An iterative school decomposition algorithm for solving the multi-school bus routing and scheduling problem

Servicing the school transportation demand safely with a minimum number of buses is one of the highest financial goals for school transportation directors. To achieve that objective, a good and efficient way to solve the routing and scheduling problem is required. Due to the growth of the computing power, the spotlight has been shed on solving the combined problem of the school bus routing and scheduling. Some recent attempts have tried to model the routing problem in a way that maximizes the trip compatibilities with the hope of requiring fewer buses. However, an overcounting problem associated with trip compatibility could diminish the performance of these models. An extended model is proposed in this paper to resolve this over-counting problem along with an iterative solution algorithm. The result shows better solutions for 8 test problems can be found with a fewer number of buses (up to 25%) and shorter travel time (up to 7% per trip).