In this post you will see how to linearize max functions, min functions, and absolute value functions. These can be expressed mathematically as:

Let’s start with the modulus, as the other two depend on it.

Here you simply replace that one constraint by the following two:

The min function can be linearized as:

First, we decompose the min function into a max and a modulus.

Then we get rid of the max.

Finally, the answer is using the following five constraints:

Remember to penalize and such that only one of them will be different from zero in any solution.

The max function can be linearized as follows:

From here on things are very similar to the min function…

And finally, the five necessary constraints are:

And again, remember to penalize  and .

Thanks to Lieke van der Heide.

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