Abstract
Forests are among the most sensitive systems in nature. This is attributed to the fact that, forests are directly affected by fluctuations in price of fossil fuels. Wood products and especially forest fuel products are accessible by anyone, without any prior processing. As forest fuel is a subsidy for fossil fuels (oil) for heating purposes, households turn to forest fuel especially in countries that are heavily impacted by economic recession. The over-exploitation of this natural resource leads the forest to abnormal situation and eventually to deforestation. The exhaust of the natural resource capital has negative impact not only on the local economy, where fuelwood market contributes especially in mountainous regions, but also on the environmental stability of ecosystems. In this paper, two multi-period Linear Programming models are proposed for management of coppice forests. The aim of these models is to maximize the Net Present Value, which is constructed as a function of the revenue from trading fuelwood (price times the logged quantities) minus the transportation cost from the forest to merchants. Two aspects have been investigated in this paper; sustainability and maximum yield. The sustainability aspect is guaranteed by imposing constraints for equalization of non-logged areas at the end of the planning horizon. With maximum yield aspect, the maximization of the logged quantities (and therefore the maximization of the objective function) is guaranteed. The model is solved for various scenarios regarding transportation cost. The applicability of the model is demonstrated through a real-world case study of an even coppice forest in Achladochori–Aggistro–Sidirokastro. The proposed model is easy to be implemented, since it uses only the initial conditions of the forest (area) and can be applied to even and uneven aged forests.
Similar content being viewed by others
References
Adame, P., Del Rìo, M., & Cañellas, I. (2010). Ingrowth model for pyrenean oak stands in north-western Spain using continuous forest inventory data. European Journal of Forest Research, 129(4), 669–678.
Arabatzis, G., Petridis, K., Galatsidas, S., & Ioannou, K. (2013). A demand scenario based fuelwood supply chain: A conceptual model. Renewable and Sustainable Energy Reviews, 25, 687–697.
Bussieck, M. R., & Meeraus, A. (2007). Algebraic modeling for IP and MIP (gams). Annals of Operations Research, 149(1), 49–56.
Carlsson, D., & Rönnqvist, M. (2005). Supply chain management in forestry—case studies at Södra Cell AB. European Journal of Operational Research, 163(3), 589–616.
Delgado-Matas, C., & Pukkala, T. (2014). Optimisation of the traditional land-use system in the Angolan highlands using linear programming. International Journal of Sustainable Development & World Ecology, 21(2), 138–148.
Demirci, M., & Bettinger, P. (2015). Using mixed integer multi-objective goal programming for stand tending block designation: A case study from Turkey. Forest Policy and Economics, 55, 28–36.
Diaz-Balteiro, L., Bertomeu, M., & Bertomeu, M. (2009). Optimal harvest scheduling in Eucalyptus plantations: a case study in Galicia (Spain). Forest Policy and Economics, 11(8), 548–554.
Dreyfus, P. (2012). Joint simulation of stand dynamics and landscape evolution using a tree-level model for mixed uneven-aged forests. Annals of Forest Science, 69(2), 283–303.
Ekşioğlu, S. D., Acharya, A., Leightley, L. E., & Arora, S. (2009). Analyzing the design and management of biomass-to-biorefinery supply chain. Computers & Industrial Engineering, 57(4), 1342–1352.
Flisberg, P., Frisk, M., Rönnqvist, M., & Guajardo, M. (2015). Potential savings and cost allocations for forest fuel transportation in Sweden: A country-wide study. Energy, 85, 353–365.
Freppaz, D., Minciardi, R., Robba, M., Rovatti, M., Sacile, R., & Taramasso, A. (2004). Optimizing forest biomass exploitation for energy supply at a regional level. Biomass and Bioenergy, 26(1), 15–25.
Galatsidas, S., Petridis, K., Arabatzis, G., & Kondos, K. (2013). Forest production management and harvesting scheduling using dynamic Linear Programming (LP) models. Procedia Technology, 8, 349–354.
