Challenges in Home to School Transport: Large-Scale School Bus Routing inclusive of Special Needs Students and Heterogeneous Fleets in the North West

规划校车接送孩子上下学的路线是运筹学文献中广泛研究的问题（Park & Kim, 2010），有数百篇论文对此进行了研究。接送儿童是一个可以理解的敏感话题，校车路线的规划对学校政策有影响，如学校预算和打卡时间（Bertsimas等人，2019）和特殊需要学生的包容性（Caceres等人，2019）。大量文献的另一个原因是这个问题可能的变体范围很广。在其最基本的形式中，目标是决定每辆公共汽车何时必须到达每个站点，满足有关时间表，公共汽车容量等的要求，同时尽量减少旅行时间。然而，现实世界的变体比这种基本形式复杂得多（Caceres等人，2019；Ellegood等人，2020）。例如，公共汽车路线应该包括有特殊需要的学生，他们在公共汽车上的时间应该尽可能地减少，这可能需要车辆有轮椅的空间或额外的座位为个人助理。在英国，公交车队往往是相对较小的容量和异质性，即不同的配置座位和轮椅的容量。此外，公共汽车本身的行驶时间可能不是最重要的标准，而是有一些相互冲突的标准，涉及公共汽车容量的利用率，从不同类型学生的角度出发的乘车时间，所需的公共汽车数量。等。另一个挑战是，英格兰的学区往往很大，包括数千名学生，这超出了经典数学优化方法能够处理的范围（Riera-Ledesma & Salazar-González, 2013; Schittekat et al., 2013）。Spada等人（2005）通过使用元启发式方法，能够解决一个学区约10,000名儿童的问题。

Planning the routes of school buses to transport children from/to school is a widely studiedproblem in the operations research literature (Park & Kim, 2010) with hundreds of papers writtenabout it. Transporting children is an understandably sensitive topic and the planning of school busrouting has implications for school policies such as school budget and bell-times (Bertsimas et al.,2019) and the inclusivity of special-needs students (Caceres et al., 2019). Another reason for thisvast literature is the broad range of possible variants of the problem.In its most basic form, the goal is to decide when each stop must be visited by each bus, satisfyingrequirements about timetables, bus capacity, etc., while trying to minimise the travel time. Real-world variants, however, are much more complex than this basic form (Caceres et al., 2019;Ellegood et al., 2020). For example, bus routes should be inclusive of special needs students,whose time in the bus should be minimised as much as possible and which may require vehicleswith space for wheelchairs or additional seats for personal assistants. In England, bus fleets tendto be of relatively small capacity and heterogeneous, i.e., with different configurable seats andwheelchair capacities. In addition, travel-time of the bus itself may not be the most importantcriterion, but rather there are a number of conflicting criteria related to the utilisation of the bus'scapacity, the riding time from the point of view of various types of students, the number of busesrequired. etc. A further challenge is that school districts in England tend to be large and includethousands of students, which is beyond what classical mathematical optimisation methods areable to handle (Riera-Ledesma & Salazar-González, 2013; Schittekat et al., 2013). By usingmetaheuristics, Spada et al., (2005) were able to tackle a school district of about 10,000 children.