School bus planning is usually divided into routing and scheduling because of the complexity of solving them concurrently. However, the separation between these two steps may lead to worse solutions with higher overall costs than from solving them together. When the minimal number of trips in the routing problem is being determined, neglecting trip compatibility could increase the number of buses needed in the scheduling problem. This paper proposes a new formulation for the multischool homogeneous fleet routing problem that maximizes trip compatibility while minimizing total travel time. This plan incorporates the trip compatibility for the scheduling problem in the routing problem. A proposed heuristic algorithm for solving this problem decomposes the problem by schools. To compare the performance of the model with traditional routing problems, eight midsize data sets were generated. Importing the generated trips of the routing problems into the bus scheduling (blocking) problem shows that the proposed model can reduce the buses needed by up to 25%. A sensitivity analysis on coefficients of the model illustrates the effect of the weight of trip compatibility.
Performance characterization of reinforcement learning-enabled evolutionary algorithms for integrated school bus routing and scheduling problem
