Abstract
This work presents a nonlinear goal programming model with binary variables used to plan the management of a tree plantation, taking economic and environmental objectives into account. The aims are to stay within the limits of a given harvesting volume, limit the age of basic units targeted for clearcutting, obtain a forest with a balanced age distribution, and surpass the minimum net present value set at each planning period. This has to be achieved bearing in mind technical restrictions regarding treatments, and spatial adjacency constraints that limit the maximum adjacent surface area to which clearcutting can be applied. The outcome is a highly complex problem that is solved by applying a metaheuristic method based on Scatter Search. The proposed model has been validated by applying it to a Cuban plantation located in the region of Pinar del Río.
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References
Bobko, A., & Aldana, E. (1981). Ordenación de montes. Centro Universitario de Pinar del Río, Cuba.
Borges, J. G., Hoganson, H. M., & Falcão, A. O. (2002). Heuristics in multi-objective forest planning. In T. Pukkala (Ed.), Multi-objective forest planning. Dordrecht: Kluwer Academic.
Buongiorno, J., & Gilless, J. K. (2003). Decision methods for forest resource management. San Diego: Academic Press.
Caballero, R., Rey, L., & Ruiz, F. (1998). Lexicographic improvement of the target values in convex goal programming. European Journal of Operational Research, 107, 644–655.
Caro, F., Constantino, M., Martins, I., & Weintraub, A. (2003). A 2-opt tabu search procedure for the multiperiod forest harvesting problem with adjacency, green-up, old growth, and even flow constraints. Forest Science, 49, 738–751.
Coello, C., Van Veldhuizen, D. A., & Lamont, G. B. (2007). Evolutionary algorithms for solving multi-objective problems (2nd edn.). Dordrecht: Kluwer Academic.
Díaz-Balteiro, L., & Romero, C. (1998). Modelling timber harvest scheduling problems with multiple criteria: an application in Spain. Forest Science, 44(1), 47–57.
Diaz-Balteiro, L., & Romero, C. (2007). Multiple criteria decision-making in forest planning: recent results and current challenges. In A. Weintraub, C. Romero, & T. Bjø(Eds.), International series in operations research & management science: Vol. 99. Handbook of operations research in natural resources. New York: Springer.
Diaz-Balteiro, L., & Romero, C. (2008). Making forestry decisions with multiple criteria: A review and an assessment. Forest Ecology and Management, 44(1), 47–57.
Erhgott, M., & Gandibleux, X. (2004). Approximate solution methods for multiobjective combinatorial optimization. Top, 12(1), 1–88.
Falcão, A., & Borges, J. (2002). Combining random and systematic search heuristic procedures for solving spatially constrained forest management scheduling models. Forest Science, 48, 608–621.
Field, D. B. (1973). Goal programming for forest management. Forest Science, 19, 125–135.
Glover, F., Laguna, M., & Martí, R. (2000). Fundamentals of Scatter Search and Path Relinking. Control and Cybernetics, 29(3), 653–684.
Gómez, T., Hernández, M., León, M. A., & Caballero, R. (2006). A forest planning problem solved via a linear fractional goal programming model. Forest Ecology and Management, 227, 79–88.
Goycoolea, M., Murray, A. T., Barahona, F., Epstein, R., & Weintraub, A. (2005). Harvest scheduling subject to maximum area restrictions: exploring exact approaches. Operational Research, 53, 490–500.
Jones, D. F., Mirrazavi, S. K., & Tamiz, M. (2002). Multiobjective metaheuristics: an overview of the current state of the art. European Journal of Operational Research, 137, 1–9.
Liu, G., Han, S., Zhao, X., Nelson, J. D., Wang, H., & Wang, W. (2006). Optimisation algorithms for spatially constrained forest planning. Ecological Modelling, 194, 421–428.
McDill, M. E., Rebain, S. A., & Braze, J. (2002). Harvest scheduling with area-based adjacency constraints. Forest Science, 48, 631–642.
Mendoza, G. A., & Martins, H. (2006). Multi-criteria decision analysis in natural resource management: a critical review of methods and new modelling paradigms. Forest Ecology and Management, 230, 1–22.
Molina, J., Laguna, M., Marti, R., & Caballero, R. (2007). SSPMO: A scatter tabu search procedure for non-linear multiobjective optimization. JOC, 19(1), 91–100.
Murray, A. T., & Weintraub, A. (2002). Scale and unit specification influences in harvest scheduling with maximum area restrictions. Forest Science, 48, 779–789.
Murray, A. T. (1999). Spatial restrictions in harvest scheduling. Forest Science, 45, 1–8.
Pukkala, T. (2002). Multi-objective forest planning. Dordrecht: Kluwer Academic.
Pukkala, T., & Heinonen, T. (2006). Optimizing heuristic search in forest planning. Nonlinear Analysis, 7, 1284–1297.
Romero, C. (1991). Handbook of critical issues in goal programming. Elmsford: Pergamon.
Weintraub, A., & Murray, A. T. (2006). Review of combinatorial problems induced by spatial forest harvesting planning. Discrete Applied Mathematics, 154, 867–879.
Weintraub, A., Romero, C., Bjørndal, T., & Epstein, R. (Eds.) (2007). In International series in operations research & management science: Vol. 99. Handbook of operations research in natural resources. New York: Springer.
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Gómez, T., Hernández, M., Molina, J. et al. A multiobjective model for forest planning with adjacency constraints. Ann Oper Res 190, 75–92 (2011). https://doi.org/10.1007/s10479-009-0525-4
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DOI: https://doi.org/10.1007/s10479-009-0525-4