An integer programming model for a forest harvest problem in Pinus pinaster stands
AbstractThe 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.
Bredström D, Jönsson P, Rönnqvist M. 2010. Annual planning of harvesting resources in the forest industry. Intl Trans in Op Res 17, 155-177.
Bravo F, Bravo-Oviedo A, Dias-Balteiro L. 2008. Carbon sequestration in Spanish Mediterranean forests under two management alternatives: a modeling approach. Eur J Forest Res 127, 225-234.
Constantino M, Martins I, Borges JG., 2008. A new mixedinteger programming model for harvest scheduling subject to maximum area restrictions. Operations Research 56, 542–551.
Díaz-Balteiro L, Romero C. 2008. Making forestry decisions with multiple criteria: a review and an assessment. For Ecol Manage 255, 3222-3241.
Epstein R, Karlsson J, Rönnqvist M, Weintraub A. 2007. Harvest operational models in Forestry. In: Handbook of operations research in natural resources (Weintraub A, Romero C, Bjorndal T, Epstein R., eds). Springer International Series in Operations Research & Management Science, 99, NY, USA. pp. 365-377.
Fonseca TF. 2004. Modelação do crescimento, mortalidade e distribuição diamétrica, do pinhal bravo no Vale do Tâmega. Doctoral thesis. University of Trás-os-Montes e Alto Douro, Vila Real.
Fonseca TF, CP Marques, BR Parresol. 2009. Describing maritime pine diameter distributions with Johnson’s SB distribution using a new all-parameter recovery approach. For Sci 55, 367-373.
Johnson NL. 1949. Systems of frequency curves generated by methods of translation. Biometrika 36, 149 –176.
Luis JS, Fonseca TF. 2004. The allometric model in the stand density management of Pinus pinaster in Portugal. Ann For Sci 61, 1-8.
Marques CP. 1991. Evaluating site quality of even-aged maritime pine stands in northern Portugal using direct and indirect methods. For Ecol Manage 41, 193-204.
Martell DL, Gunn EA, Weintraub A. 1998. Forest management challenges for operational researchers. Eur J Oper Res 104, 1-17.
Moreira AM, Fonseca TF. 2002. Tabela de produção para o Pinhal do Vale do Tâmega. Silva Lusitana 10, 63-71.
Murray AT. 1999. Spatial restrictions in harvest scheduling. For Sci 45, 1-8.
Nemhauser GL, Wolsey LA, 1988. Integer and Combinatorial Optimization, John Wiley & Sons, New York. 763 pp.
Parresol BR, TF Fonseca, CP Marques. 2010 Numerical details and SAS programs for parameter recovery of the SB distribution. Gen Tech Rep SRS-122. USDA, USA, 27 pp.
Weintraub A. 2007. Integer programming in forestry. Ann Oper Res 149, 209-216.
Weintraub A, Church RL, Murray AT, Guignard M. 2000. Forest management models and combinatorial algorithms: analysis of state of the art. Ann Oper Res 96, 271-285.
Weintraub A, Romero C, Bjorndal T, Epstein R. 2007. Handbook of operations research in natural resources. Springer International Series in Operations Research & Management Science, NY, USA, 99. 640 pp.
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