  We consider the Single School Routing Problem (SSRP) where students from a
single school are picked up by a fleet of school buses, subject to a set of
constraints. The constraints that are typically imposed for school buses are
bus capacity, a maximum student 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 come up with a simplified formulation for
solving the SSRP by introducing the connection between the SSRP 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 pruning
techniques that perform well in practice. We show that the compressed problem
leads to an Integer Linear Program (ILP) of reduced dimensionality that can be
solved efficiently using off-the-shelf ILP solvers. Numerical experiments on
the synthetic Boston Public School (BPS) instances are conducted to evaluate
the performance of our approach. Meanwhile, our proposed SSRP formulation
allows a natural extension for introducing alternate transportation modes to
students, which effectively reduces the number of buses needed for each school
and leads to a 15\% cost reduction on average. Moreover, two state-of-art
large-scale SSRP solving techniques are compared with our proposed approaches
on benchmark networks and our methods outperform both techniques under a single
school setting.
