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

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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.