Duality in Linear Programming – LPP

While going through the dual model of LPP it is encountered that it consists of alternative modeling instance which would further enable to identify varied information related to original problem which is referred as primal model. So, it is considerate enough to solve any one problem either primal or dual so that optimal solution can be obtained and through which optimal value can be generated through equivalent problem.

Characteristics of dual problem

When it comes to duality in linear programming, it states the following characteristics:

• It is said dual of the dual is regarded as primal
• In case two problems comes up with an infeasible solution, then the value of the other is certain to become unbounded
• In case any primal or dual problem comes with unbounded solution, then there is a possibility that the solution of other problem would be infeasible.
• If primal or dual problem offers a solution, then certainly the other has a solution too and optimal values would be equal.

Relationship between primal and dual problem

In case of linear programming, when it comes to primal problem each sub-optimal point need to satisfy the constraints and there would be a direction to move which can enhance objective function. While moving in such direction it is considered to remove slack that occurs between candidate solutions or in case of one or more constraints.

When it comes to dual problem, the dual vector has the ability to multiply constraints which can help in analyzing positions of constraints in primal. If there is a change in dual problem then it becomes equivalent to revising of upper bound in primal problem. An infeasible value when it comes to dual vector is often too low. The optimal solution can deliver with varied information related to primal and vice versa.