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.