Applying mathematical programming to reserve selection

During the last 10–15 years heuristic methods have been developed for problems in optimal reserve selection. Unfortunately, there is no guarantee that heuristics will find optimal solutions. In recognizing this limitation, analysts have formulated reserve selection problems as set covering problems, for which matrix reduction and integer (0/1) programming can be used to find optimal solutions. In this paper we restate the set covering formulation and review solution techniques. A new 0/1 programming model, which is a generalization of the set covering model, is then presented and applied to a hypothetical reserve selection problem. Objectives of minimizing the number of sites selected and maximizing the number of species represented are addressed. Solutions which characterize the tradeoffs between these objectives provide a rich set of information for planners and decision makers. Applications of mathematical programming to related problems in land use planning and forestry are also discussed.