In some areas, dedicated bus services for every school or group of schools (if they are located close together) are in place. The pupil transportation system differs from country to country and even from county to county. These two goals are conflicting in nature because high service level often requires dedicated routes for small groups of pupils which require more buses and raises costs. On the other hand, the costs of providing high quality services must be considered by the funding organization (e.g., administration). On the one hand, safety of the pupils during transportation is a crucial factor and must be ensured (i.e., short walking distances, short travel times, we will refer to this as service level).
The low density of schools in rural areas and the distribution of higher level secondary schools require most pupils to use some type of transportation system to get to school. All of the above data is taken from Statistik Austria 3 and approximated over the whole geographic region of Austria. Secondary schools have between 50 and 300 pupils and higher level secondary schools have about 200 to 800 pupils. Primary schools have between 10 and 150 pupils in rural areas. Higher level secondary schools are usually located in more densely populated areas whereas primary and secondary schools are also located in rural areas. The number of pupils per school differs substantially according to school type and location. If only rural areas are considered, the average number of nonprimary schools per district is 22, the maximum number is 38, and the average number of schools per municipality is about one. Each district consists of multiple municipalities, where the average number of schools in a municipality is 2.57, about half of them being nonprimary schools. The number of nonprimary schools ranges from one to 115 with an average of about 25 (across all districts in Austria). Austria is divided into 121 districts and, on average, each district has 51 schools in total. In the school year 2011/2012 in Austria (population: 8.42 million 1) about 1.1 million pupils attended one of the 6,120 schools 2. Our results show that allowing transfers reduces total operating costs significantly while average and maximum user ride times are comparable to solutions without transfers. The impact of transfers on the service level in terms of time loss (or user ride time) and the number of transfers is analyzed. We develop a heuristic solution framework to solve this problem and compare it with two solution concepts that do not consider transfers.
The main objective is the minimization of the total operating costs. On the other hand, transfers have an impact on the service level: the perceived service quality is lower due to the existence of transfers however, at the same time, user ride times may be reduced and, thus, transfers may also have a positive impact on service quality. On the one hand, it allows more flexibility in the bus network structure and can, therefore, help to reduce operating costs. Allowing transfers has several consequences. It deals with the transportation of pupils from home to their school in the morning taking the possibility that pupils may change buses into account.
In this article, we study the school bus routing and scheduling problem with transfers arising in the field of nonperiodic public transportation systems.
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