Optimal Regional Allocation of Future Population and Employment under Urban Boundary and Density Constraints: A Spatial Interaction Modeling Approach

Abstract

This paper develops an optimization modeling framework to select strategies of land development and population and employment densities for a growing metropolitan area. The modeling core involves a non-linear commuting model, which accounts for spatial structure variables and is empirically estimated by Tobit regression. This commuting model is then embedded into a non-linear optimization model that allocates increments in the population and employment (activities) to available land, while minimizing the total future commuting costs under various combinations of land expansion boundaries and population and employment densities. The resulting minimum cost surface is approximated via polynomial regression and combined with land development and congestion cost functions to derive the overall optimal strategy. These models are estimated and calibrated with data from the Census Transportation Planning Package (CTPP) and Auditor’s property database, and are applied to the Fredericksburg metropolitan area, Virginia. The results demonstrate that the optimal development densities are very sensitive to the congestion cost function. A land development strategy that allows for limited sprawl might be a smart policy to reduce both regional vehicle mile travel (VMT) and related congestion and pollution.