The Operations Research analyst has access to models, techniques and concepts developed in academia and industry. The historical methodologies listed below are represented by INFORMS Communities, specialized journals, entries in the Encyclopedia of Operations Research and Management Science, and other taxonomies.
The image above has been chosen to represent O.R. methodologies because it illustrates the solution path taken by the pioneering Simplex Method of linear programming on a simple problem in three variables, or dimensions.
In the illustration, feasible solutions are constrained within the green polyhedron; the method proceeds from vertex to vertex, following a path that increases the solution value towards the objective of achieving the highest obtainable value within the constraints.
The Simplex Method was developed by George Dantzig in the late 1940's, and dramatically propelled Operations Research forward as a field. As a method of constrained optimization, variants of the Simplex Method have been applied to problems with millions of variables and constraints. They are applicable when the data are deterministic, the constraint and objective values can be expressed as sums of multiples (linear combinations) of candidate values of the variables, and fractional solution values are meaningful.
Over a long history, optimization methods have been developed that accommodate stochastic data as well as nonlinear (including non-convex and integer) constraints and objectives, and many other methodologies have been developed.
The illustrative image presents a simplified view of a significant historic operations research methodology.