Risk, Dynamic and Spatial Forestry Issues

Risk, Dynamic and Spatial Decision Problems:
- Some explaining graphs
by Peter Lohmander, http://www.sekon.SLU.se/~PLO, Version 2000-09-06

This web page gives a very brief description of the field "Risk, dynamic and spatial decision problems" within economic forest management.

Figure 1.
The real (inflation adjusted) stumpage price in Sweden. Source: Swedish Board of Forestry, Yearbook of Forest Statistics, 2000. We may regard the stumpage price as a stochastic processes. There is no method available which can predict future prices without error.

Figure 2.
Each period, you observe the development of the price. If the price is higher than the reservation price, then you should harvest directly. If the price is lower than the reservation price, then you should wait longer. If the price is exactly equal to the reservation price, you may harvest directly or wait longer. The optimal reservation price function may be determined via stochastic dynamic programming. Here, you can read more about these things:

Lohmander, P., The economics of forest management under risk, Swedish University of
Agricultural Sciences, Dept. of Forest Economics,Report 79, 1987 (Doctoral
dissertation) (Doktorsavhandling), 311p

Lohmander, P., Pulse extraction under risk and a numerical forestry application,
SYSTEMS ANALYSIS -MODELLING - SIMULATION, Vol. 5, No. 4, 339-354, 1988

Lohmander, P., Adaptive decision making in forestry, in: Paredes G. (editor), Forest
management and planning in a competitive and environmentally concious world,
proceedings from: International Symposium on Systems Analysis and Management
Decisions in Forestry, March 9-12, 1993, Valdivia, Chile, 411-421, 1994

Lohmander, P., Reservation price models in forest management: Errors in the
estimation of probability density function parameters and optimal adjustment of the bias
free point estimates, Management Systems for a Global Forest Economy with Global
Resource Concerns, Society of American Foresters, Asilomar, California, September
1994, Brodie, D. & Sessions, J., (Editors),
College of Forestry, Oregon State University, Corvallis, Oregon, USA, 439-456, 1995

Lohmander, P., Optimal sequential forestry decisions under risk,
ANNALS OF OPERATIONS RESEARCH, Vol. 95, pp. 217-228, 2000

Two different optimization programs which makes it possible to study optimal harvesting decisions when prices are stochastic are found und here: http://www.sekon.slu.se/~PLO/javakod/D2.htm and http://www.sekon.SLU.se/~plo/Stump00/Stump00.htm

Figure 3.
The fungi damage percentage can not be perfectly predicted. We have to regard that as a stochastic process. Predictions will include error terms.

Figure 4.
Each period, you observe the development of the fungi damage percentage. If the percentage is higher than the reservation percentage, then you should harvest directly. If the percentage is lower than the reservation percentage, then you should wait longer. If the percentage is exactly equal to the reservation percentage, you may harvest directly or wait longer. The optimal reservation percentage function may be determined via stochastic dynamic programming.

Figure 5.
Pa and Pb denote the prices (or species specific growth parameters) of the species a and b. For reasons which are not possible to predict perfectly, Pa and Pb change over time. At Time = 0, we may invest in a mixed plantation. Then we know the values of Pa and Pb at that point in time. At Time = 0, we use available statistical methods and predict that (Pa, Pb) will come to some point in the green circle at Time = 1. At Time = 1, we know to which particular point in the green circle we came. We can, at Time = 1, select which species we want to keep growing in the forest until Time = 2. At Time = 1, we make the predictions that we come to the blue circle or to the red circle at Time = 2, depending on where we happen to be at Time = 1. Obviously, it is valuable to be able to delay the species selection decision until Time = 1. This is only possible if we start with a mixed species plantation at Time = 0. Here you can read more about these multi stage decision problems:

Lohmander, P., Flexibilitet - en ledstjarna for all ekonomisk skoglig planering,
SKOGSFAKTA, Inventering och Ekonomi, No. 23, 4p, 1990

Lohmander, P., The multi species forest stand, stochastic prices and adaptive selective
thinning, SYSTEMS ANALYSIS - MODELLING - SIMULATION, Vol. 9, 229-250, 1992

Lohmander, P., 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, Vol. 11, 287-302, 1993

Figure 6.
There are economies of scale in harvesting operations. One reason is that it is costly to move harvesters and forwarders long distances. From traditional stand level forest management optimization models, you easily get optimal solutions for individual stands. However, such solutions are usually not optimal when we consider the complete forest. If you take all spatial data and the costs of moving machines into account, it is optimal to visit each area less often and to harvest more intensively when you go there. Here you can read more about these and related issues:

Two abstracts on optimal forestry decisions in the presence of risk and economies of scale:
http://www.sekon.SLU.se/~plo/abstr/SaltLC1.htm

Lohmander, P., Optimization of decentralized adaptive truck decision rules: - A spatial
dynamic stochastic forest company problem, paper presented at the "Natural Resource
Management Cluster" of the TIMS/ORSA meeting, Los Angeles, April 23-26, 1995,
and at the general meeting of Scandinavian Society of Forest Economics, Finland, 1996, in
Saastamoinen, O. & Tikka S., (Editors), SCANDINAVIAN FOREST ECONOMICS, 36, 73-87, 1997

An optimization program which makes it possible to study how changes in the costs of moving
harvesters and forwarders affect the optimal thinning volumes and time intervals between thinnings:
http://www.sekon.SLU.se/~plo/javakod/F4.htm

Figure 7.
Many kinds of damages have spatial patterns and characteristics of relevance to optimal forest management decisions. The optimal decisions in each stand are affected by the properties of (and activities in) the other stands in the area. The graph shows the spread of a fire. The fire starts in Stand 1 in the small yellow circle. Over time, the fire spreads to the orange, to the yellow, and finally, to the red area. Of course, the wind direction affects the spread direction. Clearly, the spatial pattern of stands is of relevance to optimal forest fire management. The optimal management decisions in forest stands are affected by the probabilities that forest fires start in different parts of the area. These probabilities are to some extent endogenous to the forest management decision problem. The options to stop a fire which has already started are functions of the spatial distribution of stands. Hence, the spatial distribution of stands and of forest management activities should not be neglected. Insect-, fungi- and other damages sometimes have similar characteristics.

Figure 8.
Wind throws are economically important in some areas. Wind damages are dependent on many factors. Some of these factors make the optimization problems spatial. The physical properties and the spatial position of each stand and the properties and positions of the neighbour stands are all of importance to the optimal harvest decisions. Each stand in the area may sometimes protect some other stands from the winds. In such areas, the optimal harvest decisions can not be calculated stand by stand. It is often optimal to harvest these stands simultaneously. This means the following: Some stands should perhaps be harvested earlier than according to the optimal solution in a single stand analysis. Some other stands should perhaps be harvested later than according to the optimal solution in a single stand analysis. Please, read more about these things here:

Lohmander, P., Helles, F., Windthrow probability as a function of stand characteristics
and shelter, SCANDINAVIAN JOURNAL OF FOREST RESEARCH, Vol. 2, No. 2, 227-238, 1987

Lohmander, P., Ekonomiskt optimal avverkning med hansyn till stormfallningar,
SKOGSBRUKETS EKONOMI, Skogsfakta Konferens, No. 11, 32-37, 1988

Welcome to the home page of Peter Lohmander for more information!
http://www.sekon.SLU.se/~PLO

A forest economics java-library is found here:
http://www.sekon.SLU.se/~PLO/javakod/Jlib1.htm