shadow prices for variables

[Ziming Guan]

Hi,

After solving a minimization problem, how do I get the shadow price for
a variable? Should I use variable.dual?

Thank you,
Ziming Guan

[Paul]

Ziming Guan wrote:
> Hi,
>
> After solving a minimization problem, how do I get the shadow price for
> a variable? Should I use variable.dual?
>

If you mean the shadow price for a bound on a variable, it's
variable.rc.

/Paul

[Ziming Guan]

Hi Paul,

I mean the shadow price for a variable, i.e., by how much the cost will
go up if one more unit is added on the value of the variable.

Regards,
Ziming

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[Robert Fourer]

According to the Mathematical Programming Glossary at
glossary.computing.society.informs.org, the shadow price is "the rate at
which the optimal value changes with respect to a change in some right-hand
side that represents a resource supply or demand requirement." I do not
believe that the term shadow price is often applied to variables.

In your definition, I am not sure what you intend by "one more unit is added
on the value of the variable." Do you mean that the optimal value of the
variable is increased by one (and the other variables are adjusted
accordingly in some way), or that the objective coefficient of the variable
is increased by one, or possibly something else?

Bob Fourer
4...@ampl.com