Finding the efficient frontier of a bi-criteria, spatially explicit, harvest scheduling problem

This article evaluates the performance of five traditional methods and one new method of generating the efficient frontier for a bi-criteria, spatially explicit harvest scheduling problem. The problem is to find all possible efficient solutions, thus defining the trade-offs between two objectives: (1) maximizing the net present value of the forest and (2) maximizing the minimum area over the planning horizon in large, mature forest patches. The methods for generating the efficient frontier were tested using a hypothetical forest consisting of 50 stands. The methods were compared based on the number of efficient solutions each method can identify and on how quickly the solutions were identified. The potential to generalize these algorithms to 3- or n-criteria cases is also assessed. Three of the traditional approaches, the e- constraining; the triangles method, the decomposition algorithm based on the Tchebycheff metric; and the new, proposed method are capable of generating all or most of the efficient solutions. However, the triangles and the new method far outperformed the other approaches in terms of solution time. The new method, called alpha–delta, appears to be the simplest to generalize to the tri-criteria case.