A School Bus Routing and Scheduling Problem with Time Windows and Possibility of Outsourcing with the Provided Service Quality

Abstract

A school bus problem is one of the most important logistical issues faced by governments and school administrations, which is widely depends on route optimization and scheduling. This study presents a mathematical model for the single-load school bus problem for urban areas, which considers bus stop selection, bus route generation, and school bus scheduling simultaneously. This model considers the possibility of demand outsourcing (e.g., students using parallel systems for transportation) and time windows in the school bus routing and scheduling (SBRS) problem. Each vehicle transports students from a bus stop to their school under the given constraints. Our goal is to maximize the transportation firm’s profits and increase the quality of service provided for students. To validate the presented model, the problem is solved by GAMS software, and the results are shown and analyzed. Finally, some sensitivity analyses are performed to show the efficiency of the presented model.