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I have a constraint in a linear programming formulation with two variables: $X \ge Y$

To which I want to apply the following if-else conditions:

if Y=1:
    X=1
else:
    X=0

Where $X$ and $Y$ are binary.

How can I fit this if-else into linear programming? Do I need to define another variable? It looks as an AND operation, between $X$ and $Y$.

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This can be expressed with just the equation $X=Y$. Since $X,Y$ are zero-or-one variables, the only possible assignments that are consistent with your condition are $X=Y=0$ and $X=Y=1$.

See Express boolean logic operations in zero-one integer linear programming (ILP) for many more boolean conditions and how to express them as linear inequalities.

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