Linear programming

promramming method to achieve the best outcome in a mathematical model

Linear programming or linear optimization is a mathematical method for determining a way to achieve the best outcome. such as maximum profit or lowest cost, in a given mathematical model for some list of requirements represented as linear relationships. Linear programming is a specific case of mathematical programming or mathematical optimization.

A pictorial representation of a simple linear program with two variables and six inequalities.


Quotes are arranged alphabetically per author

A - FEdit

    • Russell L. Ackoff ( 1962) Scientific method: optimizing applied research decisions, p. 108 as cited in: Joe H. Ward, Earl Jennings (1973) Introduction to linear models. p. 4

G - LEdit

    • James Gleick (1987) Chaos: Making a New Science, p. 23 as cited in: James R. Hansen (2004) Trees of Texas: An Easy Guide to Leaf Identification. p. 246
  • Linear programming was a new branch of applied mathematics that – in the USA – came into being as a direct consequence of mathematicians’ war work. It was not done under contract with the AMP but by some of the mathematicians employed directly by the armed forces.15 The source was a concrete practical problem within the US Air Forces,16 a logistic problem that eventually led to the mathematical theory of linear programming, and from there to mathematical programming. The person normally associated with the origin of linear programming in the USA is George B. Dantzig. Dantzig was one of the mathematicians hired directly by the armed forces for the war effort. In 1941 he began working at the Combat Analysis Branch of the United States Air Force Headquarters Statistical Control under the leadership of Tex Thornstons. During the war Dantzig worked on what was called “programming planning” methods to calculate Air Force programs. An Air Force program was a kind of activity plan.

M - REdit

  • Linear Programming is a generalization of Linear Algebra. It is capable of handling a variety of problems, ranging from ﬁnding schedules for airlines or movies in a theater to distributing oil from reﬁneries to markets. The reason for this great versatility is the ease at which constraints can be incorporated into the model.
  • In another part of the management forest, the mechanistic school was gathering its forces and preparing to outflank the forces of light. First came the numbers men — the linear programmers, the budget experts, and the financial analysts — with their PERT systems and cost-benefit analyses. From another world, unburdened by most of the scientific management ideology and untouched by the human relations school, they began to parcel things out and give some meaning to those truisms, "plan ahead" and "keep records." Armed with emerging systems concepts, they carried the "mechanistic" analogy to its fullest—and it was very productive. Their work still goes on, largely untroubled by organizational theory; the theory, it seems clear, will have to adjust to them, rather than the other way around.
    • Charles Perrow, "The short and glorious history of organizational theory." Organizational Dynamics 2.1 (1973): 3-15. p. 6

See alsoEdit

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