Compactness and Flow Minimization Requirements in Reforestation Initiatives: An Integer Programming (IP) Formulation

Identifying optimal sites on raster maps is a complex problem when the sites are larger than the cell size. Optimal sites involves a tradeoff between the intrinsic characteristics of individual cells and the spatial configuration of the cells. Although there are a number of techniques to solve the site allocation problem, those solutions do not consider spatial interactions between the cells forming the site. This paper presents an Integer Programming Formulation (IP) for allocating a predefined number of cells satisfying the following criteria: 1) minimize flow (water, sediment) reaching the outlet of a watershed, 2) maximize/minimize intrinsic characteristics of the cells, and 3) form a compact patch. Although the core structure of the IP formulation can be applied for different sorts of flow and intrinsic characteristics, it is targeted to a reforestation application. The proposed approach is applied to perform several experiments in two watersheds in South Dakota in the USA for searching a given number of best cells (1) minimizing sediment reaching the watershed outlet,(2) maximizing the environmental criteria, and (3) forming a compact patch. The results obtained with the IP formulation are in agreement with expert assessments of erosion levels, slopes and distances to the riverbeds.