Read the notes, then try the practice. It adapts as you go.When you're ready.
Session Length
~17 min
Adaptive Checks
15 questions
Transfer Probes
8
Operations research (OR) is a discipline that applies advanced analytical methods to help make better decisions. Rooted in mathematical modeling, statistical analysis, and optimization techniques, OR provides a scientific basis for decision-making in complex systems. The field addresses problems involving the allocation of scarce resources, scheduling, logistics, supply chain design, and strategic planning by translating real-world challenges into mathematical formulations that can be solved systematically.
The origins of operations research trace back to World War II, when teams of scientists in Britain and the United States were assembled to apply scientific methods to military operations such as radar deployment, convoy routing, and bombing strategies. Pioneers like Patrick Blackett, Charles Kittel, and George Dantzig made foundational contributions, with Dantzig's development of the simplex method for linear programming in 1947 becoming one of the most important algorithms of the twentieth century. After the war, these techniques rapidly migrated to industry, government, and commerce.
Today, operations research is indispensable across virtually every sector. Airlines use OR for fleet scheduling and revenue management, hospitals use it for patient flow optimization, logistics companies use it for vehicle routing, and financial firms use it for portfolio optimization. With the rise of big data, machine learning, and cloud computing, OR practitioners now tackle problems of unprecedented scale and complexity, blending classical optimization with data-driven approaches to deliver actionable insights and measurable improvements in efficiency, cost, and performance.
One step at a time.
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.
Example: A factory determines the optimal mix of products to manufacture given limited raw materials, labor hours, and machine capacity in order to maximize profit.
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.
Example: A company deciding which subset of 20 possible warehouse locations to open, where each location is either fully opened or not opened at all.
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.
Example: Solving a production planning problem with 50 products and 30 resource constraints by iteratively pivoting through feasible corner-point solutions.
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.
Example: A bank uses queueing models to determine how many tellers to staff during peak hours to keep average customer wait time below five minutes.
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.
Example: A logistics company finds the shortest delivery routes across a network of cities to minimize total transportation cost and delivery time.
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.
Example: A hospital simulates patient arrivals, treatment durations, and bed availability over thousands of runs to test the impact of adding an extra operating room.
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.
Example: An oil company uses a decision tree to evaluate whether to drill at a site, considering the probabilities of finding oil, the costs of drilling, and the potential revenue.
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.
Example: Determining the optimal inventory replenishment policy over a 12-month planning horizon where each month's decision depends on the current stock level and demand forecast.
More terms are available in the glossary.
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