Nonlinear inverse optimization and link-based freight assignment of commodity and cyclic vehicle flows
The contents of this work supersedes the conference proceedings:
Chow, J.Y.J., Ritchie, S.G., 2012. A freight transshipment network model for forecasting commodity and commercial vehicle flows. Proceedings of the Transportation Research Board 91st Annual Meeting, Washington DC.
An inverse nonlinear optimization approach is developed to solve a new parameter estimation problem class where demand and output flows are given or observed in a congested network. Unlike earlier work in the inverse optimization area, the problem is nonlinear and formulated with Karush-Kuhn-Tucker conditions. It is shown to be solvable using classical nonlinear optimization methods. This approach is used to systematically calibrate a new link-based variant of the STAN model which assigns commodity flows to cyclic vehicles, where freight facility parameters are typically difficult to observe. Commodities flow from origin to destination but vehicle path information is given up in favor of tracking cyclic patterns for endogenous empty hauls. The models are first tested on a small network with up to 54 transshipment activities. The assignment model is shown to be sensitive to supply side changes on links and transshipment facilities or to fuel cost changes, while the inverse model is tested for parameter recovery and similarity in scenario sensitivity. The calibration method is then applied to California with 1,058 transfer links with 2007 data, under the circumstance where empty haul patterns and some truck patterns are unavailable. The assignment model is validated with 2010 data. The appendix includes a first application of the inverse nonlinear programming method to the inverse traffic assignment problem to demonstrate its value in other potential fields.