Limitations of Linear Programming

Following are the disadvantages of linear programming.

Linearity of relations: A primary requirement of linear programming is that the objective function and every constraint must be linear. However, in real life situations, several business and industrial problems are nonlinear in nature.

Single objective: Linear programming takes into account a single objective only, i.e., profit maximization or cost minimization. However, in today's dynamic business environment, there is no single universal objective for all organizations.

Certainty: Linear Programming assumes that the values of co-efficient of decision variables are known with certainty. Due to this restrictive assumption, linear programming cannot be applied to a wide variety of problems where values of the coefficients are probabilistic.

"Nothing is certain but death and taxes." -Benjamin Franklin

Constant parameters: Parameters appearing in LP are assumed to be constant, but in practical situations it is not so.

Divisibility: In linear programming, the decision variables are allowed to take non-negative integer as well as fractional values. However, we quite often face situations where the planning models contain integer valued variables. For instance, trucks in a fleet, generators in a powerhouse, pieces of equipment, investment alternatives and there are a myriad of other examples. Rounding off the solution to the nearest integer will not yield an optimal solution. In such cases, linear programming techniques cannot be used.

This chapter initiated your study of linear models. Linear programming is a fascinating topic in operations research with wide applications in various problems of management, economics, finance, marketing, transportation and decision making pertaining to the operations of virtually any private or public organization. Unquestionably, linear programming techniques are among the most commercially successful applications of operations research.

In this chapter, you learned how to formulate a linear programming problem, and then we discussed the graphical method of solving an LPP with two decision variables.

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