使用完美匹配启发式算法的校车出行均衡调度
Balanced scheduling of school bus trips using a perfect matching heuristic
摘要：
在校车调度问题中，影响成本的主要因素是运营所需的校车数量。然而，在分包学生交通的情况下，不平衡的旅行可能会大大增加费用，因为有些旅行的长度可能超过每日固定的驾驶目标，并将导致超时收费。针对多校校车均衡调度问题，提出了一种混合整数规划（MIP）模型和一种基于匹配的启发式算法。启发式算法保证找到最少数量的总线。启发式算法的有效性进行了测试，通过比较其解决方案与从MIP得到的解决方案时，MIP可以找到一个很好的解决方案。对于较大的情况下，MIP不能找到一个很好的解决方案，我们说明了启发式的性能，显示它如何影响旅游的持续时间。为了说明MIP和启发式的性能，我们研究了12个不同的问题，不同的旅行次数都是基于两个现实世界的问题。一个加州的案例研究与54次旅行和霍华德县公立学校系统（HCPSS）与994次旅行。数值结果表明，该算法可以在较短的时间内找到合理的解决方案。我们的算法的平衡解决方案可以节省高达16%的校车运营成本相比，最好的解决方案，从MIP模型后40小时。启发式算法的平衡阶段将游览持续时间的标准差降低了47%。
英文摘要：
In the school bus scheduling problem, the main contributing factor to the cost is the number of buses needed for the operations. However, in the case of subcontracting the transportation of pupils, unbalanced tours can increase the costs significantly as the lengths of some tours can exceed the daily fixed driving goal and will result in over-hour charges. This paper proposes a Mixed Integer Programming (MIP) model and a matching-based heuristic algorithm to solve the balanced school bus scheduling problem in a multi-school setting. The heuristic is guaranteed to find the minimum number of buses. The effectiveness of the heuristic algorithm is tested by comparing its solutions with the solutions obtained from the MIP whenever the MIP could find a good solution. For larger cases where the MIP cannot find a good solution, we illustrate the performance of the heuristic by showing how it affects the durations of the tours. To illustrate the performance of the MIP and heuristic, we examine 12 different problems with different numbers of trips which are all based on two real-world problems. A California case study with 54 trips and the Howard County Public School System (HCPSS) with 994 trips. The numerical results of testing our approach indicate that the proposed algorithm can find reasonable solutions in a significantly shorter time. The balanced solutions of our algorithm can save up to 16% of school bus operation costs compared to the best solution found from the MIP model after 40 hours. The balancing stage of the heuristic decreases the Standard Deviation of the tour durations by up to 47%.
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