Mathematical programming approaches for land use planning that limits urban sprawl

Sprawl has a detrimental effect on quality of life and the environment. For example, it increases our dependence on vehicles for daily tasks. This leads to increased vehicular pollution. It also increases traffic, which results in people spending more time on the road. With dwindling resources and increasing population, it becomes necessary that we manage sprawl. Ewing et al. defined factors to measure sprawl in the present urban structure. The measures are divided into four broad categories, which are density factors, mixed use factors, streets factor, and centers factors. These measures address various aspects that contribute to sprawl. For example, in streets factors, the local street density affects sprawl. A balance between street density and the size of the land plots would determine the smoothness of traffic and the population density. These measures are then adapted for use in future planning of metro areas.;In this research, we develop a mixed integer linear programming (MILP) model to optimize land usage subject to sprawl constraints, which are based upon the adapted sprawl measures. For a typical data-set of a city of moderate size, the MILP becomes too large for a commercial solver. In addition, all of the measures given by Ewing et al. are incorporated in the MILP as constraints as opposed to an objective function.;The MILP has a special structure; that is the constraints containing quadratic variables in the MILP that can be isolated from the rest of the model. We use Benders decomposition to attempt to solve it. Due to the enormity of the problem and the fact that the planner might be unaware of the initial bounds for the various constraints, we create a scatter plot between the total land use suitability and the violations for land mixed use bounds under varying bounds on certain constraints.;An orthogonal design of three factors is used to build the scatter plot. Land use objective value and land mixed use violations form the X-axis and Y-axis on the scatter plot. The factors used in orthogonal design are gross population density, density gradient between the central census tract and the census tracts around it, and the lower bound on the commercial activity, which determines the Central Business District (CBD). Since the normal mathematical model is intractable, the goal is to provide the planner with a tool to determine what would be a suitable land use assignment. The planner can use this tool to analyze how various factors affect the land use objective value and the violations on the land mixed use constraint.