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Linear Programming refers to the mathematical technique for finding values of the decision variable which optimize the objective function subject to certain linear constraints.

The following are certain advantages of using the linear programming technique:

1. The linear programming technique helps decision-makers to use their productive resources effectively.
2. The linear programming technique improves the quality of decisions. The decision-making approach of the user of this technique becomes more objective and less subjective.
3. The linear programming technique helps to arrive at the optimal solution to a decision problem by taking into account constraints on the use of resources. For example, saying that so many units of any product may be produced does not mean that all units can be sold.
4. Linear programming approach for solving decision problem highlight bottlenecks in the production processes. For example, when a bottleneck occurs, the machine cannot produce the sufficient number of units of a product to meet demand. Also, machines may remain idle.

In spite of having many advantages and wide areas of applications, there are some limitations associated with this technique. These are as follows:

1. Linear programming assumes linear relationships among decision variables. However, in real-life problems, decision variables, neither in the objective function nor in the constraints are linearly related.
2. While solving an LP model there is no guarantee that decision variables will get an integer value. For example, how many men/machines would be required to perform a particular job, a non-integer valued solution will be meaningless. Rounding off the solution to the nearest integer will not yield an optimal solution.
3. The linear programming model does not take into consideration the effect of time and uncertainty.
4. Parameters in the model are assumed to be constant but in real-life situations, they are frequently neither known nor constant.
5. Linear programming deals with only a single objective, whereas in real-life situations a decision problem may have conflicting and multiple objectives.

References:

Operations Research Theory and Applications – JK Sharma

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