add a constrain for two related variables
回答済みhello,
In my case study, I have two variables that can not take a value at the same time. which means if one of them takes a value the other should be zero. Can I add a constant like that?
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Hi!
This sounds like Indicator constraints might be helpful here. These allow modeling such variable relations.
Cheers,
Matthias0 -
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thank you so much, but I did not recognize well how to use it. How to give the indicator a value. Can you give me a simple example, please?
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To help give an example, could you tell us a bit more about your variables? What variable type are they (integer, binary, continuous)? Do they have bounds?
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I have two continuous variables, I want one of them to be 0 when the other takes a value more than 0. such as battery charging/discharging variables. they cannot have values more than 0 at the same time.
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For 2 continuous variables, one way to formulate what you want would be
\[\begin{align}
x_1 &\leq \delta_1 x_1^U\\
x_2 &\leq \delta_2 x_2^U\\
\delta_1 + \delta_2 &= 1\\
\delta_1 &, \delta_2 \in \{0,1\}\\
x_1 &\in [0,x_1^U], x_2 \in [0, x_2^U]
\end{align}\]This way, when \(x_1 > 0\), then \(\delta_1 = 1\) and thus \(\delta_2=0\) and \(x_2=0\). An analogous statement holds when \(x_2 > 0\). Please note that it is possible that \(x_1=x_2=0\).
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