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），有数百篇论文是关于它的。运输孩子是一个可以理解的敏感话题，校车路线的规划对学校政策，如学校预算和铃声时间有影响（Bertsimas等人，2019）和特殊需要学生的包容性（Caceres等人，2019年）。这篇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必须在何时访问每个车站，满足时间表，公共汽车容量等方面的要求，同时尽量缩短旅行时间然而，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年）。例如，公共汽车路线应包括有特殊需要的学生，他们在公共汽车上的时间应尽可能减少，这可能需要车辆有轮椅空间或个人助理的额外座位。在英格兰，巴士车队往往是相对较小的容量和异构，即，with different不同configurable可配置seats座位and wheelchair轮椅capacity容量.此外，巴士本身的行程时间可能不是最重要的标准，而是有一些相互冲突的标准，涉及巴士的容量利用，从各种类型的学生的角度来看，乘车时间，所需的巴士数量。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所能处理的范围（Riera-Ledesma & Salazar-González，2013; Schittekat等人，2013年）。Spada等人使用元分析法，（2005年）能够解决一个约10,000名儿童的学区。

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.