All regions of Operations Research
Search across topics, filter by region, difficulty, or type. Click any card to open a dedicated guide page with key concepts, applications, a table of contents, and curated resources.
Foundations of OR
The vocabulary of decisions: variables, objectives, constraints, uncertainty, and algorithms.
What is Operations Research?
The discipline of building analytical models to improve decisions.
Modeling Decisions
Translate a real situation into variables, objectives, and constraints.
Objectives, Constraints & Uncertainty
Tradeoffs made explicit: cost, service, risk, fairness, resilience.
Algorithms & Computation
The methods that find exact, approximate, or robust decisions.
Probability & Statistics for OR
The measurement and uncertainty toolkit behind OR models.
Model Validation & Sensitivity
Check whether a model is useful, credible, and stable.
Multi-Objective Optimization
Make cost, service, risk, fairness, and emissions visible together.
Data Envelopment Analysis
Benchmark efficiency across comparable units.
Forecasting for OR
Turn historical data into decision inputs, not just predictions.
Spreadsheet & Algebraic Modeling
Build transparent OR models in spreadsheets and modeling languages.
Optimization Core
Mathematical programming — the engine room of OR.
Mathematical Optimization
The central modeling language of OR.
Linear Programming
Linear objective, linear constraints — the workhorse of OR.
Integer & Mixed-Integer Programming
Discrete decisions: yes/no, counts, assignments, logic.
Nonlinear Programming (NLP)
When objectives or constraints stop being linear.
Convex Optimization
Where every local optimum is global.
Dynamic Programming
Sequential decisions decomposed into stages and states.
Second-Order Cone Programming (SOCP - Beta)
A convex nonlinear model class inside conic optimization.
Stochastic Programming
Optimize decisions before uncertain futures are revealed.
Robust Optimization
Find decisions that survive bounded uncertainty.
Decomposition Methods
Split large models into pieces solvers can actually handle.
Constraint Programming
Search and propagation for rich logical constraints.
Heuristics & Metaheuristics
Good answers when exact optimization is too slow or brittle.
Global Optimization & MINLP
Nonconvex models with continuous and discrete structure.
Combinatorial Optimization
Optimize over sets, sequences, trees, matchings, and routes.
Quadratic Programming (QP)
Linear constraints with a quadratic objective function.
Quadratically Constrained Quadratic Programming (QCQP - Beta)
Quadratic objectives with quadratic constraints.
Polyhedral Theory & Cutting Planes
Understand the geometry that makes integer optimization effective.
Complementarity & Equilibrium Models
Model markets, traffic, contact, and KKT systems with either-or conditions.
Goal Programming
Optimize deviations from multiple aspiration levels.
Postoptimal & Parametric Analysis
Understand how optimal solutions change when inputs move.
Uncertainty & Stochastic Systems
Modeling randomness, queues, simulation, and decisions under risk.
Stochastic Processes
Systems that evolve randomly over time.
Queueing Theory
Waiting lines, service systems, and congestion.
Markov Chains
State-to-state stochastic models without decisions.
Simulation
Imitating system behavior when analysis is too hard.
Decision Analysis
Structured choice under uncertainty and multiple criteria.
Markov Decision Processes
Controlled stochastic systems with state, action, and reward.
Reliability & Maintenance
Keep systems available under failure, aging, and repair.
Risk Analysis
Quantify downside, tail events, and risk appetite.
Simulation Optimization
Optimize systems whose performance is estimated by simulation.
Networks, Games & Systems
Flows, strategy, sequencing, and structured combinatorial problems.
Game Theory
Strategic interaction among decision-makers.
Network Optimization
Flows, paths, matchings, and connectivity on graphs.
Scheduling
Allocating work over time on machines, people, rooms, or vehicles.
Matching & Assignment
Pair resources, people, tasks, and markets optimally.
Vehicle Routing
Plan routes for fleets with capacity, time windows, and uncertainty.
Facility Location
Choose where to place warehouses, clinics, depots, and capacity.
Traveling Salesperson Problem
Find a minimum-cost tour visiting each location once.
Project Management, PERT & CPM
Schedule project activities under precedence, time, and resource limits.
Optimal Control
Optimize decisions in dynamic physical and engineered systems.
System Dynamics & Feedback Models
Model feedback loops, delays, and policy resistance.
Operations Applications
Inventory, logistics, supply chains, and revenue — where OR meets industry.
Inventory Theory
How much to order, when, and where to hold it.
Transportation & Logistics
Move goods and people efficiently.
Supply Chain Optimization
Plan flows of materials, information, and money end-to-end.
Revenue Management
Prices, availability, and capacity controls under demand uncertainty.
Production Planning & Manufacturing
Plan capacity, lots, materials, and shop-floor execution.
Service Operations & Staffing
Match people, capacity, and service levels under variable demand.
Healthcare Operations Research
Improve access, flow, capacity, treatment, and health policy.
Energy & Power Systems
Dispatch, commit, expand, and balance energy systems.
Finance, Portfolio & Risk
Allocate capital under risk, constraints, and market uncertainty.
Public Sector & Policy OR
Allocate public resources with equity, transparency, and constraints.
Telecom, Cloud & Computing Systems
Route traffic, allocate compute, and manage congestion.
Sports & Entertainment Scheduling
Build fair, feasible schedules for leagues, venues, and media.
Agriculture & Natural Resources
Plan land, water, harvest, conservation, and extraction.
Modern OR Practice
Analytics, ML, software, datasets, and the contemporary practice stack.
Analytics, Data Science & ML
Predict, then prescribe.
OR in Industry
Where models meet practice across sectors.
Software Tools & Solvers
Modeling languages, libraries, and solvers.
Datasets & Benchmarks
Standard problems to test, learn, and compete.
Prescriptive Analytics
Move from insight to recommended action.
Data-Driven Optimization
Learn decisions from data, not just parameters.
Digital Twins & What-If Systems
Living simulations connected to operational data.
Solver Engineering & Deployment
Turn models into reliable production decision services.
Responsible OR & Decision Governance
Make automated decisions auditable, fair, and resilient.
OR Communication & Change
Get models trusted, adopted, and improved.
Behavioral OR & Human Decisions
Account for how people actually use, resist, and adapt to models.