An integer programming model for a forest harvest problem in Pinus pinaster stands

  • T. Fidalgo Fonseca Department of Forest Science and Landscape Arquitecture, University of Tras-os-Montes e Alto Douro, 5001-801 Vila Real.
  • A. Cerveira Department of Mathematics, University of Tras-os-Montes e Alto Douro, 5001-801 Vila Real. Centro de Investigação Operacional (CIO), University of Lisbon, Lisboa.
  • A. Mota Associação Florestal de Ribeira de Pena, Ribeira de Pena.


The study addresses the special case of a management plan for maritime pine (Pinus pinaster Ait.) in common lands. The study area refers to 4,432 ha of maritime pine stands in North Portugal (Perímetro Florestal do Barroso in the county of Ribeira de Pena), distributed among five common lands called baldio areas. Those lands are co-managed by the Official Forest Services and the local communities, essentially for timber production, using empirical guidance. As the current procedure does not guarantee the best thinning and clear-cutting scheduling, it was considered important to develop “easy-to-use” models, supported by optimization techniques, to be employed by the forest managers in the harvest planning of these communitarian forests. Planning of the thinning and clear-cutting operations involved certain conditions, such as: (1) the optimal age for harvesting; (2) the maximum stand density permitted; (3) the minimum volume to be cut; (4) the guarantee of incomes for each of the five baldios in at least a two year period; (5) balanced incomes during the length of the projection period. In order to evaluate the sustainability of the wood resources, a set of constraints lower bounding the average ending age was additionally tested. The problem was formulated as an integer linear programming model where the incomes from thinning and clear-cutting are maximized while considering the constraints mentioned above. Five major scenarios were simulated. The simplest one allows for silvicultural constraints only, whereas the other four consider these constraints besides different management options. Two of them introduce joint management of all common areas with or without constraints addressing balanced distribution of incomes during the plan horizon, whilst the other two consider the same options but for individual management of the baldios. The proposed model is easy to apply, providing immediate advantages for short and mid-term planning periods compared to the empirical methods of harvest planning. Results showed that maximization of production is reached when there are silvicultural restrictions only and when forest management units are regarded as a joint undertaking. The individualized management with a balanced distribution of incomes is an interesting option as it does not drastically reduce the optimal solution while assuring benefits at least every two years.


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How to Cite
FonsecaT. F., CerveiraA., & MotaA. (2012). An integer programming model for a forest harvest problem in Pinus pinaster stands. Forest Systems, 21(2), 272-283.
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