Garcia-Gonzalo, J., Palma, J., Freire, J., Tomé, M., Mateus, R., Rodriguez, L., et al. (2013). A decision support system for a multi stakeholder’s decision process in a Portuguese National Forest. Forest Systems, 22(2), 359–373.
Giménez, J. C., Bertomeu, M., Diaz-Balteiro, L., & Romero, C. (2013). Optimal harvest scheduling in Eucalyptus plantations under a sustainability perspective. Forest Ecology and Management, 291, 367–376.
Gómez, T., Hernández, M., León, M., & Caballero, R. (2006). A forest planning problem solved via a linear fractional goal programming model. Forest Ecology and Management, 227(1), 79–88.
Grigoroudis, E., Petridis, K., & Arabatzis, G. (2014). RDEA: A recursive DEA based algorithm for the optimal design of biomass supply chain networks. Renewable Energy, 71, 113–122.
ILOG, IBM: Cplex Optimizer v12.7.1 User’s Manual (2017). URL https://www.ibm.com/support/knowledgecenter/en/SSSA5P_12.7.1. Accessed on June 30, 2017.
Johnson, K. N., & Scheurman, H. L. (1977). Techniques for prescribing optimal timber harvest and investment under different objectives-discussion and synthesis. Forest Science, 23(1), a0001–z0001.
Kim, J., Realff, M. J., & Lee, J. H. (2011). Optimal design and global sensitivity analysis of biomass supply chain networks for biofuels under uncertainty. Computers & Chemical Engineering, 35(9), 1738–1751.
Kim, J., Realff, M. J., Lee, J. H., Whittaker, C., & Furtner, L. (2011). Design of biomass processing network for biofuel production using an MILP model. Biomass and Bioenergy, 35(2), 853–871.
Kossenakis, T. (1939). Yield tables of coppice stands of Quercus frainetto, Fagus sylvatica and Castanea sativa. Techincal Report: Forest Research Publications Bureau, Ministry of Agriculture, Athens, Greece.
Maros, I., Arampatzis, G., & Sifaleras, A. (2009). Special issue on optimization models in environment and sustainable development. Operational Research, 9(3), 225–227.
Nautiyal, J., & Pearse, P. (1967). Optimizing the conversion to sustained yield—A programming solution. Forest Science, 13(2), 131–139.
Öhman, K., & Eriksson, L. O. (2002). Allowing for spatial consideration in long-term forest planning by linking linear programming with simulated annealing. Forest Ecology and Management, 161(1), 221–230.
Petridis, K. (2015). Optimal design of multi-echelon supply chain networks under normally distributed demand. Annals of Operations Research, 227(1), 63–91.
Salehi, A., & Eriksson, L. O. (2010). A management model for Persian oak—A model for management of mixed coppice stands of semiarid forests of Persian oak. Mathematical and Computational Forestry & Natural Resource Sciences, 2(1), 20.
Termansen, M. (2007). Economies of scale and the optimality of rotational dynamics in forestry. Environmental and Resource Economics, 37(4), 643–659.
Voudouris, K., Polemio, M., Kazakis, N., & Sifaleras, A. (2010). An agricultural decision support system for optimal land use regarding groundwater vulnerability. International Journal of Information Systems and Social Change, 1(4), 66–79.
Yoshida, T., & Kamitani, T. (2000). Interspecific competition among three canopy-tree species in a mixed-species even-aged forest of central Japan. Forest Ecology and Management, 137(1), 221–230.
Zhang, F., Johnson, D. M., & Johnson, M. A. (2012). Development of a simulation model of biomass supply chain for biofuel production. Renewable Energy, 44, 380–391.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Petridis, K., Arabatzis, G. & Sifaleras, A. Mathematical optimization models for fuelwood production. Ann Oper Res 294, 59–74 (2020). https://doi.org/10.1007/s10479-017-2697-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-017-2697-7