The objective function includes  crop(s) = median(0, s, 1)
where the range of s includes both negative values and values > 1 .

The set defined is not convex and so cannot be defined purely with
linear constraints.
One can get around the need for a binary by using optimality.

Add nonnegative auxillary variables p0, n0, p1 and n1.
s = p0-n0
s = p1-n1+1
Adjust the objective to ensure that p0 or n0 is zero
at optimality and that p1 or n1 is zero at optimality.

0<=crop(s)<=1
crop(s)<=p0
crop(s)>=1-n1

--
Michael   [email protected]
"Sorry but your password must contain an uppercase letter, a number,
a haiku, a gang sign, a heiroglyph, and the blood of a virgin."
                                                             --  someeecards

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