Bike-sharing systems play an important role in the multimodal transit system. This study investigates the truck fleet sizing problem for bike relocation that integrates strategic and tactical decisions taking into account the stochastic nature of demand. We develop a multi-period bike relocation model at the tactical level and derive the bike shortage formulation coupling relocation decisions with midterm demand. Based on this thorough analysis, the objective of spatial fairness of bike shortage is explicitly measured. The problem is formulated as a multi-stage stochastic programming model to capture the demand uncertainty, in which bike relocation decisions relating to station inventory are integrated with decisions that determine the truck fleet size. We develop a data-driven multi-stage scenario tree generation approach that can incorporate midterm demand spatial and temporal dependence. To prevent the loss of information and mitigate the “curse of dimensionality”, we propose a novel “multi-stage approximate stochastic programming” by integrating the traditional multi-stage stochastic programming and Response Surface Methodology. A conditional value-at-risk criterion () is introduced into each decision node to capture the service provider’s risk aversion and make more informed decisions (and thus the risk-hedging ability of the solution). To work with this nonconvex model, we develop a fast and effective hybrid metaheuristic algorithm. The modeling approach and algorithm are tested on a large-scale case in New York. Results show that there is a trade-off between total cost minimization and bike shortage equilibration. We also conduct extensive experiments to evaluate our stochastic model and discuss practical implications relative to the deterministic model.

中文翻译：

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具有随机需求的自行车搬迁的帕累托卡车车队规模：风险规避的多阶段近似随机规划

自行车共享系统在多式联运系统中发挥着重要作用。本研究研究了自行车搬迁的卡车车队规模问题，该问题综合了战略和战术决策，同时考虑了需求的随机性。我们在战术层面开发了多周期自行车搬迁模型，并得出将搬迁决策与中期需求相结合的自行车短缺公式。基于这种彻底的分析，自行车短缺的空间公平性目标得到了明确的衡量。该问题被表述为多阶段随机规划模型，以捕获需求不确定性，其中与车站库存相关的自行车重新安置决策与确定卡车车队规模的决策相结合。我们开发了一种数据驱动的多阶段场景树生成方法，可以结合中期需求的空间和时间依赖性。为了防止信息丢失并减轻“维数灾难”，我们通过集成传统的多阶段随机规划和响应面方法，提出了一种新颖的“多阶段近似随机规划”。每个决策节点都引入了条件风险价值准则 ()，以捕获服务提供商的风险规避并做出更明智的决策（从而提高解决方案的风险对冲能力）。为了使用这种非凸模型，我们开发了一种快速有效的混合元启发式算法。建模方法和算法在纽约的大规模案例中进行了测试。结果表明，总成本最小化和自行车短缺平衡之间存在权衡。我们还进行了大量的实验来评估我们的随机模型并讨论相对于确定性模型的实际影响。