Natural Hazards

, Volume 72, Issue 2, pp 375–387 | Cite as

The optimal rotation of a flammable forest stand when both carbon sequestration and timber are valued: a multi-criteria approach

  • Luis Diaz-BalteiroEmail author
  • David L. Martell
  • Carlos Romero
  • Andrés Weintraub
Original Paper


This paper proposes a multi-criteria approach that accounts for the risk of fire when determining the optimal rotation of a forest stand that is being managed for both timber production and carbon sequestration purposes. The multi-criteria framework uses in a combined way, multi-objective optimization and compromise programming methods. The proposed approach is computationally simple and allows for the quantification of conflicts between the criteria considered through the elicitation of the corresponding Pareto frontiers. Once the best portion or compromise sets of the Pareto frontiers are determined, then some indications of the increase in social welfare due to a potential reduction in the risk of fire are obtained. We illustrate the use of our methodology by applying it to an example that has previously been investigated in the forestry literature. Finally, some potential policy implications derived from the results obtained are highlighted.


Carbon capture Compromise programming Forestry Multiple criteria decision making Fire risk Pareto frontiers 



A preliminary version of this paper was presented at the Workshop “Novas Tecnologias em Gestao Florestal Sustentable. A Gestão do Risco de Incendio e a Gestão da Cadeia de Valor (October 2010, Lisbon, Portugal).” The work of Luis Diaz-Balteiro and Carlos Romero was funded by the Autonomous Community of Madrid under projects Q100705066 and QM100705026 and by the Spanish Ministry of Education and Science under project AGL2011-25825. David Martell’s contribution was supported by the Natural Sciences and Engineering Research Council of Canada. Andrés Weintraub was supported by grants from Milenium Institute Complex Engineering Systems and Fondecyt 1100265. Partial support for this research was provided by ForEAdapt project and funded by the European Union Seventh Framework Programme (FP7-PEOPLE-2010-IRSES) under grant agreement no PIRSES-GA-763 2010-269257. Thanks are also given to the referees for their useful comments.


  1. Amacher GS, Malik AS, Haight RG (2005) Not getting burned: the importance of fire prevention in forest management. Land Econ 81:284–302Google Scholar
  2. Ballestero E, Romero C (1991) A theorem connecting utility function optimization and compromise programming. Oper Res Lett 10:421–427. doi: 10.1016/0167-6377(91)90045-Q CrossRefGoogle Scholar
  3. Bussoni Guitart A, Estraviz Rodriguez LC (2010) Private valuation of carbon sequestration in forest plantations. Ecol Econ 69:451–458. doi: 10.1016/j.ecolecon.2009.10.005 CrossRefGoogle Scholar
  4. Daigneault AJ, Miranda MJ, Sohngen B (2010) Optimal forest management with carbon sequestration credits and endogenous fire risk. Land Econ 86:155–172Google Scholar
  5. Diaz-Balteiro L, Romero C (2008) Making forestry decisions with multiple criteria: a review and an assessment. For Ecol Manag 255:3222–3241. doi: 10.1016/j.foreco.2008.01.038 CrossRefGoogle Scholar
  6. Englin J, Boxall P, Hauer G (2000) An empirical examination of optimal rotations in a multiple-use forest in the presence of fire risk. J Agr Resour Econ 25:14–27Google Scholar
  7. Faustmann M (1849) Gerechnung des Werthes welchen Waldboden sowie noch nicht haubare Holzbestänce für die Waldwirtschaft besitzen. Allgemeine Forst und Jagd-Zeitung 25:441–455. Also included in: Faustmann M (1995) Calculation of the value which forest land and immature stands possess for forestry. J Forest Econ 1:7–44Google Scholar
  8. Hartman R (1976) The harvesting decision when a standing forest has value. Econ Inq 14:51–58. doi: 10.1111/j.1465-7295.1976.tb00377.x CrossRefGoogle Scholar
  9. Kuboyama H, Oka H (2000) Climate risks and age-related damage probabilities—effects on the economically optimal rotation length for forest stand management in Japan. Silva Fenn 34(2):155–166Google Scholar
  10. LINGO (2007) LINGO the modeling language and optimizer. LINDO Systems Inc., Chicago, ILGoogle Scholar
  11. Martell DL (1980) The optimal rotation of a flammable forest stand. Can J For Res 10:30–34CrossRefGoogle Scholar
  12. Neher PA (1990) Natural resource economics—conservation and exploitation. Cambridge University Press, CambridgeGoogle Scholar
  13. Pasalodos-Tato M, Pukkala T, Rigueiro-Rodríguez A, Fernández-Núñez E, Mosquera-Losada MR (2009) Optimal management of Pinus radiata silvopastoral systems established on abandoned agricultural land in Galicia (north-western Spain). Silva Fenn 43:831–845CrossRefGoogle Scholar
  14. Reed WJ (1984) The effects of the risk of fire on the optimal rotation of a forest. J Environ Econ Manag 11:180–190. doi: 10.1016/0095-0696(84)90016-0 CrossRefGoogle Scholar
  15. Reed WJ (1987) Protecting a forest against fire: optimal protection patterns and harvest policies. Nat Resour Model 2:23–53Google Scholar
  16. Romero C, Rehman T (2003) Multiple criteria analysis for agricultural decisions. Elsevier, AmsterdamGoogle Scholar
  17. Romero C, Ríos V, Diaz-Balteiro L (1998) Optimal forest rotation age when carbon captured is considered: theory and applications. J Oper Res Soc 49:121–131. doi: 10.1057/palgrave.jors.2600497 CrossRefGoogle Scholar
  18. Routledge RD (1980) The effect of potential catastrophic mortality and other unpredictable events on optimal forest rotation policy. For Sci 26:389–399Google Scholar
  19. Stollery KR (2005) Climate change and optimal rotation in a flammable forest. Nat Resour Model 18:91–112. doi: 10.1111/j.1939-7445.2005.tb00150.x CrossRefGoogle Scholar
  20. Teeter L, Dyer AA (1986) A multiattribute utility model for incorporating risk in fire management planning. For Sci 32:1032–1048Google Scholar
  21. Van Kooten GC, Binkley CS, Delcourt G (1995) Effect of carbon taxes and subsidies on optimal forest rotation age and supply of carbon services. Am J Agric Econ 77:365–374CrossRefGoogle Scholar
  22. Yu PL (1973) A class of solutions for group decision problems. Manag Sci 19:936–946. doi: 10.1287/mnsc.19.8.936 CrossRefGoogle Scholar
  23. Zeleny M (1974) A concept of compromise solutions and the method of the displaced ideal. Comput Oper Res 1:479–496. doi: 10.1016/0305-0548(74)90064-1 CrossRefGoogle Scholar
  24. Zeleny M (1982) Multiple criteria decision making. McGraw-Hill, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Luis Diaz-Balteiro
    • 1
    Email author
  • David L. Martell
    • 2
  • Carlos Romero
    • 1
  • Andrés Weintraub
    • 3
  1. 1.Department of Forest Economics and Management, Forestry SchoolTechnical University of MadridMadridSpain
  2. 2.Faculty of ForestryUniversity of TorontoTorontoCanada
  3. 3.Department of Industrial EngineeringUniversity of ChileSantiago de ChileChile

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