Performing sensitivity analysis

To perform sensitivity analysis, the Interactive Optimizer supports these options.

Sensitivity analysis of the objective function and righthand side provides meaningful insight about ways in which the optimal solution of a problem changes in response to small changes in these parts of the problem data.

Sensitivity analysis can be performed on the following features of a solution:

• objective function;

• righthand side values;

• bounds.

To view the sensitivity analysis of the objective function, enter the command:

display sensitivity obj -

You can also use a wildcard to query solution information, like this:

display sensitivity obj *

For our example, CPLEX displays the following ranges for sensitivity analysis of the objective function:

                                  OBJ Sensitivity Ranges   

Variable Name  Reduced Cost      Down   Current          Up
x1                   3.5000   -2.5000    1.0000   +infinity
x2                     zero   -5.0000    2.0000      3.0000
x3                     zero    2.0000    3.0000   +infinity

CPLEX displays each variable, its reduced cost and the range over which its objective function coefficient can vary without forcing a change in the optimal basis. The current value of each objective coefficient is also displayed for reference. Objective function sensitivity analysis is useful to analyze how sensitive the optimal solution is to the cost or profit associated with each variable.

Similarly, to view sensitivity analysis of the righthand side, type the command:

display sensitivity rhs -

For our example, CPLEX displays the following ranges for sensitivity analysis of the righthand side (RHS):

                                  RHS Sensitivity Ranges   

Constraint Name Dual Price       Down   Current          Up
c1                  2.7500   -36.6667   20.0000   +infinity
c2                  0.2500  -140.0000   30.0000    100.0000

CPLEX displays each constraint, its dual price, and a range over which its righthand side coefficient can vary without changing the optimal basis. The current value of each RHS coefficient is also displayed for reference. Righthand side sensitivity information is useful for analyzing how sensitive the optimal solution and resource values are to the availability of those resources.

CPLEX can also display lower bound sensitivity ranges with the command

display sensitivity lb

and upper bound sensitivity with the command

display sensitivity ub 

display sensitivity identifier