School Bus Routing with Stochastic Demand and Duration Constraints
研究了校车路径问题中通过超售提高车辆利用率的方法，提出机会约束规划模型和级联简化算法，在真实学区数据上验证了成本节约效果。
The school bus routing problem (SBRP) is crucial because of its impact on economic and social objectives. A single bus is assigned to each route, picking up students and arriving at the school within a specified time window. SBRP aims to find the fewest buses needed to cover all of the routes while minimizing the total travel distance and meeting required constraints. We propose a mathematical formulation responding to the overbooking policies applied in a real-world school district. According to our empirical studies, the probability of a student riding a bus varies from 22% to 77%, opening the opportunity to overbook the buses to improve utilization of their capacity. However, SBRP with overbooking has not attracted much attention in previous studies. In this work, overbooking is modeled via chance constrained programming. Additionally, to account for the uncertainty of the total travel time of the buses, a constraint limiting the probability of being late to school is also proposed in this paper. As a result of the NP-hard nature of the problem, a cascade simplification algorithm is proposed to partition the multiple stage SBRP problems into multiple multi-depot and one-school subproblems that are solved sequentially, where the results for one are data inputs for the next. Furthermore, we develop column-generation-based algorithms to solve the scheduling problem, and different instances of the problem are examined. Our computational experiments on a real-world school district demonstrate desirable cost savings in terms of the total number of buses used.