A forest planning problem solved by a linear fractional goal programming model | Un problema de ordenación forestal resuelto mediante un modelo de metas fraccional lineal

Spanish; Castilian. En este trabajo se presenta un modelo de programación por metas fraccional lineal para planificar el aprovechamiento de una plantación en la isla de Cuba, de manera que se alcance una distribución equilibrada de la superficie por clase de edad. El principal propósito en el contexto cubano es ordenar el bosque, lo cual conlleva variar significativamente la composición actual por edades que es bastante irregular, en un turno de 25 años. Este deseo lo hemos formalizado mediante metas fraccionales que inciden en el aspecto dinámico del problema y aseguran el equilibrio de una forma paulatina y flexible. No obstante, el modelo propuesto trata de alcanzar esta ordenación sin olvidar los aspectos económico y ecológico de los bosques. Con objeto de contrastar su potencialidad, lo hemos aplicado a una plantación cubana perteneciente a la Empresa Forestal Integral Pinar del Río, obteniendo diversas soluciones que equilibran el bosque y respetan los objetivos ecológicos y económicos del centro decisor.

English. In this work, a linear fractional goal programming model is developed in order to plan the exploitation of a plantation of pure species with timber production purposes in the Cuban island. Cuban forests have been suffering an indiscriminate exploitation for many years. Consequently, great efforts are presently being devoted to regenerate these forests, and conservationists position are being considered, which causes that the forest masses are growing older. As a consequence, such forests have an unbalanced composition by ages. Therefore, the model that is presented in this work makes it possible to organize the forest during the planning horizon, making also economic and ecological objectives compatible with this organization. Given the complexity, as well as the multiplicity, of purposes and interests involved in this problem, a multicriteria approach has been used, and as the objectives have been turned into goals that have to be satisfied, a Goal Programming problem has been formulated in order to find the desired planning. As it has been just said, one of the main objectives in this model is to reach an age-balanced structure in the forest at the end of the planning horizon. To reach this end, some of the goals of the goal programming model are linear fractional functions that represent a natural way of modeling this wish of equilibrium because these fractional goals point out the centered in pure plantations of Pinus Caribaea, which a dynamic aspect of the problem. The study isre being used for wood production purposes. The model has been contrasted with data provided by the Integral Forest Enterprise of Pinar del Río (Cuba). Given that the linear fractional goal programming problem is not easy to solve, a brief theoretical study of the technique used in order to solve it is also presented in this paper. Once the resulting problem is solved, several solutions are obtained satisfying all the goals established in the model. All the solutions that satisfy the goals are different possibilities of planning the exploitation of the plantation, but it is ensured that all of them reach an homogeneous composition of the areas covered by the different age groups at the end of the horizon. Among all of these solutions, the Decision Maker has to select the one that he or she prefers, being in this case the one that achieves the greatest Net Present Value, that represents the economic objective of the Decision Maker. Finally we have to point out that the scheme presented in this paper is applicable to other plantations with timber production purposes.