I'm trying to generate the non-projective tree of the sentence:
But with the Stanford Core NLP tool (https://corenlp.run/), I obtain a projective tree:
Why this behavior?
The analysis provided by the Stanford parser is controversial. The Stanford annotation scheme assumes that function words are dependents of content words. Hence it shows the auxiliary is as a dependent of scheduled and the preposition on as a dependent of issue. The result of these assumptions is a tree structure that is relatively flat. The flatter the parse structure, the fewer the discontinuities (=projectivity violations). The first analysis is the better analysis insofar as it shows a dependency structure that is motivated by linguistic insights, such as the results of tests for constituents. I have examined the relevant matters surrounding these competing parses in detail. See the article here.
Using a different convention for showing dependencies, the first parse in the question can be rendered as follows (ignoring the status of punctuation marks):
Observe that there are five levels shown (excluding the bottom level where the string of words is given) and that the projectivity violation, which is due to extraposition, is clearly visible in the form of crossing lines. The second parse, i.e. the Stanford parse, is rendered as follows:
There are now just three levels shown due to the fact that the auxiliary verb and preposition are positioned as dependents rather than as heads. The flatter structure is such that there is less chance for a discontinuity to occur. Actually, though, there should still be a discontinuity present even for the Stanford parser, since if one were to extend a dependency from hearing to issue, crossing lines would again be present despite the flatter structure. Either the Stanford parser has overlooked the presence of extraposition or it has already performed an adjustment to the parse to avoid the projectivity violation.
Another analysis is given next, one that is along the lines of the first analysis but that avoids the projectivity violation by attaching the dependents in violation of projectivity to a word higher in the tree:
The dashed dependency edges indicate the presence of "rising", that is, the dependents in violation of projectivity have risen to attach to words that dominate their governors. If there is interest, I can easily provide more information about such analyses, since there is a tradition of doing this to overcome projectivity violations. The result is completely projective dependency analyses.
Finally, it could be the case that, as suggested above, the Stanford parser is manipulating the tree analyses to avoid the projectivity violation. That strikes me as unlikely, though, since I am not aware that the Stanford parser assumes that all structures are non-projective. It seems more likely that it has simply overlooked the presence of extraposition in the sentence.