A problem consists of a linear function of variable called objective function subject to set of linear equation or inequalities called constraints, are known as linear programming problem.
In LP model the various parameters namely the objective function coefficients, R.H.S, coefficients of the constraints and resource values are certainly known and their value do not change with time. Thus the profit or cost per unit of product, availability of labour and material, market demand is known with certainty.That’s why it is called deterministic in nature.
Assumptions of Linear programming Models
1. Proportionality
2. Additivity
3. Continuity
4. Certainty.
Application of linear programming.
A.Industrial Applications
1. Product Mix problem
2. Blending problem
3. Production Scheduling problem
4. Trim loss problem
5. Sub contract problem.
B.Management Problems
1. Media selection problem
2. Transportation problem
3. Assignment problem
4. Man power scheduling problem
5. Agricultural Applications
6. Military Applications.
Advantages
1. It helps in attaining the optimum use of productive factors.
2. It improves the quality of decisions. The individual who makes use of linear programming methods becomes more objective than subjective.
3. It also helps in providing better tools for adjustment to meet changing conditions.
4. It highlights the bottlenecks in the production processes.
5. Most business problems involve constraints like raw materials availability, market demand etc. which must be taken into consideration. Just we can produce so many units of product does not mean that they can be sold. Linear programming can handle such situation also.
Limitations
1. In some problems objective functions and constraints are not linear. LPP under non linear condition usually results in an incorrect soIution
2. LPP deals with problems that have a single objective. Real life problem may involve multiple objectives.
3. Parameters appearing in the model are assumed to be constant. But in real life situation they are neither constant nor deterministic.
4. It is applicable to only static situations since it does not take into account the effect of time.
5. LPP can not be used efficiently for large scale problems, the computational difficulties are enormous, even when the large digital computer is available.
6. LPP may get fractional valued answers for the decision variables, whereas it may happen that only integer values of the variable are logical.
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