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A sequential approach in mathematical programming to include spatial aspects of biodiversity in long range forest management planning

von Kerkvoorde, Michiel (1996). A sequential approach in mathematical programming to include spatial aspects of biodiversity in long range forest management planning. Umeå: (S) > Dept. of Forest Resource Management
(NL, NJ) > Dept. of Forest Resource Management
, Sveriges lantbruksuniversitet. Arbetsrapport / Sveriges lantbruksuniversitet, Institutionen för skoglig resurshushållning och geomatik ; 15

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In the discussion about forest management the maintenance of biodiversity is coming more and
more to the fore. Like 120 other countries, Sweden committed itself to a sustainable use of for­
ests at the convention of Rio de Janeiro. Sweden has a long tradition of forest management fo­
cusing on woodproduction. This implies that almost all the forest land is managed and that the
area of natural forests is very small. The maintenance of biodiversity should therefor not be
limited to reserved areas but it should be incorporated into the management of the total forest
area. There is a need for improved methods to balance the economic and ecological benefits of
forest management. In this study I designed an algorithm for mathematical programming that
includes the determination of a contiguous area of old forest into a long range forest manage­
ment plan that strives for the sustainable production of wood as well as the maintenance of
The boreal forests of Sweden were characterised by two main disturbance patterns. In dry and
mesic forests, fires determined the structure of the forest. This resulted in large scale pattern
where Scots pine and broad-leaved trees dominated. In the wetter forests, dominated by Nor­
way spruce, small scale disturbances like windthrow brought about a heterogeneous forest
structure with a long continuity. With the management of the forests for woodproduction, some
characteristic features disappeared. The amount of old-growth forests, deciduous trees and
coarse woody debris decreased significantly and large scale clearcuts resulted in a loss of re­
tained trees, characteristic for an area after forest fire. Especially these features are of impor­
tance for the maintenance of biodiversity. Rare and sensitive species are largely dependent on
structures determined by natural disturbance patterns.
The objective function in the long range forest management plan is a maximisation of the Net
Present Value of the woodproduction. To ensure a sustainable supply of wood in the future this
objective function is bounded by even flow and ending stock constraints. For the maintenance
of biodiversity, constraints are implemented as well. These constraints stem from the assump­
tion that the biodiversity benefits by the establishment of certain features abundant in natural
forests and scarce in managed forests. Special attention is paid to a certain contiguous area of
old forest. This is a conversion of the current attention for spatial aspects in biodiversity. A
contiguous area of old forest ensures a core area without any edge effects. Many red-listed
species depend on this.
In natural resource management, Linear Programming (LP) is most common among the
mathematical programming techniques. It gives an optimal solution and is efficient. The model
described above can largely be solved with LP. The constraint on the contiguous area of old
forest will however cause problems. The way this constraint is formulated is known as a Quad­
ratic Assignment Problem (QAP). This kind of problem is hard to solve and LP is not suitable.
Other exact solution methods like the Branch and Bound method can only solve very small
problems. Heuristics are a good alternative. Although they do not guarantee an optimal solu­
tion, they are able to solve large problems in an acceptable amount of time. Simulated Anneal­
ing (SA) is a heuristic method that gives high quality solutions because it has the ability to
overcome local optima and convergence to a high value. I have designed a sequential approach.
Herein the strong points of both methods are united. First the QAP is solved using SA. After
that, the rest of the problem is solved by LP. This part is bounded by the outcome of the SA. In
the objective function for the SA, next to a measure for the contiguous area of forest, the Net
Present Value is added. A weightfactor determines the relative importance of these two ele­
ments in relation to each other. With this the SA solution will fit as effective as possible into
the final solution for the whole problem, that is at the least costs.
The algorithm is tested on validity, reliability and efficiency. Validity relates to the question if
the algorithm does what it is perceived to do. The test revealed some points that need extra attention. The determination of the parameters for the so called cooling down of the SA is some­
what troublesome and needs to be regarded from case to case. Focusing strongly on either the
contiguous area or the NPV in the SA-objective function gives results that are poor in relation
to the results of an objective function wherein the two are balanced. The inclusion of the NPV
in the SA-objective function does make the SA-solution effective in terms of the final outcome.
In general the performance of the algorithm is as expected. The algorithm turned out to be very
reliable, that means that a repetition gives about the same value all the time. For a sample for­
est of sixteen stands with more than 900 possible management regimes the algorithm could
produce a solution within a minute, indicating that it is efficient.
In a case study the sequential approach algorithm is applied on the Brattaker area, near Umea
in Northern Sweden. The Simulated Annealing created contiguous old forest areas. The results
are some more or less contiguous areas of between 100 and 150 hectares. The outcome is lim­
ited by the actual situation in the area. Not all forest can be old in fifty years. Next to that the
algorithm shows a preference for small stands, causing a large part of the area, a part consist­
ing of large stands, to be without old forest. The costs for contiguous old forest are relatively
small compared to non contiguous old forest. The Simulated Annealing algorithm has the ca­
pability to form contiguous old forest in an efficient way. If the contiguous old forest is worth
the additional costs, compared to non contiguous old forest, is a question for the decision mak­
ers. The Linear Programming produces a long range forest management plan. In this plan the
features of importance for biodiversity are all established. With this it is assumed that biodi­
versity is maintained the coming fifty years. The sustainable provision of wood is guaranteed
for this period. But this is at the expanse of the further future because the age structure is se­
verely distorted. The main reason for this seems to be the combination of interest rate, initial
age structure and the requirement for old forest. The used interest rate caused a strong prefer­
ence for a present income to a future income. Because of that, and the initial age structure, the
cut volume in the first period is extraordinary high, which has its effects on the age structure
after 50 years. The requirement for old forest is in conflict with the age structure, which might
cause problems for the provision of old forest after the planning horizon of 50 years.
The main conclusion is that the algorithm can give good results. It shows some of the possibili­
ties to link a heuristic method with Linear Programming. An improvement could be the use of a
shape index for the formation of contiguous old forest. It became clear that the situation and
parameters in a case study have a major influence. The interest rate and an already unbalanced
age structure limited the possibilities to test the algorithm. To generate data that is of use in the
decision making process the algorithm needs more refinement. The site characteristics should
be taken into account and a situation should be created that will ensure the sustainable provi­
sion of wood and biodiversity also after the planning horizon.

Authors/Creators:von Kerkvoorde, Michiel
Title:A sequential approach in mathematical programming to include spatial aspects of biodiversity in long range forest management planning
Series Name/Journal:Arbetsrapport / Sveriges lantbruksuniversitet, Institutionen för skoglig resurshushållning och geomatik
Year of publishing :1996
Number of Pages:63
Place of Publication:Umeå
Publisher:Institutionen för skoglig resurshushållning, Sveriges lantbruksuniversitet
Publication Type:Report
Full Text Status:Public
Agris subject categories.:K Forestry > K10 Forestry production
P Natural resources > P01 Nature conservation and land resources
U Auxiliary disciplines > U10 Mathematical and statistical methods
Subjects:(A) Swedish standard research categories 2011 > 4 Agricultural Sciences > 401 Agricultural, Forestry and Fisheries > Forest Science
Agrovoc terms:forest management, planning, biodiversity, mathematical models, case studies, Sweden
Keywords:forest management, planning, biodiversity
Permanent URL:
ID Code:8856
Department:(S) > Dept. of Forest Resource Management
(NL, NJ) > Dept. of Forest Resource Management
Deposited By: Bo Jonsson
Deposited On:25 May 2012 11:39
Metadata Last Modified:02 Dec 2014 10:50

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