On Wed, 29 May 2013, Roland Roberts wrote:
On 05/29/2013 01:27 PM, Michael Hennebry wrote:
On Tue, 28 May 2013, Roland Roberts wrote:
The basic problem is that I classes c, student groups g, time periods p,
and days d. We're breaking each day into 15-minute "modules" which have to
be schedule. A class has to span 3-8 modules on any give day. Some classes
have a minimum number of modules per week that have to be completed. With
just the above, I can specify the constraints by thinking of this as a
4-dimensional array X[c,g,p,d] and the constraints are various sums. The
problem I run into is specifying the the continuity constraint on
scheduling. It's not sufficient to have 3 modules for class C1, they have
to be 3 contiguous modules.
How do I specify this sort of thing?
Is each class a fixed length?
No, that's the first thing the school wants to relax with the modular
My previous constraints were necessary, but not sufficient.
They would allow breaking the day into 3 or
more parts with middle parts being too short.
The following are sufficient
to ensure all blocks have at least 4 periods:
X[c,g,p1,d]-X[c,g,p2,d]+X[c,g,p3,d]>=0 for p1< p2< p3<=p1+4, c,g,d...
where periods outside of a day are implictly 0.
Note that the constraints are numerous (quadratic
in the size of a minimum block) and rather loose.
--
Michael [email protected]
"On Monday, I'm gonna have to tell my kindergarten class,
whom I teach not to run with scissors,
that my fiance ran me through with a broadsword." -- Lily
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