--- title: "Sensitivity analysis" source: "https://systems-analysis.info/eng/Sensitivity_analysis" wiki: "systems-analysis.info/eng" article: "Sensitivity_analysis" language: "en" categories: - "Category:English" - "Category:Mathematical modeling" - "Category:Operations research" - "Category:Science" revision_id: 345 wiki_created_at: 2026-09-06T22:22:24Z wiki_modified_at: 2026-09-06T22:22:24Z downloaded_at: 2026-09-07T22:22:51Z --- # Sensitivity analysis **Sensitivity analysis** is a method for studying mathematical or simulation models. It assesses how changes in a model's input data, parameters, or assumptions affect its output results (e.g., the optimal solution, the value of the [objective function](https://systems-analysis.info/eng/Objective_function "Objective function"), or other key indicators). Sensitivity analysis is an important tool in [operations research](https://systems-analysis.info/eng/Operations_research "Operations research"), [optimization](https://systems-analysis.info/eng/Optimization "Optimization"), [decision theory](https://systems-analysis.info/eng/Decision_theory "Decision theory"), [risk management](https://systems-analysis.info/eng/Risk_management "Risk management"), economic analysis, and [systems analysis](https://systems-analysis.info/eng/Systems_analysis "Systems analysis"). ## Essence and Purpose The main goal of sensitivity analysis is to understand how **stable** (robust) the results of modeling or [optimization](https://systems-analysis.info/eng/Optimization "Optimization") are to [uncertainty](https://systems-analysis.info/eng/Uncertainty "Uncertainty") or variations in the initial data. It helps answer questions such as: - "What will happen to the optimal solution if a resource's cost changes by 10%?" - "How much will profit change with fluctuations in market demand?" - "Which [model](https://systems-analysis.info/eng/Model "Model") parameters have the greatest impact on the final result?" - "How reliable is the forecast obtained using the [model](https://systems-analysis.info/eng/Model "Model")?" Key tasks of sensitivity analysis include: - Assessing robustness:\* To determine if the optimality or acceptability of a solution is maintained when parameters change. - Identifying critical parameters: To identify input data or [model](https://systems-analysis.info/eng/Model "Model") parameters whose small changes lead to significant changes in the output results. - Increasing confidence in the model: To demonstrate that the model behaves predictably and logically in response to changes in input data. - Supporting decision-making: To provide the decision-maker with information about the range of possible outcomes and the [risks](https://systems-analysis.info/eng/Risk "Risk") associated with the [uncertainty](https://systems-analysis.info/eng/Uncertainty "Uncertainty") of the initial data. - Guiding further research: To indicate which data collection or refinement of which [model](https://systems-analysis.info/eng/Model "Model") parameters is most important. ## Methods of Sensitivity Analysis Various methods for conducting sensitivity analysis exist, ranging from simple to complex: - Local analysis (One-at-a-Time, OAT/OFAT): One input parameter is changed at a time, while all other parameters remain fixed. This is the simplest method, but it does not allow for assessing the interaction effects between parameters. - Derivative-based analysis (local sensitivity): Assesses the impact of small parameter changes through the partial derivatives of output variables with respect to input parameters. - Scenario analysis: Several discrete scenarios (e.g., optimistic, pessimistic, most likely) corresponding to different sets of input parameter values are considered. - Global sensitivity analysis: Studies the effect of simultaneously changing all (or many) parameters within their ranges of uncertainty. Statistical methods are often used: - Monte Carlo methods: A large number of random sets of input parameters are generated to estimate the distribution of output results. - Regression analysis: A regression model is built to link output results with input parameters. - Analysis of variance (ANOVA) and variance-based methods: Allow for quantitatively assessing the contribution of each parameter (and their interactions) to the total variance (uncertainty) of the output result. ## Role in Operations Research and Optimization In [operations research](https://systems-analysis.info/eng/Operations_research "Operations research"), sensitivity analysis is a standard step after finding an optimal solution. It allows for determining: - **Stability