Optimization of Forestry, Infrastructure and Fire Management

Document Type : Research Paper


Optimal Solutions, Umea, Sweden, in Cooperation with Linnaeus University


Forests, sensitive to fires, cover large parts of our planet. Rational protection of forests against fires, forest fire management, is a very important topic area. Our planet is facing the serious problem of global warming. The probabilities of long dry periods and strong winds are increasing functions of a warmer climate. Heat, dry conditions and strong winds increase the probabilities that fires start. Furthermore, if a fire starts, the stronger winds make the fires spread more rapidly and the destruction increases. Under the influence of global warming, we may expect more severe problems in forestry caused by wild fires. For all of these reasons, it is essential to investigate and optimize the general principles of the combined forestry and wild fire management problem. In this process, we should integrate the infrastructure and the fire fighting resources in the system as decision variables in the optimization problem. First, analytical methods are used to determine general results concerning how the optimal decisions are affected by increasing wind speed. The total system is analyzed with one dimensional optimization. Then, different combinations of decisions are optimized. The importance of optimal coordination is demonstrated. Finally, a particular numerical version of the optimization problem is constructed and studied. The main results, under the influence of global warming, are the following: In order to improve the expected total results, we should reduce the stock level in the forests, increase the level of fuel treatment, increase the capacity of fire fighting resources and increase the density of the road network. The total expected present value of all activities in a forest region are reduced even if optimal adjustments are made. These results are derived via analytical optimization and comparative statics analysis. They have also been confirmed via a numerical nonlineaer programming model where all decisions simultaneously are optimized.


Alexander, ME 1985, Estimating the length-to breadth ratio of elliptical fire patterns, Proceedings of the Eight Conference on Fire and Forest Meteorology, April 29-May 2, Detroit Michigan, LR, Donoghue & RE, Martin (editors). Society of American Foresters, Bethesda, Maryland. SAF Publication, 85-04: 287-304.
Alexandridis, A, Russo, L, Vakalis, D, Bafas, GV, Siettos, CI 2011, Wildland fire spread modelling using cellular automata: evolution in large-scale spatially heterogeneous environments under fire suppression tactics, International Journal of Wildland Fire, 20: 633-647.
Braun, M 1983, Differential equations and their applications, Applied Mathematical Sciences, Springer-Verlag, New York.
Crawl, D, Block, J, Lin, K, Altintas, I 2017, Firemap: A dynamic data-driven predictive wildfire modeling and visualization environment, Procedia Computer Science, 108C: 2230-2239.
Cruz, MG, Alexander, ME 2019, The 10% wind speed rule of thumb for estimating a wildfire’s forward rate of spread in forests and shrublands, Annals of Forest Science, 76: 44.
FAO 2001, International handbook on forest fire protection, Technical guide for the countries of the Mediterranean basin, 1-163.
Finney, Mark 2004, Chapter 9: Landscape fire simulation and fuel treatment optimization. USDA Forest Service - General Technical Report PNW, 117-131.
Finney, M 2005, The challenge of quantitative risk analysis for wildland fire, Forest Ecology and Management, 211: 97-108.
Green, DG, 1983, Shapes of simulated fires in discrete fuels, Ecological Modelling, 20, 21-32.
Hosseini-Motlagh, S, Ebrahimi, S & Farshadfar Z 2020, Coordination of R&D effort, pricing, and periodic review replenishment Decisions in a Green Supply Chain through a Delay in Payment Contract, Iranian Journal of Management Studies, 13: 317-344.
Lohmander, P 2000, Optimal sequential forestry decisions under risk. Annals of Operations Research, 95: 217-228.
Lohmander, P 2007, Adaptive Optimization of Forest Management in a Stochastic World, In: A, Weintraub et al. (Editors), Handbook of Operations Research in Natural Resources, Springer, Springer Science, International Series in Operations Research and Management Science, New York, USA, pp. 525-544.
Lohmander, P 2018, Applications and Mathematical Modeling in Operations Research, In: Cao, BY (ed.) Fuzzy Information and Engineering and Decision. IWDS 2016. Advances in Intelligent Systems and Computing, Springer, Cham, vol. 646.
Lohmander, P 2019a, Control function optimization for stochastic continuous cover forest management, International Robotics and Automation Journal, 5: 85-89.
Lohmander, P 2019b, Market Adaptive Control Function Optimization in Continuous Cover Forest Management, Iranian Journal of Management Studies, 12: 335-361.
Lohmander, P 2020a, Dynamics and control of the CO2 level via a differential equation and alternative global emissions strategies, International Robotics & Automation Journal, 6: 7-15.
Lohmander, P 2020b, Fundamental principles of optimal utilization of forests with consideration of global warming and other related objectives, Central Asian Journal of Environmental Science and Technology Innovation, 1: 171-180.
Nemati, Y, Madhoushi, M, Safaei Ghadikolaei, A 2017, Towards supply chain planning integration: Uncertainty analysis using Fuzzy mathematical programming approach in a plastic forming company. Iranian Journal of Management Studies, 10: 335-364.
Palma, CD, Cui, W, Martell, DL, Robak, D, Weintraub, A 2007, Assessing the impact of stand-level harvests on the flammability of forest landscapes, International Journal of Wildland Fire, 16: 584-592.
Rasay, H, Fallahnezhad, M, Zaremehrjerdi, Y 2018, Integration of the Decisions Associated with Maintenance Management and Process Control for a Series Production System. Iranian Journal of Management Studies, 11: 379-405. 
Rideout, DB, Wei, Y, Kirsch, AG, Botti, SJ 2008, Toward a unified economic theory of fire program analysis with strategies for empirical modeling, In: TP, Holmes et al. (editors), The Economics of Forest Disturbances: Wildfires, Storms and Invasive Species, Springer Science, 361-380.
Russo, L, Russo, P, Vakalis, D, Siettos, C 2014, Detecting weak points of wildland fire spread: A cellular automata model risk assessment simulation approach, Chemical Engineering Transactions, 36: 253-258.
SvT 2020, Rapport. Swedish Television, May 5, 19:30.
Wei, Y, Rideout, D, Kirsch, A 2008, An optimization model for locating fuel treatments across a landscape to reduce expected fire loss. Canadian Journal of Forest Research, 38: 868-877.
Yadegari, E, Najmi, H, Ghomi-Avili, M, Zandieh, M 2015, A flexible integrated forward/ reverse logistics model with random path-based memetic algorithm. Iranian Journal of Management Studies, 8: 287-313.
Yousefnejad, H, Rabbani, M, Manavizadeh, N 2019, A simulation-optimization model for capacity coordination in make to stock/make to order production environments. Iranian Journal of Management Studies, 12: 235-253.
Zheng, Z, Huang, W, Li, S & Zeng, Y 2017, Forest fire spread simulating model using cellular automaton with extreme learning machine, Ecological Modelling, 348: 33-43.