Estimating the optimal rotation age of Pinus nigra in the Spanish Iberian System applying discrete optimal control

Ignacio Lopez, Sigfredo Ortuño, Ángel Julián Martín, Carmen Fullana


This study proposes a model based on discrete optimal control for estimating the optimal rotation age of Pinus nigra in the Spanish Iberian System. The model was constructed using the NPV (alternately LEV) of forest management as objective function and a model of stand evolution represented by a finite difference equation. The optimal rotation ages obtained corresponding to the 2-4% discount rate interval were between 60 and 100 years for the NPV strategy (50 and 70 years for the LEV strategy). With regard to the optimal management schedule, the results have shown the need to intensify the harvesting at 40-60 years in order to maximize the production of posts in view of the high price they command on the market.


Pinus nigra; optimal rotation age; optimal harvesting schedule; discrete optimal control.

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Anderson F.J., 1976. Control theory and optimum timber rotation. Forest Science 22(3), 242-246.

Bhattacharyya R.N., Snyder D.N., Biswan B., 1989. The optimal forest rotation: some economic dimensions. Indian Economic Journal 37(2), 69-82.

Clark C.W., 1976. Mathematical bioeconomics: the optimal management of renewable resources. John Wiley and Sons, New York, USA.

Clarke H.R., Reed W.J., 2009. The tree cutting problem in a stochastic environment: the case of age-dependent growth. Technical Reports (Mathematics and Statistics). University of Victoria, British Columbia, Canada.

Díaz Balteiro L., 1997. Turno forestal económicamente óptimo: una revisión. Revista Española de Economía Agraria, pp. 181-224.

Faustman M., 1849. Calculation of the value which forest land and immature stands possess for forestry. Journal of Forest Economics 1(1), 7-44 (1995).

Front Line Systems, 2008. Solver Premium Platform. Incline Village, Nevada, USA. Web:

Gómez Loranca J.A., 1998. Modelo de crecimiento y producción para Pinus nigra Arn. en el Sistema Ibérico. Montes Revista de Ámbito Forestal 54, 5-18, Available online at: aspx?id=155

González-Olabarría J.R., Palahí M., Pukkala T., Trasobares A., 2008. Optimising the management of Pinus nigra Arn. stands under endogenous risk of fire in Catalonia. Invest Agrar: Sist Recur For 17(1), 10-17.

Grande M.A., García Abril A., Rodríguez Solano R. (eds), 2004. Gestión forestal sostenible de los pinares de Pinus nigra Arn. Alto Tajo, Serranía de Cuenca, Sierras de Cazorla y Segura. Madrid, Spain.

Haight R.G., 1985. A comparison of dynamic and static economic models of uneven-aged stand management. Forest Sci 31(4), 957-974.

Hartman R., 1976. The harvesting decision when a standing forest has value. Economic Inquiry 16: 52-58.

HM Treasury-United Kingdom, 2007. The Green Book – Appraisal and Evaluation in Central Government.London, United Kingdom. Available online at:

IASB, 2004. International Accounting Standard 41, Agriculture. International Accounting Standards Board (IASB), «International Financial Reporting Standards». 2004.

Kangas A., Kangas J., Kurttila M., 2008. Decision support for forest management. Springer Science.

Koskella E., Ollikanen M., 2001. Forest taxation and rotation age under private amenity valuation: new results. Journal of Environmental Economics and Management 42(3), 374-384.

Kronrad G.D., Huang C.-H., 2002. Financially optimal thinning and final harvest schedules for loblolly pine plantations on nonindustrial private forestland in east Texas. Southern Journal of Applied Forestry 26(1), 13-17.

López I., Ortuño S., García F., Fullana C. Are the economically optimal harvesting strategies of unevenaged Pinus nigra stands always sustainable and stabilizing? (Under review by the Canadian Journal of Forest Research).

MAPA (Ministerio De Medio Ambiente Y Medio Rural Y Marino), 2008. Boletín Mensual de Estadística 1994-2008.

MAPLE Version 13.0, Maplesoft, Ontario, Canada, 2009.

Montero G., Rojo A., Alía R., 1992. Determinación del turno de Pinus sylvestris L. en el Sistema Central. Revista Montes 29, 42-47.

Newman D., 1988. The optimal forest rotation: a discussion and annotated bibliography. Department of Agriculture, Forest Service, USA.

Ohlin B., 1995. Concerning the question of the rotation period in forestry. Journal of Forest Economics 1, 89-114.

Palahi M., Pukkala T., 2003. Optimising the management of Scots Pine (Pinus sylvestris L.) stands in Spain based on individual-tree models. Annals Forest Science 60, 105-114.

Plantinga A.J., 1998. The optimal timber rotation: an option value approach. Forest Science 44, 192-202.

Row C., Kaiser H.F., Sessions J., 1981. Discount rate for Long-Term Forest Service Investments. Journal of Forestry 79(6), 367-369, 376.

Sagl W., 1995. Bewertung in Forstbetrieben. Pareys Studientexte 80. Berlin, Oxford [a.o.]: Blackwell Verlag.

Samuelson P., 1976. Economics of forestry in an evolving society. Economic Inquiry 14, 466-492.

Schütz J.-P.H., 1997. Sylviculture 2. La gestion des forêts irrégulières et melangées. Presses Polytechniques et Universitaires Romandes, Lausanne, Switzerland.

Sethi S.P, Thompson G.L., 2000. Optimal control theory: applications to management science and economics, 2nd ed. Kluwer Academic Publishers Group, Dordrecht, The Netherlands.

Siegel W., Hoover W., Haney H., Liu K., 1995. Forest owners' guide to the federal income tax. United States Department of Agriculture, Forest Service, Agriculture Handbook No. 708.

Sohngen B., Sedjo R., 2005. Impacts of climate change on forest product markets: implications for North American producers. The Forestry Chronicle 81(5), 669-674.

Synder D.L., Bhattacharyya R.N., 1990. A more general dynamic economic model of the optimal rotation of multiple-use forests. Journal of Environmental Economics and Management 18(2), 168-175.

Tahvonen O., Seppo S., Kuuluvainen J., 1998. Forest rotation periods and land value under borrowing constraint. Finnish Forest research Institute, Research Papers, 706.

Tahvonen O., 2004. Optimal harvesting of forest age classes: a survey of some recent results. Mathematical Population Studies 11, 205-232.

Termansen M., 2007. Economies of scale and the optimality of rotational dynamics in forestry. Environmental and Resource Economics 37, 643-659.

Tiscar P.A., 2004. Estructura, regeneración y crecimiento del Pinus nigra en el área de la reserva Navahonda-Guadahornillos (Sierra de Cazorla, Jaén). Tesis doctoral. ETSI Montes, Madrid, Spain. PMid:15372930

Tiscar P.A., 2007. Dinámica de regeneración de Pinus nigra Subs. Salzmannii al sur de su área de distribución: etapas, procesos y factores implicados. Invest Agrar: Sist Recurs For 16(2), 124-135.

Trasobares A., Pukkala T., 2004. Optimising the management of uneven-aged Pinus sylvestris L. and Pinus nigra Arn. Mixed stands in Catalonia, north-east Spain. Annals of Forest Science 61, 747-758.

DOI: 10.5424/fs/2010193-8560