Forest management optimisation models when carbon captured is considered: a goal programming approach Luis Dı ´az-Balteiro a,1 , Carlos Romero b,* a University of Valladolid, Escuela Te ´cnica Superior de Ingenierı ´as Agrarias, A ´ rea de Economı ´a Agraria y Forestal, Avenida de Madrid, 57, 34071 Palencia, Spain b Technical University of Madrid, Departamento de Economı ´a y Gestio ´n Forestal, E.T.S. Ingenieros de Montes, Avenida Complutense s/n, 28040 Madrid, Spain Received 6 April 2001; received in revised form 20 December 2001; accepted 18 February 2002 Abstract Nowadays, the need to incorporate the carbon captured by the forest ecosystems as a complementary objective into the corresponding management optimisation models is accepted. This paper proposes an approach, based upon goal programming that let us undertake this task in a very efficient manner. The models derived from the proposed approach are simple in computational terms and the corresponding solutions can be interpreted in utility terms. All the theoretical aspects of this paper are applied to the Spanish forest ‘‘Pinar de Navafrı ´a’’ located in the mountains of ‘‘Sierra de Guadarrama’’ near Madrid. The results reveal the marked difficulty in obtaining from an economic and forestry viewpoint good harvest schedules compatible with high levels of carbon captured. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Forest management; Goal programming; Carbon sequestration 1. Introduction In the last few years there has been an increasing tendency to consider forest ecosystems as possible sinks of carbon dioxide (CO 2 ). In this way, an attempt is done to reduce the dramatic increase of global CO 2 emissions in the industrialised countries and conse- quently to contribute to the mitigation of climate warming. In fact, although water vapour is contribut- ing more to the greenhouse effect, CO 2 is most important among antropogenic gases (Lewis et al., 1996; van Kooten et al., 1999). In this context, the methods usually used in forest management needs a certain kind of adaptation to the new context. Thus, the classic methods to determine optimal forest rotation age are not straightforwardly applicable to a context of carbon captured. In fact, we are now dealing with two outputs: timber produced and carbon stored in the timber biomass. In this direction some efforts have been undertaken to devise methods able to incorporate the capture of CO 2 into classic methods based upon Faustmann formula (Hoen, 1994; van Kooten et al., 1995; Romero et al., 1998). Another direction that the new situation requires to explore consists in the formulation of forest manage- ment optimisation models that explicitly incorporate Forest Ecology and Management 174 (2003) 447–457 * Corresponding author. Tel.: þ34-91-336-63-93; fax: þ34-91-543-95-57. E-mail addresses: ldbalteiro@montes.upm.es (L. Dı ´az-Balteiro), auggiegp@montes.upm.es (C. Romero). 1 Tel.: þ34-91-3367122; fax: þ34-91-5439557. 0378-1127/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII:S0378-1127(02)00075-0