Environmental Modeling to Identify Compact Contiguous Activity Areas that Maintain Maximum Size Restrictions

The selection of areas for land use activity has long been of interest in environmental modeling. Such areas have been referred to as patches, blocks, districts and zones, representing activities like nature preserves, harvest operations, hazard mitigation, residential developments, industrial processing plants and storage facilities, among others. Many important spatial attributes of these areas are often necessary or desired, including compactness, contiguity and dispersion. This paper introduces a modeling approach to simultaneously address these goals. A linear integer model is structured to optimize total activity benefit along with compactness while ensuring contiguity and size restrictions among individual areas. Application results highlight environmental mitigation patches designed to reduce regional wildfire risk and vulnerability. Further, the role of perimeter as a surrogate for addressing compactness and consistency with alternative measures and metrics of compactness are considered.