Introduction to Sensitivity Analysis
March 14, 2025 | Yuasha Wijesinghe
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 :
B: Matrix corresponding to BV
D: Matrix corresponding to NBV
CB: Coefficients of BV
CD: Coefficients of NBV
b: rhs values
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.
Importance of Sensitivity Analysis
It allows decision-makers to prioritize resources by focusing on critical variables.
Ensures that the model behaves realistically under varying conditions.
Helps in understanding uncertainties and potential risks associated with model predictions.
Aids in optimizing system performance by adjusting influential parameters.
Applications of Sensitivity Analysis
Engineering: Assessing the reliability and performance of complex systems.
Economics: Evaluating economic models and policy decisions.
Finance: Portfolio optimization and risk management.
Environmental Science: Assessing climate change models and ecological impacts.
Healthcare: Evaluating cost-effectiveness of treatments and interventions.
Tools and Software for Sensitivity Analysis
Microsoft Excel
Python
R
MATLAB
In conclusion sensitivity analysis helps in understanding the impact of input variables on model outcomes, enabling better decision making and risk management.
