Operations research

Operations research uses mathematical models, statistics, and optimization to analyze complex systems and improve decisions under constraints.

Linear programming: A mathematical method for optimizing a linear objective subject to linear constraints. It models resource-allocation decisions with explicit objectives and limits.
Frederick W. Lanchester: A British engineer who developed mathematical models of military combat in the early twentieth century. His equations showed how quantitative models could inform operational strategy.
Vehicle routing problem: The problem of designing efficient routes for vehicles serving a set of locations. It captures the routing and capacity constraints faced by delivery systems.
Management science: The application of analytical methods to organizational and managerial decisions. It overlaps closely, but often frames the work around management and organizations.
Integer programming: Optimization with some or all decision variables restricted to integer values. Whole-number choices such as staffing or facility locations require discrete variables.
Patrick Blackett: A British physicist who led wartime scientific teams applying quantitative analysis to military operations. His teams helped establish the practical style of wartime operations research.
Supply chain management: The coordination of sourcing, production, inventory, and delivery across organizations. Optimization helps balance cost, service, and resilience across connected operations.
Industrial engineering: An engineering discipline that designs and improves integrated systems of people, materials, information, and equipment. It shares optimization methods while also emphasizing system design and implementation.
Dynamic programming: A method for solving problems by combining solutions to overlapping subproblems. It handles sequential decisions by relating each choice to future states.
Battle of the Atlantic: The prolonged campaign between Allied and Axis forces over control of Atlantic sea routes during World War II. Analysis of convoy protection and submarine warfare became a defining early application.

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