A matching-based heuristic algorithm for school bus routing problems

School bus planning problem (SBPP) has drawn much research attention due to the huge costs of school transportation. In the literature, the SBPP is usually decomposed into the routing and scheduling subproblems due to its complexity. Because of the nature of the decomposition, even if all the subproblems are solved to optimality, the final solution may not be as good as the solution from the integrated model. In this paper, we present a new approach that incorporates the scheduling information (namely the trip compatibility) into the routing stage such that the interrelationship between the subproblems is still considered even in the decomposed problems. A novel two-step heuristic adopting the trip compatibility idea is presented to solve the school bus routing problem. The first step finds an initial solution using an iterative minimum cost matching-based insertion heuristic. Then, the initial trips are improved using a Simulated Annealing and Tabu Search hybrid method. Experiments were conducted on randomly generated problems and benchmark problems in the literature. The result shows that our two-step heuristic improves existing solutions up to 25% on the benchmark problems.