Optimal school locations: controlling excess travel and assignment switches in a spatially dynamic urban growth context.

Urban dynamics including both sprawl and infill poses serious long-term planning challenges for public facilities. In those situations, it is deemed vital to expand (or contract) an existing network of public facilities to meet anticipated changes in the level of demand. We present a dynamic capacitated median model applied to a school network that minimizes excess travel and reduces switches in school assignments to a minimum. In addition, our model is flexible in (1) restricting schools recently open to close, and (2) to modify school capacities to accommodate demand fluctuations over the time horizon considered. We test the robustness of our model under different weighting schemes and growth scenarios. The applicability of our model is illustrated on a large school district (Charlotte-Mecklenburg, North Carolina). Solutions of the proposed model are highly sensitive to the geographic distribution of the demand: the addition of new schools is critical in peripheries where demand may grow rapidly, while modular equipment is necessary when demand exceeds permanent school capacity, especially in the inner sections of the city where schools cannot be closed due to age restrictions. The proposed formulation of the model and the simulations for several urban growth scenarios provide a basis for decision makers and urban planners seeking to improve the long term provision and efficiency of public services.