The sensitivity analysis provides information about how sensitive the optimal solution and the value of the objective function to changes in the data model of linear programming .
In case you want to study the effects of the variation of more than one parameter (or one parameter beyond the “tolerance range”), you must reprogram the problem.
If the change that occurs in the considered parameter falls within the limits of variation, then it can be said that the variables that were basic in the original solution will continue to be so in the new solution. If they fall outside the range, it can already be said that this will not be the case in the new solution.
Problem areas studied by sensitivity analysis
Sensitivity Analysis is used to examine the effects of changes in four distinct areas of the problem:
- Objective coefficients (objective coefficients): Changes in the objective coefficients do not affect the shape of the feasible region, so they will not affect the optimal solution, although they do affect the value of the objective function.
- Technological coefficients (coefficients that affect the variables of the constraints, located to the left of the inequality): Changes in these coefficients will cause substantial changes in the shape of the feasible region. Graphically (in the case of 2 variables) what varies is the slope of the lines that represent the constraints.
- Available resources (independent terms of each constraint, located to the right of the inequality): the changes in the available resources suppose parallel shifts of the lines associated with the constraints, which will change the shape of the feasible region and, with it, to the optimal solution.
- Adding a new variable: Sensitivity analysis studies the effect on the optimal solution and the objective function if a new variable is added or a new constraint changes.
