Optimal shade location for urban environments

In this paper we develop a model for determining the optimal location of shading entities in urban environments. Shading entities include various tree species and shade structures. Using a fine temporal and spatial grid, the model maximizes customer comfort subject to a budget constraint. The model considers solar path, existing building and shade structures, orientation and boundaries of the urban area, desired area usage patterns, the set of shading entity types available along with their cost and coverage properties, and the available budget. Construction heuristics and exact solution approaches are compared for obtaining solutions. Downtown Phoenix serves as a case study to evaluate the model.