> To get tighter relaxations, use the smallest big M's that will work.

This effectively limits the range of values for the unknowns.
If that range is very small, then I can directly use a binary encoding
for numbers, and use a SAT solver - in fact that's what I've been doing
for some time. I was hoping that MIP gives another feasible approach.
But as they say, "there's no free lunch".

PS: I find the slight inconsistencies between gmpl and zimpl
http://zimpl.zib.de/
super annoying. (syntactically: e.g., "subject to"/"subto", and
semantically:
default lower bound is -infinity and 0, resp.)

J.W.

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