Questions tagged [indicator-constraints]

For questions on constraints controlled by binary variables.

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Modelling Question

Let $W^C_t$, $W_t$ be binary variables and $p$ an integer variable with $1 \leq p \leq 3$ The variables are related through the following equation: $$W^C_t = \sum_{\theta=1}^{p} W_{t-\theta}$$ I can ...
Clement's user avatar
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Indicator function for integer variable with inequality constraint

I have $n$ integer variables $\vec{x}$ with the following integer programming problem. $$ COST = \sum^{n-1}_{i = 0} a_i x_i + \sum^{n-1}_{j=0} b_j I(x_j > 0) $$ Here, $a_i, b_j \in \mathbb{R}_+$ ...
Omar Shehab's user avatar
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Linearization of Conditional Constraints for MIP using Cplex

I'm currently working on a mixed-integer programming (MIP) problem and I'm trying to implement a set of conditional constraints in CPlex. These constraints involve decision variables that are indexed ...
B.Kim's user avatar
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The rule of the slack variable in an indicator constraint

In some cases I have seen, the indicator constraint can be written as indcons(expression, binary_var). Then it is interpreted as follows: $$LHS - slack (\leq = \geq)...
A.Omidi's user avatar
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Multiple conditions in indicator constraint of Gurobi

I'm working on a vehicle routing problem, in which a vehicle need to pick up amounts of things in some nodes. I'm trying to solve it by Gurobi optimizer. Except for meeting the time windows of each ...
kaiyu wei's user avatar
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[OR-Tools][CP-SAT] Implement an indicator function in a constraint

Good morning ! I would like to implement this constraint using CP-SAT (see image below). x_i,j is a boolean variable, a and b are given. The problem is that I don't know how to implement the ...
Arthursbr's user avatar