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Let's consider following pair of constraints:

$$x-M*b\le0$$ $$x-a*b\ge0$$

Where $M$ is a huge number and $a$ is a usually quite small one ($a

This pair of constraints represent a logical $XOR$ hence, the quantity of $x$ is eighter $0$ or $\ge a$. Especially the second one causes some trouble while solving the whole model. The performance of the solving process depends heavily on the value of $a$. In some cases, the model becomes even infeasible.

Does someone has an idea on how to efficiently relax the constraint or a way to determine a proper value of $a$ beforehand? I've tried lagrange relaxation so far but I wasn't impressed by the results.

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    what does the first constraint have to do with the question you asked? – 2017-01-04
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    Nothing. The first one just ensures that the binary variable is turned to 1 in case that x is greater than 0. – 2017-01-04

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