The random-utility-based multiregional input–output model: solution existence and uniqueness

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The random-utility-based multiregional input–output model: solution existence and uniqueness

Zhao, Yong / Kockelman, Kara M.

AbstractA number of operational land use-transportation models make use of spatial input–output (SIO) models, some of which are based on random-utility theory. The random-utility-based multiregional input–output (RUBMRIO) model has been solved in practice by iteratively applying a set of equations. Each of the model equations describes relationships among key model variables. This paper examines the existence and uniqueness of the RUBMRIO solution, which represents the spatial allocation of productive activities and commodity flows. Formulating the set of equations as a fixed-point problem illuminates these two key properties, and provides a general solution algorithm. Several numerical examples illustrate the solution uniqueness and algorithm convergence. These results are valuable for efficient application of such models to large-scale problems. By proving that a unique solution does exist and offering an algorithm that is guaranteed to converge, this work adds valuable support to the growing popularity of this integrated transportation-land use modeling framework.