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Next: Slack Up: Linear Constraint Attributes Previous: ConstrName


Pi

Type: double
Modifiable: No

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

Given a linear programming problem

\begin{displaymath} \begin{array}{ll} \mathrm{minimize} & c'x \ \mathrm{subject to} & Ax \ge b \ & x \ge 0 \end{array}\end{displaymath}

and a corresponding dual problem


\begin{displaymath} \begin{array}{ll} \mathrm{maximize} & b'y \ \mathrm{subject to} & A'y \le c \ & y \ge 0 \end{array}\end{displaymath}

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.

next up previous
Next: Slack Up: Linear Constraint Attributes Previous: ConstrName