conditional constraint in Gurobi
AnsweredI am trying to model a conditional constraint in Guuobi python:
if a>= b then c == 1, otherwise c == 0
a and c are both model variables and c is binary
[assume a = I, b = safetystock, and c = X]
I have the following code based on https://support.gurobi.com/hc/en-us/articles/4414392016529-How-do-I-model-conditional-statements-in-Gurobi- but something is not correct as I cannot obtain the optimal answer. My code is:
Constraint4 = LP.addConstrs((I[months[a],item] >= safety_stock[item] + eps - M * (1 - X[months[a],item])
for item in items
for month in months
if month == months[a]), name="BigM1")
Constraint5 = LP.addConstrs((I[months[a],item] <= safety_stock[item] + M * X[months[a],item]
for item in items
for month in months
if month == months[a]), name="BigM2")
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Official comment
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Gurobi Staff
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Since your condition is \(a\geq b\), your have to use the \(\epsilon\) in your second big-M constraint, i.e.,
\[\begin{align*}
a &\geq b - M \cdot (1 - c)\\
a &\leq b - \epsilon + M \cdot c
\end{align*}\]You could alternatively try using Gurobi's indicator constraints
\[\begin{align*}
c = 1 &\rightarrow a \geq b\\
c = 0 &\rightarrow a \leq b - \epsilon
\end{align*}\]If none of the above works, could you please elaborate further what exactly does not work in your case?
Best regards,
Jaromił0 -
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Thanks, this works.
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Hi Oscar,
it is possible to define conditional statements like the one from this post using java?
Yes, is is possible. You can use the addGenConstrIndicator method. An example of its usage can be found at Genconstr.java.
In your particular case, you will have to model
\[\begin{align*}
z_{uv} &= PC_{uv} + PC_{vu}\\
w_{uv} &= PC_{uu} + PC_{vv} - 2\\
z_{uv} &= 1 \rightarrow T_{uv} = 0\\
w_{uv} &= 0 \rightarrow T_{uv} = \alpha\\
z_{uv}, &w_{uv} \in \{0,1\}
\end{align*}\]The reason for introducing the auxiliary binary variables \(z,w\) is that the addGenConstrIndicator method only accepts single optimization variables as input.
Best regards,
Jaromił0 -
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Hi Oscar,
it is possible to use the variable T_{uv} as an upper bound for another variable?
You can define an inequality constraint \(\text{some variable} \leq T_{uv}\).
Best regards,
Jaromił0 -
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