School Bus Routing Problem with Open Offer Policy: A case study in a New York school district

This paper introduces the School Bus Routing Problem with Open Offer Policy (SBRP-OOP), which aims to minimize fleet and transportation costs by offering monetary incentives to students who opt-out of using the bus. We propose a mathematical formulation to optimize the pricing strategy, balancing the trade-off between incentive payments to students who forgo bus service and the expected savings from reducing fleet size and improving route efficiency. To evaluate the effectiveness of the policy, we conduct a series of simulations using both synthetic and real-world data from a school district in New York State. Our findings show that the policy can yield substantial cost reductions, particularly in low-ridership contexts such as middle and high schools, with the potential to reduce the number of required buses by up to three in certain cases.