Teachers
Each teacher has their own subjects, available periods, working days, and constraints that the timetable needs to respect.
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Education · Scheduling · Optimization
How do you build a timetable when almost every move affects ten other things?
The application for the Isidor Bajić Music School is not really a table-layout problem. It is a problem of connecting a large number of rules into one valid, practical, and high-quality solution.
Next.js · PostgreSQL · Prisma · Optimization · CP-SAT
Problem
A valid timetable is not the same as a good timetable.
If every lesson is simply placed somewhere inside an allowed time slot, the problem is still not solved.
A teacher can end up with too many gaps. Students can get a poorly structured day. The same subject can be repeated at inconvenient times. A classroom can introduce another conflict. Moving one lesson can damage the schedules of several other people.
The system therefore has to distinguish between rules that must never be violated and quality criteria that should be optimized as far as reasonably possible.
Constraints
One timetable. Many different kinds of rules.
Students and classes
Lessons must fit without overlaps while keeping the daily schedule as practical as possible and minimizing unnecessary gaps.
Classrooms
Every activity needs an appropriate classroom, including subjects that use their own default or assigned room.
Allowed periods
Not every time slot is equally possible. Different grades, teachers, and activities have different allowed time windows.
Conflicts
A single change can trigger a chain of problems elsewhere, so a locally good move may still make the overall timetable worse.
Timetable quality
Being valid is not enough. The system also needs to reduce gaps, poor lesson repetition, and unnecessary teacher working days.
Approach
When local adjustments stop being enough, the problem becomes global optimization.
At some point it is no longer rational to repair the timetable one move at a time and hope that the same problem does not appear somewhere else.
The system therefore gained a solver-based approach that considers many activities and constraints as one connected problem, while clearly separating hard rules from quality objectives.
01
Hard constraints
Teacher, student, and classroom conflicts, as well as forbidden periods, must never exist in a valid solution.
02
Optimization
Among valid solutions, the solver searches for one that produces a better overall timetable.
03
Human control
Automatic optimization does not replace the editor. The system still supports review and controlled manual changes.
04
Validation
Every important version is validated before it can become a candidate for publishing.
System
The solver is only one part of the application.
A school does not need a mathematical model that only runs in a terminal. It needs a complete product where data enters the system, the timetable is generated, reviewed, edited, validated, and eventually published.
01
Import and processing of school data
02
Draft timetable for further work
03
Automatic conflict detection
04
Optimization across a large number of interacting constraints
05
Manual editing and controlled drag & drop
06
Versioning and timetable publishing
07
Public timetable view
08
Daily teacher view
Result
0
gaps in teachers' schedules in the validated candidate
Quality starts to matter once the system stops being merely “valid”.
The accepted optimization result reached zero gaps in teachers' schedules with only one remaining student gap — a level of quality good enough to stop aggressive further optimization and move into real use.
This is also why optimization is not an endless search for mathematical perfection. The goal is a system that solves the real problem well enough to be useful.
What this project demonstrates
Not every problem is a CRUD application.
This project is particularly important to me because it combines traditional full-stack development with constraint modelling, optimization, validation, and the real operating rules of a school.
The interface is only the final layer. Most of the value comes from understanding the problem correctly and turning a large number of interdependent rules into a usable system.
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