individuals, the groups they belong to, and society as a whole
raises critical concerns around fairness, transparency and robustness, among others. As
the complexity and scale of ML systems and of the settings in which they are deployed
grow, so does the need for responsible ML methods that address these challenges while
providing guaranteed performance in deployment.
Mixed-integer optimization (MIO) offers a powerful framework for embedding
responsible ML considerations directly into the learning process while maintaining
performance. For example, it enables learning of inherently transparent models that
can conveniently incorporate fairness or other domain specific constraints. This tutorial
paper provides an accessible and comprehensive introduction to this topic discussing
both theoretical and practical aspects. It outlines some of the core principles of
responsible ML, their importance in applications, and the practical utility of MIO for
building ML models that align with these principles. Through examples and mathematical
formulations, it illustrates practical strategies and available tools for efficiently
solving MIO problems for responsible ML. It concludes with a discussion on current
limitations and open research questions, providing suggestions for future work.

Speakers:

Nathan Justin, Qingshi Sun, Andrés Gómez, and Phebe Vayanos

Back To Top

The Institute for Operations Research and the Management Sciences

5521 Research Park Drive, Suite 200
Catonsville, MD 21228 USA

phone 1 443-757-3500

phone 2 800-4INFORMS (800-446-3676)

fax 443-757-3515

email

Get the Latest Updates

Copyright 2025 INFORMS. All Rights Reserved