  School bus planning is usually divided into routing and scheduling due to the
complexity of solving them concurrently. However, the separation between these
two steps may lead to worse solutions with higher overall costs than that from
solving them together. When finding the minimal number of trips in the routing
problem, neglecting the importance of trip compatibility may increase the
number of buses actually needed in the scheduling problem. This paper proposes
a new formulation for the multi-school homogeneous fleet routing problem that
maximizes trip compatibility while minimizing total travel time. This
incorporates the trip compatibility for the scheduling problem in the routing
problem. Since the problem is inherently just a routing problem, finding a good
solution is not cumbersome. To compare the performance of the model with
traditional routing problems, we generate eight mid-size data sets. Through
importing the generated trips of the routing problems into the bus scheduling
(blocking) problem, it is shown that the proposed model uses up to 13% fewer
buses than the common traditional routing models.
