What is linear programming?
Linear programming is a mathematical method used to find the best possible outcome or solution from a given set of parameters or a list of requirements represented in terms of linear relationships. It is most commonly used in computer modeling or simulation to find the best solution for allocating finite resources such as money, energy, manpower, machine resources, time, space, and many other variables. In most cases, the 'best outcome' required by linear programming is maximum profit or lowest cost.
Linear programming is also called because of its nature linear optimization designated.
Used as a mathematical method of determining and planning for the best results, linear programming was developed by Leonid Kantorovich in 1937 during World War II. It was a method of planning expenses 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' because it is literally used to find the most optimized solution to a given problem. A very simple example of using linear optimizations is logistics, or the 'method of moving things around efficiently'. Suppose there are 1000 boxes of the same size of 1 cubic meter each; 3 trucks that can transport 100 boxes, 70 boxes and 40 boxes; several possible routes; and 48 hours to deliver all boxes. Linear programming provides the mathematical equations to determine the optimal truck load and route to be traveled to meet the requirement of getting all the boxes from point A to B with the least reciprocation and of course the lowest cost, 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 cost, or simply the value that needs to be optimized.
Limitations - These represent how any decision variable would use limited amounts of resources.
Data - This quantifies the relationships between the objective function and the constraints.