# Questions tagged [logical-constraints]

For questions about constraints that can be expressed in (usually propositional) logic.

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### Enforcing Order in a Linear Programming Question

I have an optimization model to fulfill the water requirements of a city's distribution network. The model includes water sources from rainfall collection, river extraction, reservoir storage, and ...
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### Activating a sequence of the binary variables in a multi-dimensional array

Suppose we have an array of binary variables $\{x_{i,t,n}, \ \forall i \in I, t \in T, n \in N \}$. If we want to define a condition as, if any of $x_{i,t,n} = 1$ in an arbitrary index $i$, then the ...
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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 ...
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### How to enforce logical implication $\sum_j a_j x_j \le b \implies \sum_j c_j x_j \le d$

Some modeling languages and solvers support indicator constraints of the form $$y=\hat{y} \implies \sum_j a_j x_j \le b,$$ where $y$ is a binary decision variable and $\hat{y}\in\{0,1\}$ is a constant....
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### Equivalence between constraints in ILP

Let's have binary variables $x$ and $y$. I'd like to define a helping binary variable $z$ such that $$z = 1 \; \;\; \mathrm{iff} \; \; \; x + y = 2.$$ If I wanted to express the equivalence between ...
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### The linearization of the logical constraints

I know the logical constraints can be linearized by either the logical representation of whose relation, (for pure binary variables e.g. CNF/DNF) or for general form by using Big-M formulation. As I ...
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