# 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 ...
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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, $a_i, b_j \in \mathbb{R}_+$ ...
• 251
1 vote
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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 ...
• 11
1 vote
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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)...
• 9,258
1 vote
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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 ...
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### Disjunctive bidirectional implications between two pairs of Non-negative Continuous or Integer Variables

Say for instance, I have four non-negative continuous or integer variables, $x$, $y$, $a$, $b$. I would like to ask about the constraints representing the following implications, whereby at any one ...
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