Limitations 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.
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"Nothing is certain but death
and taxes." -Benjamin Franklin |
Due to this restrictive assumption, linear programming cannot be applied
to a wide variety of problems where values of the coefficients are
probabilistic.
- 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.
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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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