American Master Schedules
The American master schedules can be ranked as the most difficult in the world when compared to other countries.
Even though other countries have different schedules for different days their master schedule usually has a maximum of four or five blocks.
Added to this complexity courses usually for a year which is 1 semester where the American high school schedule courses run over semesters.
World Comparison Chart
Below is a table showing the permutation complexity per student when a student is being placed into the blocks.
Block placement permutations per student |
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1 Semester | 2 Semesters | 3 Semester | 4 Semester | |
1 Block | 1 | 2 | 3 | 4 |
2 Block | 2 | 4 | 6 | 8 |
3 Blocks | 6 | 12 | 18 | 24 |
4 Blocks | 24 (uk) | 48 | 72 | 96 |
5 Blocks | 120 (Aus) | 240 | 360 | 480 |
6 Blocks | 720 | 1440 | 2160 | 2880 |
7 Blocks | 5040 | 1 0080 | 15 120 | 20 160 |
8 Blocks | 40 320 | 80 640 | 120 60 | 161 280 |
9 Blocks | 362 880 | 725 760 | 1 088 640 | 1 451 520 |
The above table is showing the student block placement per student - so if you have the school running on an 8 block, two semester system , and you have 500 students, then the total complexity, when only balancing the students would be 40 320 000.
This would only be to place the students into the completed master schedule and does not include master scheduler building, which needs to test each student along the way, as each course is being placed. Very quickly the calculations start running into the billions and having a fast computer is not the answer, since it comes down to having the correct search and prediction algorithms.
You can see why master scheduling is such a complex phenomenon.