We consider the classic School Bus Routing Problem (SBRP) with a multi modal
generalization, where students are either picked up by a fleet of school buses
or transported by an alternate transportation mode, subject to a set of
constraints. The constraints that are typically imposed for school buses are a
maximum fleet size, a maximum walking distance to a pickup point and a maximum
commute time for each student. This is a special case of the Vehicle Routing
Problem (VRP) with a common destination. We propose a decomposition approach
for solving this problem based on the existing notion of a shareability
network, which has been used recently in the context of dynamic ridepooling
problems. Moreover, we simplify the problem by introducing the connection
between the SBRP and the weighted set covering problem (WSCP). To scale this
method to large-scale problem instances, we propose i) a node compression
method for the shareability network based decomposition approach, and ii)
heuristic-based edge compression techniques that perform well in practice. We
show that the compressed problem leads to an Integer Linear Programming (ILP)
of reduced dimensionality that can be solved efficiently using off-the-shelf
ILP solvers. Numerical experiments on small-scale, large-scale and benchmark
networks are used to evaluate the performance of our approach and compare it to
existing large-scale SBRP solving techniques.Comment: 41 pages, 27 figure