max tricks

The following condition

can be easily written as

 

However when we have:

 

then we need more sophistication. Something like:

Here we introduced a variable y that assumes the value of the maximum of the x’s. The following expression will give a good big-M value:

See also: http://orinanobworld.blogspot.com/2012/01/maxmin-bounds.html

A slightly more direct formulation would be:

If we are really want to show off, we can only generate this if

and use the simpler adjustment of bounds

otherwise.