DEFINITION:
"Linear programming is a mathemathical technique of solving maximisation or minimisation problems where the constraints and functions to be maximised or minimised are linear and thus can be represented by straight lines".
- Maddla & Miller.
BASIC REQUIREMENT OF LINEAR PROGRAMMING TECHNIQUE:
i) Objective function:
linear programming problem must have well defined explicit clear objective function to optimise. the objective may be maximistion of profit, revenue, sales or minimisation of cost etc. It should be expressed as linear function of decision variables.
ii) Constraints:
There must be limitation or restrictions on the resources which are to be allocated among various competing activites. These resources may be raw material,capital, time, manpower etc.Inequalites of the form greater than(>) which explain that the total requirement of resoures will be higher than the given amount. If the constraint are of the form less than(<), then they indicate that the total resources must be smaller than the specified amount.
iii) Quantitative measurement:
It is must that each elementof the problem is capable of being quantified or numerically expressed.
iv) Linearity:
All relationship among decision variables in objective function and constraint must exhibit linerity (i.e) relationship among decision variables must be directly proportional.
v) Non- negative Restriction:
All variable used in the objective function and constraint must assume non- negative values as negative values of physical quantities is meaningless and irrelevant.
Uses:
Linear programming is a considerable field of optimization for several reasons. Many practical problems in operations research can be expressed as linear programming problems. Certain special cases of linear programming, such as network flow problems and multicommodity flow problems are considered important enough to have generated much research on specialized algorithms for their solution. A number of algorithms for other types of optimization problems work by solving LP problems as sub-problems. Historically, ideas from linear programming have inspired many of the central concepts of optimization theory, such as duality, decomposition, and the importance of convexity and its generalizations. Likewise, linear programming is heavily used in microeconomics and company management, such as planning, production, transportation, technology and other issues. Although the modern management issues are ever-changing, most companies would like to maximize profits or minimize costs with limited resources. Therefore, many issues can boil down to linear programming problems.
Advantages of Linear Programming :
1.The linear programming technique helps to make the best possible use of available productive resources (such as time, labour, machines etc.)
2. In a production process, bottle necks may occur. For example, in a factory some machines may be in great demand while others may lie idle for some time. A significant advantage of linear programming is highlighting of such bottle necks.
Disadvantages of Linear Programming :
1. Linear programming is applicable only to problems where the constraints and objective function are linear i.e., where they can be expressed as equations which represent straight lines. In real life situations, when constraints or objective functions are not linear, this technique cannot be used.
2. Factors such as uncertainty, weather conditions etc. are not taken into consideration.
