A bi-level school bus routing problem with bus stops selection and possibility of demand outsourcing

This paper develops a bi-level mathematical model for the school bus routing problem aiming at designing an efficient transportation system considering the possibility of predicting the students’ response. In the real world, the demand for using private cars depends on how well public transportation systems are operating especially in metropolitan cities. An inefficient public transportation will lead to an increase in the demand for using private cars. This issue will result in problems such as increased traffics and urban pollutions. To address this issue, an efficient public transportation system is designed by developing a new bi-level mathematical model. In the proposed model, the designer of the public transportation system, as the upper-level decision-maker, will locate appropriate bus stops and identify bus navigation routes. Subsequently, the decision regarding the allocation of students to transportation systems or outsourcing them will be made at the lower level which is considered as an operational-level decision-making. To solve this problem, two hybrid metaheuristic approaches named GA-EX-TS and SA-EX-TS have been proposed based on location-allocation-routing (LAR) strategy. The performance of these proposed methods is compared with exact solutions achieved from an explicit enumeration approach followed in the small-scale instances. Finally, the proposed approaches are used to solve 50 random instance problems. Comparing the results of the two tuned hybrid algorithms and conducting the sensitivity analysis of the model provide evidence for the good performance of the proposed approach.