limits of the optimal solution:** The range in which the parameters of the [objective function](https://systems-analysis.info/eng/Objective_function "Objective function") or [constraints](https://systems-analysis.info/eng/Constraints "Constraints") can vary while the found optimal solution remains optimal. - **Shadow prices (dual values):** How much the value of the [objective function](https://systems-analysis.info/eng/Objective_function "Objective function") will change with a small change (relaxation) of a constraint (e.g., by adding one unit of a scarce resource). Shadow prices indicate the value of resources. - **Allowable ranges for parameter changes:** The ranges of change for the coefficients of the [objective function](https://systems-analysis.info/eng/Objective_function "Objective function") or the right-hand sides of the [constraints](https://systems-analysis.info/eng/Constraints "Constraints") within which the current structure of the optimal solution (the set of basic variables in linear programming) is preserved. These results help the decision-maker understand how critical the initial data is and which resources are the most valuable ("bottlenecks"). ## Role in Modeling and Decision-Making In the broader context of modeling and [decision-making](https://systems-analysis.info/eng/Decision_theory "Decision theory"), sensitivity analysis helps to: - **Assess [risks](https://systems-analysis.info/eng/Risk "Risk"):** To identify the factors that contribute the most [uncertainty](https://systems-analysis.info/eng/Uncertainty "Uncertainty") to the result. - **Validate the [model](https://systems-analysis.info/eng/Model "Model"):** To check the adequacy of the [model](https://systems-analysis.info/eng/Model "Model")'s behavior under changing conditions. - **Compare alternatives:** To evaluate which of the alternatives is more robust to changes in external conditions. - **Improve understanding of the [system](https://systems-analysis.info/eng/System "System"):** To identify key driving forces and relationships in the modeled [system](https://systems-analysis.info/eng/System "System"). ## Interpretation of Results - **High sensitivity** to a parameter means that even small errors in its estimation or its variability can significantly affect the result. Such parameters require special attention. - **Low sensitivity** indicates that the result of the [model](https://systems-analysis.info/eng/Model "Model") or solution depends little on changes in a given parameter within the considered range, i.e., the solution is robust with respect to that parameter. ## Advantages - Increases the reliability and validity of [models](https://systems-analysis.info/eng/Model "Model") and solutions. - Helps identify [risks](https://systems-analysis.info/eng/Risk "Risk") and uncertainties. - Improves understanding of the [system](https://systems-analysis.info/eng/System "System") and the [model](https://systems-analysis.info/eng/Model "Model"). - Guides efforts in data collection and [model](https://systems-analysis.info/eng/Model "Model") refinement. ## Limitations - Can be computationally expensive, especially with a large number of parameters (global analysis). - Simple methods (OAT) may fail to identify interaction effects between parameters. - The results depend on the chosen ranges of parameter variation and the [model](https://systems-analysis.info/eng/Model "Model")'s assumptions. ## External links - Sensitivity analysis — Wikipedia ## See also - [Operations research](https://systems-analysis.info/eng/Operations_research "Operations research") - [Optimization](https://systems-analysis.info/eng/Optimization "Optimization") - [Mathematical modeling](https://systems-analysis.info/eng/Mathematical_modeling "Mathematical modeling") - [Simulation modeling](https://systems-analysis.info/eng/Simulation_modeling "Simulation modeling") - [Decision theory](https://systems-analysis.info/eng/Decision_theory "Decision theory") - [Risk management](https://systems-analysis.info/eng/Risk_management "Risk management") - [Uncertainty](https://systems-analysis.info/eng/Uncertainty "Uncertainty") - [Linear programming](https://systems-analysis.info/eng/Linear_programming "Linear programming") ## Literature - *Saltelli, A., et al.* Global Sensitivity Analysis: The Primer. — Wiley, 2008. - *Hillier, Frederick S.; Lieberman, Gerald J.* Introduction to Operations Research. — McGraw-Hill Education. (11th ed., 2021) (Contains sections on sensitivity analysis in LP) - *Taha, Hamdy A.* Operations Research: An Introduction. — Pearson. (10th ed., 2017) (Contains sections on sensitivity analysis in LP)