SBRP Algorithm: The School Bus Routing Problem Explained
Twice a day, millions of students board school buses across Türkiye. What looks like a simple operational task harbors one of the most mathematically complex problems in logistics: the School Bus Routing Problem (SBRP). vitaRoute solves it with reinforcement learning.
What Is SBRP?
SBRP (School Bus Routing Problem) is the combinatorial optimization problem of routing school buses as efficiently as possible. It answers: given constraints (vehicle capacity, maximum walking distance, district boundaries, school hours), how do you transport students to school most efficiently?
SBRP consists of three interlinked sub-problems: (1) Stop generation — where to place stops; (2) Student assignment — which students walk to which stop; (3) Route construction — in what order vehicles visit stops.
Why Is It NP-Hard?
SBRP is NP-hard — meaning the number of possible solutions grows exponentially as problem size increases (more students, more vehicles). Exact algorithms cannot complete computations in practical time.
For a simple SBRP with 100 students and 5 vehicles, the solution space exceeds 10⁴⁰. Even the fastest computer evaluating one billion solutions per second would require longer than the age of the universe.
- Solution space grows exponentially with stop count
- Vehicle capacity, time and distance constraints multiply the dimension
- Real-world variables (traffic, road closures) don't fit static models
- Daily changing student lists require dynamic re-optimization
Classical SBRP Solution Methods
Several approaches have been developed over the years, each with trade-offs:
- Greedy algorithms — Fast but produce suboptimal solutions
- Genetic algorithms — Good quality but slow computation
- Simulated annealing — Escapes local minima but requires parameter tuning
- Tabu search — Powerful but requires domain knowledge
- Integer linear programming (ILP) — Optimal but only for small instances
RL-SBRP: Reinforcement Learning Meets SBRP
vitaRoute's RL-SBRP framework integrates reinforcement learning with the classical SBRP formulation. Developed through our TÜBİTAK-backed R&D process, this approach achieves meaningful improvements in both solution quality and computation speed over classical methods.
The RL agent was trained on thousands of virtual Turkish scenarios, accounting for Türkiye's real road network and district constraints.
- 40-60% faster computation than classical methods
- Maximum 10 seconds for 1,000 students
- Support for Türkiye-specific road network and district constraints
- Dynamic re-optimization for daily changing student lists
Student Transport in Türkiye: Special Constraints
Turkish school transport operations include constraints beyond the standard SBRP formulation — vitaRoute models all of them:
- Maximum walking distance per MEB regulations (500 m for primary school)
- District boundary constraints
- Last-stop time constraints based on school start time
- Multi-school split route support
- Two-way morning/afternoon route generation
SBRP may appear to be a simple operational problem, but it is a profound mathematical challenge that has been on the research agenda for decades. vitaRoute's RL-SBRP approach turns that challenge into a practical, scalable solution.