Modeling Mixed Load School Bus Routing

Abstract

Transporting pupils to and from schools is a complex and expensive logistics problem for many public school districts, especially in rural areas where travel distances are longer. In many regions of the world, students ride public transit to school, but public school districts in the US and Canada generally provide transportation in dedicated school buses. Each bus typically makes a sequence of trips each morning and each afternoon, where each trip serves a separate school, usually with staggered start times for different school levels (elementary school, intermediate school, high school). This research explores whether the successful business logistics practice of mixed loading can be applied to school bus transportation. Mixed load school bus trips carry students for more than one school at the same time, and a mixed load routing policy reduces the number of stops to pick up and drop off students, but it adds travel distance at the end of a trip to visit multiple schools. We first provide a general strategic analysis using continuous approximation modeling to assess the conditions under which mixed loading is likely to be beneficial. Then we present a discrete algorithm for finding mixed load bus trips. Results for benchmark data sets explore the tradeoffs between minimizing the number of buses used and minimizing the travel distance. We also present a case study for a Missouri school district to illustrate the application of the models in practice. Results show that mixed load bus routing can be beneficial when students are sparsely distributed, when a large percentage of bus stops are shared by students of different schools, and when schools are closer together.