Sensitivity Analysis of the Dynamic Fleet Management Problem with Applications in Fleet-Sizing, Pricing and Terminal Capacity Planning

这笔拨款为开发算法提供资金，用于评估当模型参数（如车队规模、负载可用性或终端容量）发生变化时，车队管理模型的性能指标将如何变化。车队管理模型的主要目标是做出车辆与负载的分配和车辆重新定位的决策，从而优化利润、滞车里程或服务负载数量等绩效指标。然而，这些模型通常忽略的一个问题是，所讨论的性能度量将如何响应某些模型参数的变化而变化。例如，货运公司感兴趣的是，如果他们在系统中引入额外的车辆，或者如果他们提供额外的负载，他们的利润会增加多少。铁路公司想要估算出满足随机托运人需求所需的最小轨道车辆数量。来自近似动态规划、无穷小摄动分析和组合优化的思想将用于构建这些“敏感性分析”算法，这些算法随后将用于制定战术决策，例如船队规模、定价和终端容量规划。总的来说，货运公司使用独立的、不协调的模型来进行战术和操作决策。这项研究将有助于他们更好地协调战术和作战决策。目前，敏感性分析是通过耗时的方法进行的，包括“物理”调整参数和重新运行模型。所开发的敏感性分析算法能够快速地为决策者指出关键参数，从而提高决策质量和效率。调查结果还将用于为互联网上的货运匹配网站制定价格竞标政策，托运人在这些网站上发布他们的货物，以获得承运人的报价。最后，这项工作将有助于近似动态规划的一般理论和随机控制问题的灵敏度分析。

This grant provides funding for the development of algorithms that assess how the performance measures of a fleet management model would change, if a model parameter, such as fleet size, load availability or terminal capacity, were modified. The primary objective of the fleet management models is to make vehicle-to-load-assignment and vehicle-repositioning decisions, so that a performance measure, such as profit, deadhead miles or number of served loads, is optimized. However, a question that is commonly overlooked by these models is how the performance measure in question would change in response to changes in certain model parameters. For example, freight carriers are interested in how much their profits would increase if they introduce an additional vehicle into the system or if they serve an additional load. Railroad companies want to estimate the minimum number of railcars necessary to cover random shipper demands. Ideas from approximate dynamic programming, infinitesimal perturbation analysis and combinatorial optimization will be utilized to build these "sensitivity analysis" algorithms, which will subsequently be used to make tactical decisions, such as fleet-sizing, pricing and terminal-capacity planning.By and large, freight carriers use separate and uncoordinated models for their tactical and operational decisions. This research will help them to coordinate their tactical and operational decisions better. Currently, sensitivity analyses are carried out by time-consuming methods that involve "physically" adjusting the parameters and rerunning the models. The developed sensitivity analysis algorithms will quickly point out the critical parameters to the decision makers, and thereby, increase the decision quality and efficiency. Findings will also be used to build price-bidding policies for the freight-matching sites on the Internet, where the shippers post their loads to get price offers from the carriers. Finally, this work will contribute to the general theory of approximate dynamic programming and sensitivity analysis of stochastic control problems.