Market Adaptive Control Function Optimization in Continuous Cover Forest Management

Document Type : Research Paper

Author

Optimal Solutions in Cooperation with Linnaeus University, Umea, Sweden

Abstract

Economically optimal management of a continuous cover forest is considered here. Initially, there is a large number of trees of different sizes and the forest may contain several species. We want to optimize the harvest decisions over time, using continuous cover forestry, which is denoted by CCF. We maximize our objective function, the expected present value, with consideration of stochastic prices, timber quality variations and dynamically changing spatial competition. The problem is solved using an adaptive control function. The parameters of the control function are optimized via the first order optimum conditions based on a multivariate polynomial approximation of the objective function. The second order maximum conditions are investigated and used to determine relevant parameter ranges. The procedure is described and optimal results are derived for a general function multi-species CCF forest. Concrete examples from Germany, with beech, and from Sweden, with Norwegian spruce, are used to illustrate the methodology and typical numerical results. It is important to make market adapted harvest decisions. If the stochastic price variations are not considered when the harvest decisions are taken, the expected present value is reduced by 23%.

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References

Attari, H. & Nasseri, S. H. (2014). New concepts of feasibility and efficiency of solutions in fuzzy mathematical programming problems. Fuzzy Information and Engineering, 6(2), 203-221.
Hatami, N., Lohmander, P., Moayeri, M.H., & Mohammadi Limaei, S. (2017). A basal area increment model for individual trees in mixed species continuous cover stands in Iranian Caspian forests, National Conference on the Caspian Forests of Iran, Conference Report, University of Guilan, Rasht, Iran, 5 pages.
Hessenmöller, D., Bouriaud, O., Fritzlar, D., Elsenhans A. S. & Schulze E. D. (2018). A silvicultural strategy for managing uneven-aged beech-dominated forests in Thuringia, Germany: A new approach to an old problem. Scandinavian Journal of Forest Research, 33(7), 668-680.
Lohmander, P. (1986). Continuous extraction under risk. International Institute for Applied Systems Analysis, Systems and Decisions Sciences, Wien, Austria, Working Paper No. 1986-16, 36 pages. 
Lohmander, P. (1987). The economics of forest management under risk, PhD thesis, Dept. of Forest Economics, Swedish University of Agricultural Sciences, Research Report No. 79, 1987.
Lohmander, P. (1988). Continuous extraction under risk. Systems Analysis – Modelling - Simulation, 5(2), 131-151.
Lohmander, P. (1990). A quantitative adaptive optimization model for resource harvesting in a stochastic environment. Systems Analysis – Modelling - Simulation, 7(1), 29-49.
Lohmander, P. (1992a). The multi species forest stand, stochastic prices and adaptive selective thinning. Systems Analysis – Modelling - Simulation, 9(1), 229-250. 
Lohmander, P. (1992b). Continuous harvesting with a nonlinear stock dependent growth function and stochastic prices: Optimization of the adaptive stock control function via a stochastic quasi-gradient method, with software, Swedish University of Agricultural Sciences, Dept. of Forest Economics, Research Report No. 144, 44 pages.
Lohmander, P. (1992c). Continuous harvesting with a nonlinear stock dependent growth function and stochastic prices: Optimization of the adaptive stock control function via a stochastic quasi-gradient method. In M. Hagner, (Ed.), Silvicultural Alternatives, Proceedings from an internordic workshop, Umea, Sweden. Swedish University of Agricultural Sciences, Dept. of Silviculture, pages 198-214.
Lohmander, P. (1993). Economic two stage multi period species management in a stochastic environment: The value of selective thinning options and stochastic growth parameters. Systems Analysis – Modelling - Simulation, 11(1), 287-302.
Lohmander, P. (2000). Optimal sequential forestry decisions under risk. Annals of Operations Research, 95(1-4), 217-228.
Lohmander, P. (2007). Adaptive optimization of forest management in a stochastic world. In: A., Weintraub, et al. (Eds.). Handbook of Operations Research in Natural Resources (525-544). New York: Springer.
Lohmander, P. (2017a). ICMDS 2016 Conference report. Fuzzy Information and Engineering, 9(2), 269-270.
Lohmander, P. (2017b). Two Approaches to Optimal Adaptive Control under Large Dimensionality. International Robotics and Automation Journal, 3(4), pages 328-330.
Lohmander, P. (2017c). A General Dynamic Function for the Basal Area of Individual Trees Derived from a Production Theoretically Motivated Autonomous Differential Equation. Iranian Journal of Management Studies, 10(4), 917-928.
Lohmander, P. (2018a). Applications and Mathematical Modeling in Operations Research. In BY. Cao (Ed). Fuzzy Information and Engineering and Decision. International Conference of Mathematics and Decision Science, September 2016, Guangzhou, China. Advances in Intelligent Systems and Computing, 646. Springer, pages 46-53.
Lohmander, P. (2018b). Optimal Stochastic Dynamic Control of Spatially Distributed Interdependent Production Units. In BY. Cao (Ed). Fuzzy Information and Engineering and Decision. International Conference of Mathematics and Decision Science, September 2016, Guangzhou, China. Advances in Intelligent Systems and Computing, 646. Springer, pages 115-122.
Lohmander, P., & Mohammadi, S. (2008). Optimal Continuous Cover Forest Management in an Uneven-Aged Forest in the North of Iran. Journal of Applied Sciences, 8(11), 1995-2007. 
Lohmander, P., Olsson, J. O., Fagerberg, N., Bergh, J., & Adamopoulos, S. (2017). High resolution adaptive optimization of continuous cover spruce forest management in southern Sweden. Toth, S., (Editor), University of Washington, Seattle, Washington, USA,  Symposium on Systems Analysis in Forest Resources, pages 37-38.
Moradi Dalini, M., & Noura, A. (2018). Relation Between Imprecise DESA and MOLP Methods. Iranian Journal of Management Studies, 11(1), 23-36.
Nasseri, S., Bavandi, S. (2018). Amelioration of Verdegay̕s approach for fuzzy linear programs with stochastic parameters. Iranian Journal of Management Studies, 11(1), 71-89.
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(2), 335-364.
Schütz, J-P. (2006). Modelling the demographic sustainability of pure beech plenter forests in Eastern Germany. Annals of Forest Science, 63(1), 93-100.
Shahbazi, S., Sajadi, S., Jolai, F. (2017). A Simulation-Based Optimization Model for Scheduling New Product Development Projects in Research and Development Centers. Iranian Journal of Management Studies, 10(4), 883-904.
Interdisciplinary Journal of Management Studies (Formerly known as Iranian Journal of Management Studies)
Volume 12, Issue 3
September 2019
Pages 335-361

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