The p-median problem (PMP) is one of the most applied location problems in urban and regional planning. As an NP-hard problem, the PMP remains challenging to solve optimally, especially for large-sized problems. A number of heuristics have been developed to obtain PMP solutions in a fast manner. Among the heuristics, the Teitz and Bart (TB) algorithm has been found effective for finding high-quality solutions. In this article, we present a spatial-knowledge-enhanced Teitz and Bart (STB) heuristic method for solving PMPs. The STB heuristic prioritizes candidate facility sites to be examined in the solution set based on the spatial distribution of demand and service provision.Tests based on a range of PMPs demonstrate the effectiveness of the STB heuristic. This new algorithm can be incorporated into current commercial GIS packages to solve a wide range of location-allocation problems.

BackgroundValley fever is a fungal infection occurring in desert regions of the U.S. and Central and South America. Environmental risk mapping for this disease is hampered by challenges with detection, case reporting, and diagnostics as well as challenges common to spatial data handling.Design and methods.Using 12,349 individual cases in Arizona from 2006 to 2009, we analyzed risk factors at both the individual and area levels.Results.Risk factors including elderly population, income status, soil organic carbon, and density of residential area were found to be positively associated with residence of Valley fever cases. A negative association was observed for distance to desert and pasture/hay land cover. The association between incidence and two land cover variables (shrub and cultivated crop lands) varied depending on the spatial scale of the analysis.ConclusionsThe consistence of age, income, population density, and proximity to natural areas supports that these are important predictors of Valley fever risk. However, the inconsistency of the land cover variables across scales highlights the importance of how scale is treated in risk mapping.Significance for public healthWith the increasing use of spatially explicit data in public health comes uncertainty related to spatial resolution, data compatibility at different scales, and appropriate model selection. Using soil-borne Valley fever, we quantify how risk mapping changes by scale and provide advice on how to assess and explore uncertainty within an analysis.

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Incorporating big data in urban planning has great potential for better modeling of urban dynamics and more efficiently allocating limited resources. However, big data may present new challenges for problem solutions. This research focuses on the p-median problem, one of the most widely used location models in urban and regional planning. Similar to many other location models, the p-median problem is non-deterministic polynomial-time hard (NP-hard), and solving large-sized p-median problems is difficult. This research proposes a high performance computing-based algorithm, random sampling and spatial voting, to solve large-sized p-median problems. Instead of solving a large p-median problem directly, a random sampling scheme is introduced to create smaller sub- p-median problems that can be solved in parallel efficiently. A spatial voting strategy is designed to evaluate the candidate facility sites for inclusion in obtaining the final problem solution. Tests with the Balanced Iterative Reducing and Clustering using Hierarchies (BIRCH) data set show that random sampling and spatial voting provides high-quality solutions and reduces computing time significantly. Tests also demonstrate the dynamic scalability of the algorithm; it can start with a small amount of computing resources and scale up and down flexibly depending on the availability of the computing resources.