Duality is a very important concept associated with linear programming.
The term 'Duality' implies that every linear programming problem, whether
of maximization or minimization, is associated with another linear programming
problem based on the same data.
The original problem in this context
is called the primal problem, whereas the other is called its dual problem. The formulation of the dual linear programming
is sometimes referred to as duality. The notion of duality will deepen
your understanding of what is really happening in the simplex method.
Why duality must be studied?
Duality in Linear Programming is an interesting feature of LP. Following
are some reasons why duality must be studied.
- If the primal problems contain larger number of rows (constraints)
and smaller number of columns (variables), converting it into dual
can reduce the computational burden.
- Calculation of the dual checks the accuracy of the primal problem.
- It establishes the interconnections for all of the sensitivity analysis
(post optimality analysis) techniques.
- It yields a number of powerful theorems, which add substantially
to our understanding of linear programming approach.