Sensitivity Analysis - Week 3

SA - Goals

1.To understand the concepts of managerial sensitivity (post-optimality) analysis. 2.To understand the process of managerial sensitivity (post-optimality) analysis. 3.To understand the value of sensitivity analysis in mathematical programming problems.

SA - Premise

Mathematical programming results in an optimal solution to some managerial problem. That solution is based on deterministic data inputs that may be inaccurate or change over time. Sensitivity analysis allows managers to examine alternative solutions to the problem under different conditions (data) to determine how sensitive the model is to data changes.

Names for SA

Optimality Analysis Right-hand side ranging Post-optimality analysis parametric programming

Sensitivity Analysis

Quantifies the degree of change to the optimal solution

Sensitivity (Post-Optimality) Analysis

Sensitivity analysis is an important part of analyzing the results of any problem. Sensitivity analysis determines how sensitive the solution, objective function, or other problem conditions are to changes in problem data. When the problem solution is very sensitive to changes in the input data and model specification, additional testing should be performed to make sure that the model and input data are accurate and valid. Even if the input data is accurate, sensitivity analysis will allow a manager to identify how changing conditions will affect the objective and decisions without actual implementation. This also allows managers to anticipate decision/policy changes in advance of changing market conditions. The ability to ask and answer these sorts of managerial "what-if" questions makes management more nimble with respect to decision making efficiency and effectiveness.

Surplus

amount to be added to the right-hand side to make the constraint binding (extra production)

Slack

amount to be subtracted from the right-hand side to make the constraint binding (extra resources)

Reduced Cost

change in an objective function coefficient necessary to have a positive optimal value for that variable

binding constraint

constraint that holds as an equality in the optimal solution, i.e. the constraint is 'active'

Dual/Shadow Price

rate of improvement in the objective function if a constraint's right-hand side increases by 1 (price of extra resources or savings on extra production)