Sunday, October 15, 2006

Sensitivity Analysis

Sensitivity analysis is also known as post-optimality analysis. And as the names indicate, it is some kind of analysis done after obtaining the optimal solution. This analysis is related to sensitivity of the solution towards possible changes in the problem.

Such analysis is very important considering that an LP represents a real life problem and there is always some possibility of changes in real life situation. So, if you formulate a LP for finding optimum product mix, solve it and the organization starts producing as per this; and one fine day the supplier of an important raw material cuts-down the supply changing the availability of the raw material. Will you have to again formulate the LP and solve? Similarly, if the management decides to introduce another product, will we have to do all the computation once again?

Sensitivity analysis analyses the impact of such changes on the optimal solution and helps us in getting the new optimal solution, if needed, without doing the entire exercise afresh. This analysis covers all possible changes such as:

-- Changes in the right hand side values in the LP,

-- Changes in the objective function coefficients,

-- Changes in the constraint coefficients,

-- Introduction or elimination of new constraint,

-- Introduction or removal of new product,

-- Changes in the valid range of decision variables, etc.

These changes can affect the optimality and feasibility of the solution. There is always a range of such changes in which the optimal solution remains unchanged. But, if a change is outside that range then the optimal solution changes. The changed optimal can be obtained easily from the previous optimal solution itself.

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