Type: double
Modifiable: No

The constraint dual value in the current solution (also known as the shadow price).

Given a linear programming problem

\mathrm{minimize} & c'x \
\mathrm{subject to} & Ax \ge b \
& x \ge 0

and a corresponding dual problem

\mathrm{maximize} & b'y \
\mathrm{subject to} & A'y \le c \
& y \ge 0

the Pi attribute returns <span>$</span>y<span>$</span>.

Of course, not all models fit this canonical form. In general, dual values have the following properties:

  • Dual values for <span>$</span>\ge<span>$</span> constraints are <span>$</span>\ge 0<span>$</span>.
  • Dual values for <span>$</span>\le<span>$</span> constraints are <span>$</span>\le 0<span>$</span>.
  • Dual values for <span>$</span>=<span>$</span> constraints are unconstrained.
For models with a maximization sense, the senses of the dual values are reversed: the dual is <span>$</span>\ge 0<span>$</span> for a <span>$</span>\le<span>$</span> constraint and <span>$</span>\le 0<span>$</span> for a <span>$</span>\ge<span>$</span> constraint.

Only available for continuous models.

For examples of how to query or modify attributes, refer to our Attribute Examples.

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.