Solving school bus routing problem with mixed-load allowance for multiple schools
Artikel i vetenskaplig tidskrift, 2020

The school bus routing problem (SBRP) is a challenging real-world problem that affects many citizens on a daily basis.
This study considers several important classes of practical requirements for SBRP that include multiple schools, mixed loads
for students boarding the same bus but from different stops and commuting to different schools, heterogeneous
fleets, various student-pickup time windows, and school-bell-ring constraints. Accordingly, a time-discretized multicommodity
network flow model is proposed based on a student-loading state-oriented space-time network. To enable
optimization of both the student-bus assignment and bus routing, we introduce an extended-state dimension to represent
the number of students commuting to different schools by buses. By implementing an augmented Lagrangian relaxation
approach, the primal SBRP is reformulated as a quadratic 0-1 programming model with linear flow balance constraints.
Furthermore, the augmented Lagrangian model can be decomposed and linearized as a series of linear multi-commodity
network flow sub-problems that can be successively solved using dynamic programming algorithms in a cyclic block
coordinate descent framework. The proposed model and approach to the solution are implemented on a nine-node test
network, a Sioux Falls network under different scenarios, and a large-scale Chicago sketch network.

multi-commodity network flow

cyclic block coordinate descent method

School bus routing

augmented Lagrangian relaxation


Pan Shang

Beijing Jiaotong University

Liya Yang

Renmin University of China

Ziling Zeng

Chalmers, Arkitektur och samhällsbyggnadsteknik, Geologi och geoteknik

Lu Tong

Beihang University

Computers and Industrial Engineering

0360-8352 (ISSN)



Transportteknik och logistik





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