Introducing a Novel Mathematical Model for School Vehicle Routing Problem and Proposing a New Algorithm to Solve It

This research presents and solves a new mathematical model for School Bus Routing Problem (SBRP). SBRP is a specific case of Vehicle Routing Problem (VRP). Despite prevalent models, this model includes location and routing simultaneously. Besides, the vehicles are non-homogenous. In addition, instead of locating schools which are the depots, we consider locating bus stops that are mentioned 'customer's in the simple Location Routing Problem (LRP). This problem itself has led to a change in sub-tour elimination constraint. In contrast to the other articles we solve location and routing simultaneously. In one of these models, students related to different schools can receive service by same station and in other models each school have specific stations. To solve this model, we proposed a meta-heuristic Scatter Search (SS) algorithm. Afterward, we coded the model by GAMS software. Finally the results derived from SS algorithm are compared with results derived from GAMS. Consequently we figured out that SS algorithm produces results in more reasonable time with acceptable errors.