Linear Programming: What-if (Sensitivity) Analysis

So far we have focused on finding an optimal solution to a linear programming model. It is important, but it is not the only information available or needed by management. Management also needs sensitivity information, or information about what happens when data values are changed.

Previously, in order to formulate a problem as a linear programming model in Excel, we had to take the data for granted or assumed that it was certain and we made decisions based on that data. In real life problems, this assumption or certainty is questionable; the data might be inaccurate. Linear programming has capability in terms of sensitivity analysis to address these uncertainties.

Sensitivity analysis is a systematic study of how sensitive solutions are to small changes in the data. There are three basic areas that sensitivity analysis provides answers: 1. How does the solution change when the objective function changes? 2. How does the solution change when resources available change? 3. How does the solution change when a constraint is added to the problem?

All these questions can be answered by the “Sensitivity Report” generated by Excel Solver. Let’s see how to create and analyze a sensitivity report through an example. The example we choose is the Wyndor Glass Co. case study we solved in Module 1. See page 163 in the Introduction to Management Science textbook for details regarding the Solver sensitivity report.

Remember, before solving the problem we have the figure below.