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Re: [Help-glpk] Newbie scheduling problem question, contiguous time inte

From: Roland Roberts
Subject: Re: [Help-glpk] Newbie scheduling problem question, contiguous time interval constraints
Date: Wed, 29 May 2013 15:24:45 -0400
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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

 SUM X[c2, g2, k, d] <= 1-X[c1, g1, p1, d]  for c2, g2, d, c1, g1, p1...

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.


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