Linear programming is commonly used in Economics and in other policy analysis fields. It is a mathematical tool for allocating limited resources to meet predetermined goals (“constraints,” as the mathematicians call them). It does this through generating system of equations (or “inequalities”) and solving them simultaneously (either algebraically or geometrically).
Think of linear programming as triangulating in on a solution. In navigation and surveying, one identifies a position along a line (a “sighting”), and then identifies a second sighting. One’s position must be where the two lines cross (i.e., at the apex of the triangle created by the two lines—hence the name). The more sightings, the more confidence one can have in the accuracy of the sighting. In linear programming, the “space” is usually conceptual rather than physical, but the principle is the same. Also, unlike a physical sighting from one’s own position (which must be a discrete point), the “sightings” (inequalities) in conceptual space are made from an “omniscient” point of view and so the system of equations may describe a “space” of possibilities rather than a single, discrete solution.
Linear programming is a powerful tool for teasing out the implications of what one knows, and for identifying an optimum solution (where one exists). In practice, most of us settle for an acceptable (rather than optimal) solution—in part because of the cost of identifying and then achieving the last marginal increment of gain. Also, linear programming is only as good as the assumptions built into the initial equations—all the relevant constraints must be specified, and the specifications must be correct (for example, specifying a relationship as linear when it is in fact exponential).
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© 1996 A.J.Filipovitch
Revised 11 March 2005