Introduction to Sensitivity Analysis

Introduction to Sensitivity Analysis

Sensitivity analysis is a fundamental technique used in various fields, including economics, engineering, finance, and environmental science, to determine how different input variables impact the output of a given model. It helps decision-makers understand the robustness of their models and identify the most influential parameters.

What is Sensitivity Analysis?

The sensitivity analysis is performed after a given linear problem has been solved, with the aim of studying how changes to the problem affect the optimal solution. In particular, the following discrete changes to the problem are considered: a change in the cost coefficients, a change in the right-hand side and a change in the constraints.

Consider the linear program:                                                              In Standard Form :

Now we can get the matrices from the rearranged table.

Case 01: changing the objective function coefficient of a NBV(x2)

Case 02: Changing the objective function coefficient of a BV(x1)

Case 03: Changing a value on rhs(b1)

Case 04 : Changing the column of a NBV(x2) 

Case 05:  Adding a new Variable

Case 06:  Adding a new Variable

First, we should check if the current optimal solution satisfies the new constraint.

If it satisfies the optimal solution will not change.

If not, there will be a new optimal solution or the solution will be infeasible.