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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.