Continuous approximation models for mixed load school bus routing

• Continuous approximation models are useful for strategic analysis of mixed load school bus routing.
• The benefits are greater when many bus stops are shared and for schools close together.
• Mixed school bus routing is likely to be more advantageous in rural or semi-rural districts.

School bus routing is a complex and expensive transportation problem for many public school districts. Typical school bus routes serve a single school, but mixed load school bus routes carry students for more than one school at the same time. A mixed load policy reduces the number of stops and distance to pick up and drop off children, but it can increase travel distance by visiting multiple schools. This paper provides a general strategic analysis using continuous approximation models to assess the conditions under which mixed loading is likely to be beneficial. We also present a case study for a semi-rural Missouri school district to illustrate the application of the models in practice. Results show that mixed load routing is more beneficial for larger districts, when a large percentage of bus stops are shared by students of different schools, and when schools are closer together.