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
scheduling. Even now, a few classes hold a weekly "double-period" but
everything is hand scheduled which basically works by severely limiting
what is offered to students. The attempt this past year to hand schedule
under the new paradigm was a failure as hand scheduling never resolved
the conflicts that we kept running into.
If so, the start time determines the end time.
Your array works if p, d refer to the start times.
In my thinking, p referred to a time slot, not necessarily the start
time. I'm reading the paper by Boland et al., and think I'll be in a
better position to describe my setup coherently once I get through that.
At the very least, I'll have a consistent set of terminology to describe
what I'm trying to do.
If c1, g1 requires 4 periods and c2, g2 requires 7 periods:
If c1, g1 starts in period p1, then c2, g2 may not start in p1-6..p1+3
p1+3
SUM X[c2, g2, k, d] <= 1-X[c1, g1, p1, d] for c2, g2, d, c1, g1, p1...
k=p1-6
Let me think about that a little. c1, g1 won't constrain c2, g2 that way
since it's a both a different class and a different group of students,
think c1=6th grade math, c2=6th grade English. But you've got me
thinking since c1, g1 will constrain c2, g1.
roland
--
PGP Key ID: 66 BC 3B CD
Roland B. Roberts, PhD RL Enterprises
[email protected] 6818 Madeline Court
[email protected] Brooklyn, NY 11220
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