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Linear Programming (LP)

Definition - What does Linear Programming (LP) mean?

Linear programming is a mathematical method that is used to determine the best possible outcome or solution from a given set of parameters or list of requirements, which are represented in the form of linear relationships. It is most often used in computer modeling or simulation in order to find the best solution in allocating finite resources such as money, energy, manpower, machine resources, time, space and many other variables. In most cases, the "best outcome" needed from linear programming is maximum profit or lowest cost.

Because of its nature, linear programming is also called linear optimization.

Techopedia explains Linear Programming (LP)

Linear programming is used as a mathematical method for determining and planning for the best outcomes and was developed during World War II by Leonid Kantorovich in 1937. It was a method used to plan expenditures and returns in a way that reduced costs for the military and possibly caused the opposite for the enemy.

Linear programming is part of an important area of mathematics called "optimization techniques" as it is literally used to find the most optimized solution to a given problem. A very basic example of linear optimization usage is in logistics or the "method of moving things around efficiently." For example, suppose there are 1000 boxes of the same size of 1 cubic meter each; 3 trucks that are able to carry 100 boxes, 70 boxes and 40 boxes respectively; several possible routes; and 48 hours to deliver all the boxes. Linear programming provides the mathematical equations to determine the optimal truck loading and route to be taken in order to meet the requirement of getting all boxes from point A to B with the least amount of going back and forth and, of course, the lowest cost at the fastest time possible.

The basic components of linear programming are as follows:

  • Decision variables - These are the quantities to be determined.

  • Objective function - This represents how each decision variable would affect the cost, or, simply, the value that needs to be optimized.

  • Constraints - These represent how each decision variable would use limited amounts of resources.

  • Data - These quantify the relationships between the objective function and the constraints.

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