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Operations Research

Definition

Operations research (OR) uses mathematical models and analytical solution methods to support optimal, or sufficiently good, decisions in practical situations. The decision problem includes an objective, available choices, and restrictions on those choices.

Interpretation

Operations research applies mathematics to practical decisions, such as how much to produce, how to route vehicles or how to pack goods. The real question is first turned into a model that can be analysed systematically, and the usefulness of the answer depends on how well that model represents the situation.

A cycle of six stages: real situation, assumed representation, mathematical model, solution, validation and implementation, with a return arrow from validation to revise the model.

The cycle shows where the mathematics sits. Only the step from a mathematical model to a solution is pure calculation. The steps before it decide what is simplified and which data are used, and the validation step asks whether the answer makes sense in the real situation. A rejected answer sends the work back to the assumptions, not just to the calculation; the OR study cycle describes these stages.

The definition allows "sufficiently good" decisions as well as optimal ones. When a problem is too hard to solve exactly, a heuristic provides a usable decision, and a relaxation shows how far from optimal it can be. Small examples of both kinds are the Giapetto model and the diet problem, solved exactly, and the bin packing and vehicle routing problems, approached with heuristics. Other names for the field are operational research and management science.

Key Results

  • Applications include production, transport, scheduling, maintenance, and inventory management.
  • An optimal model solution must still be checked against the practical situation.
  • Difficult problems may require a heuristic instead of an exact solution method.

Examples

Any stage of the OR study cycle can prompt a return to an earlier stage if validation shows that the simplified representation is inadequate.

  • Lecture scheduling allocates teaching activities to times and rooms.
  • A warehouse chooses replenishment quantities and ordering times.

Prerequisites

  • No additional prerequisites.

Sources

Aliases: OR, operational research, management science

Last updated: 20 October 2026 03:02