A Tri-objective model for the school bus routing problem with a new approach in network design

The school bus routing problem (SBRP) seeks to plan an efficient schedule for a fleet of school buses where each bus picks up students from various bus stops and delivers them to their schools. The related models are based on a graph which the bus stops are their nodes and the routes are their edges. This assumption is inconsistent with the base of the most real transportation systems in Iran. In reality, the students walk to a street where the bus passes. Therefore, the bus may stop several times along a path and pick up the students. In this paper, based on the recent approach, the streets are formulated as edges and the intersections as nodes. This approach can increase the potential of the model in the display of the real world conditions. This research presents a tri-objective integer programming model to minimize the distance of total bus travel, student walking and total student riding, in the case that we have one depot. Finally, the proposed model is applied to optimize the bus rout of transportation service which belongs to the Mazandaran University of science and technology staffs in Behshahr. Besides, the case study is analyzed by GAMS software.