combination of Mathematics and economics designed to maximize values of certain functions while subject to arbitrary linear constraints.
Uses tools from Linear Algebra.
Most operations are done with computers rather than by hand.
Also referred to as linear programming. A linear program is a problem that can be expressed as follows (the standard form:

minimize cx
subject to Ax = b
x>= 0

Where x is the vector of variables to be solved for, A is a matrix of known coefficients, and c and b are vectors of known coefficients. 'cx' is called the objective function and the equations 'Ax=b" are called the constraints.

All of these entities have consistent dimensions, and you can add transpose symbols to taste. The matrix A is usually not square, so you can't solve it just by inverting A. Usually A has more columns than rows, and Ax=b is likely to be underdetermined, leaving great latitude in the choice of x with which to minimize cx.

The word programming is used here in the sense of planning, and the relationship to computer programming was incidental to the choice of name, so the phrase 'LP program' is not redundant.

Software required to solve these problems (usually in economics or finance) often requires distributed computing.

It can be used for modeling many diferse types of problems to do with planning, routing, scheduling, assignment, and design, and can be used by any industry from energy to manufacturing to finance.

Log in or register to write something here or to contact authors.