Transportation Problem
Goods have to be transported from sources (like factories) to destinations (like warehouses) on a regular basis. The transportation problem deals with minimising the costs in doing so. Linear programming effectively deals with this problem.
Military Applications
To provide the required protection at the minimum cost, linear programming is used. This technique is useful to cause maximum damage to the enemy with minimum fuel/cost.
Operation of System Of Dams
Linear programming is used to find the variations in water storage of dams which generate power, thus maximising the energy got from the entire system.
Personnel Assignment Problem
If we are given the number of persons, number of jobs and the expected productivity of a particular person on a particular job, linear programming is used to maximise the average productivity of a person.
Other Applications
A travelling sales man can find the shortest routes to save time / fuel cost. The most economic and efficient manner of locating manufacturing plants and distribution centres may be used.
Linear programming may be used for effective and efficient production management and manpower management.Different Types (Methods) of Linear Programming
Some of the methods of linear programming are:- The Graphical Method
- The Analytical Method
- The Simplex Method
The graphical method is not applicable to linear programming problems with more than 2 variables. Then, the analytical method may be used. Here, equations are solved by assuming some variables to be zero. However, this method is tedious and time consuming.
The simplex method overcomes these difficulties and gives successive solutions that improve progressively to give the optimal solution.