Operations Research Cheat Sheet
The core ideas of Operations Research distilled into a single, scannable reference — perfect for review or quick lookup.
Quick Reference
Linear Programming
A mathematical optimization technique for maximizing or minimizing a linear objective function subject to a set of linear equality and inequality constraints. It is one of the most widely used methods in operations research.
Integer Programming
An extension of linear programming in which some or all decision variables are required to take integer values. This is essential for modeling discrete decisions such as yes/no choices, facility locations, and scheduling assignments.
Simplex Method
An algorithm developed by George Dantzig in 1947 for solving linear programming problems. It moves along the edges of the feasible polytope from vertex to vertex, improving the objective function at each step until the optimum is reached.
Queueing Theory
The mathematical study of waiting lines (queues), which models the arrival of entities, the service process, and the resulting wait times, queue lengths, and system utilization to help design efficient service systems.
Network Optimization
A branch of OR dealing with optimization problems on graphs and networks, including shortest path, maximum flow, minimum cost flow, minimum spanning tree, and network design problems.
Simulation
The use of computer models to imitate the behavior of complex real-world systems over time. Simulation allows analysts to experiment with different scenarios and policies without disrupting the actual system.
Decision Analysis
A systematic framework for evaluating complex decisions under uncertainty, using tools such as decision trees, influence diagrams, and utility functions to identify the optimal course of action given uncertain outcomes and risk preferences.
Dynamic Programming
A method for solving complex optimization problems by breaking them into simpler overlapping subproblems and solving each subproblem only once, storing the results for reuse. It is especially useful for sequential decision-making problems.
Stochastic Processes
Mathematical models that describe systems evolving over time with inherent randomness. In OR, stochastic processes such as Markov chains and Poisson processes model uncertain demand, machine failures, and customer arrivals.
Metaheuristics
General-purpose algorithmic frameworks for finding good (often near-optimal) solutions to hard optimization problems where exact methods are impractical. Examples include genetic algorithms, simulated annealing, and tabu search.
Key Terms at a Glance
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