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

这笔赠款为开发算法提供资金，这些算法评估在机队规模、负载可获得性或码头容量等模型参数被修改时，机队管理模型的性能衡量标准将如何变化。车队管理模型的主要目标是做出车辆与货物的分配和车辆重新定位的决策，以便优化诸如利润、空头里程或服务负荷数量等性能指标。然而，这些模型通常忽视的一个问题是，所讨论的业绩衡量标准将如何随着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，他们的利润将增加多少。铁路公司希望估计满足随机托运人需求所需的最低火车车厢数量。我们将利用近似动态规划、无穷小扰动分析和组合优化的思想来建立这些“敏感度分析”算法，这些算法随后将被用来做出战术决策，如船队规模、定价和码头容量规划。无论是大型货运公司，还是大型货运公司，都使用独立的和不协调的模型来进行战术和运营决策。这项研究将帮助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，这些方法涉及到“物理”调整参数和重新运行模型。所开发的灵敏度分析算法可以快速地向决策者指出关键参数，从而提高决策的质量和效率。调查结果还将被用来为互联网上的货运匹配网站制定竞价政策，发货人在那里发布货物，以从承运人那里获得价格报价。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.