Apologies for replying to myself twice, but a bit of experimenting has shown me
a partial explanation for the mystery I raised in the quoted text below. As
well as the fact that the MIP software used by the authors of the paper linked
below might have been specifically written for transport problems, I have also
found, to my surprise (though it makes sense when you think about it), that, in
a "bridge and torch" problem, the larger the number of people who are allowed
to "cross the river" in one go, the more easily GLPK is able to resolve it.
Since the large scale problems they claim to have resolved in the paper are
about optimising transport in a city, they will have been discussing buses and
trains - which, of course, carry large numbers of people simultaneously.
I wasn't expecting this, because according to the academic paper at
http://www.zib.de/Publications/Reports/SC-95-27.ps.Z (from Konrad-Zuse-Zentrum
für Informationstechnik Berlin), river crossing problems can be resolved using
integer programming with planar cuts. Would I be correct in thinking that to
achieve the level of results described in that paper, one would have to program
the planar cuts explicitly for this problem, rather than use the generalised
cuts provided with GLPK, or is there something I can do to make the model
resolve more quickly?
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