Operations Research Cheat Sheet

The core ideas of Operations Research distilled into a single, scannable reference — perfect for review or quick lookup.

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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

Assignment Problem:A combinatorial optimization problem of assigning agents to tasks on a one-to-one basis to minimize total cost.

Big-M Method:A technique in LP for handling artificial variables in the simplex method by assigning a very large penalty coefficient.

Branch and Bound:An algorithmic framework for solving integer programming problems by exploring and pruning a tree of subproblems.

Combinatorial Optimization:Finding an optimal solution from a finite but very large set of discrete alternatives.

Constraint:A mathematical condition that restricts the set of feasible solutions in an optimization problem.

Convex Optimization:Optimization of a convex objective function over a convex feasible set, guaranteeing that any local optimum is global.

Decision Variable:A variable whose value is determined by the optimization model, representing a choice to be made.

Dijkstra's Algorithm:A graph algorithm for finding the shortest path from a source node to all other nodes with non-negative weights.

Dual Problem:A companion optimization problem derived from the primal LP that provides bounds and economic interpretation of constraints.

Dynamic Programming:A method of solving problems by breaking them into overlapping subproblems and storing their solutions.

Feasible Solution:A solution that satisfies all the constraints of an optimization problem.

Heuristic:A practical method for finding good-enough solutions to problems where exact methods are too slow or impractical.

Integer Programming:An optimization problem in which some or all decision variables are restricted to integer values.

Linear Programming:Optimization of a linear objective function subject to linear equality and inequality constraints.

Markov Chain:A stochastic process satisfying the memoryless property where the future depends only on the present state.

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