Convex Land Acquisition with Zero-One Programming

The land-acquisition problem involves selecting multiple discrete parcels to be acquired for a particular land use. In previous models, typical selection criteria have been land cost, land area, and spatial attributes such as contiguity and compactness. Here I introduce a new spatial attribute, convexity. I develop a way to approximate convex shapes in continuous space with ‘cellularly convex’ shapes composed of grid cells. A zero-one programming model is formulated for finding minimum-cost cellularly convex regions of specified area. Computational experience with 144-cell and 1024-cell demonstration problems is reported, and results and extensions are discussed.