Here are some basic things that make scheduling for our MS/HS school tricky and difficult:

- We share facilities (such as art pavillion, cafeteria, and gym) with the elementary school. So, all of those classes are blocked out during certain days and certain times.
- We are an IB school, which means that kids get to choose in Grade 11 and Grade 12 (and to a lesser extent, in Grades 9 and 10 as well) any combination of high-level and standard-level classes from our offerings based on their interest. Because we truly believe in kid's choice, we don't limit the types of combinations they can have, but it also means that we need to weave together the classes to allow for a variety of combinations.
- Imagine kid 1: English-High, Math-Standard, Chemistry-Standard, History-High, Economics-High, Music-Standard.
- Imagine kid 2: English-High, Math-High, Biology-High, History-Standard, Economics-Standard, Spanish-Standard.
- Imagine kid 3: English-Standard, Math-Standard, Physics-High, Economics-High, Music-High, Art-Standard.
- All of these combinations of schedules (and all other possible combinations) need to be supported, which comes into conflict with our next constraint....
- Because we are a relatively small school (only about 60 kids per grade), that limits the number of classes that can be offered. So, for example, there is only 1 section of High-level mathematics in Grade 11. All 10 or so kids who are interested in taking that class will need to be able to fit that one class into their schedules. We cannot afford to open up an additional section of High-level math in Grade 11, when there are only about 10 kids total who are capable of taking math at that level. Same with kids in High-level classes of most other subjects, probably.
- FYI: High-level IB math is really intense. It goes into differential equations and stuff, well beyond Calculus AB of the A.P. system.
- In the IB, each kid is
*required*to choose 3 High-level classes to take. Again, this means we need to have a master schedule that supports the variety of possible combinations of High-level classes that kids might wish for. A TOTAL MATH PROBLEM!!!! - Because we want to allow the flexibility of students changing their choices of high- and standard- level classes during the year (typically in Grade 11), we need to piece together department schedules in a way that allows a student to change options without too many problems during the year. Hopefully as well, this means that they will incur minimal changes in teachers of their other classes.

So very interesting, eh? Have you worked with scheduling before? Can you chime in to say something about the mathematical nature of this problem? Notice that we're not even talking about physical space constraints above. This is mathematical problem-solving at its richest!

omg. We used to do this from 12-2 AM the night before school started via whiteboard and Excel. So clearly, I have no advice or solutions, since the existence of your computer program probably means you are thinking about it in a way more sophisticated way than we did.

ReplyDeleteBut this post definitely brought back memories; our constraints were similar in terms of scheduling standard/AP at the same time, students following many different paths (sometimes even multiple grade-levels due to retention), having <350 students, and teachers with multiple preps. No teacher had his/her own classroom, so that added a physical space constraint. And, we also took into consideration class sizes and combinations of students + teacher strength (e.g. we assumed that veteran teachers could handle any grouping, but paid more attention to likely-feistiness for first-year classrooms).

This is not a comment about the mathematical nature of the problem. Just its difficulty :)

I've been doings scheduling for 6 years and I've also been thinking about the mathematical modeling of this problem. I was a Math minor in college, but I'm intrigued by how one can measure the complexity of the course requests vs. the number of determined courses. We typically figure out from the requests how many sections/classes of a course will be taught (and we're also small like you), but for me the equation is largely based on singletons/doubletons as well as the various faculty/room constraints. I'm sure there's a way to model and come up with some coefficient of complexity. That would help me prove why some years are harder to schedule than others...

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