Optimal Forest Management Under Risk International Seminars in Life Sciences Universidad Polit

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Optimal Forest Management Under Risk
International Seminars in Life Sciences
Universidad Politécnica de Valencia Thursday
2007-02-22

• Peter Lohmander
• Professor of Forest Management and Economic
  Optimization
• SLU, Swedish University of Agricultural Sciences
• Umea, Sweden
• http//www.Lohmander.com
• Version 2007-02-18

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Schedule of Peter Lohmander from Claudio
Benavent,International Officer ETSMRE - ETSIA

• Thursday 2007-02-22
• 1030 Welcome at ETSMRE
• 1045-1345 Visits on campus and
  interviews with UPV Colleagues
• 1400 Lunch on campus offered by ETSMRE
• 1630 Conference in International
  Seminars
• 1930 Free programme
• Friday 2007-02-23
• 1030 Interview with Prof. Penny
  McDonald, Coordinator of the
• course "Preparation for International
  Study"
• 1100-1215 Institutional Presentation of
  your home Institution
• 1230-1330 International Office ETSMRE
• 1400 Lunch on campus offered by ETSMRE
• 1530 Free programme
• Location
• ETSMRE International Office (Avda. Blasco
  Ibáñez, 19-21).

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AMBITION

• Research that leads to economically profitable
  and practical solutions and at the same time
  leads to new discoveries of methods and practical
  general approaches to problems in operations
  research in general and to forest economics.
• Environmentally friendly solutions are
  sometimes discovered also to be economically
  optimal!

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Stochastic Dynamic Optimization

• The future state of the world is hard to predict
  perfectly.
• Some decisions must be made before the future is
  perfectly known.
• Stochastic Dynamic Programming is the relevant
  approach.

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The unpredictable world and the decision problems
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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.
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Stochastic prices and optimal adaptive harvest
decisions
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Stochastic windthrows and optimal adaptive
spatial harvest
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Optimal initial species mix and optimal adaptive
selective thinnings
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Stochastic spatial forest fires and
optimal adaptive planning
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Stochastic fungi damages and optimal adaptive
harvesting
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Stochastic spatial harvesting and economies of
scale
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Stochastic Price
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Stochastic Price
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Low Correlation between Energy Prices and Pulp
Prices (Source Statistics Sweden)
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Low Correlation between Energy Prices and Pulp
Prices
Price of Electricity (li) Export Price of Kraft Paper and Kraft Board
Price of Electricity (li) 1 0,2450
Export Price of Kraft Paper and Kraft Board 0,2450 1
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Low Correlation between Energy Prices and Pulp
Prices

• It has been proved that the expected marginal
  capacity value of a production plant increases
  with price variation when different products are
  produced with the same type of raw material and
  the correlation between product prices is less
  than 1. (Lohmander 1989)

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Low Correlation between Energy Prices and Pulp
Prices

• As a consequence, the most profitable investment
  level in production capacity, for instance a
  power plant, is higher with prices that are not
  perfectly predictable than according to what you
  find with traditional calculation.

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Joint probability density function with
correlation 0.25 (which corresponds to the
prices of electricity and kraft paper)
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Stochastic dynamic example with heating and pulp
plants
P2
Time
P2
P2
P1
P1
P1
The prices of electricity and kraft paper are not
known many years in advance.
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Stochastic dynamic example with heating and pulp
plants
Time
Stock level
The stock level can be changed over time. The
most profitable extraction (harvest) in a
particular period is affected by the prices of
kraft paper and energy. This is one reason why it
has to be sequentially optimized, based on the
latest price information from the markets.
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Stochastic dynamic example with heating and pulp
plants
P2
Time
P2
P2
P1
P1
Time
P1
Stock level
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The stochastic dynamic optimization problem
We maximize the expected present value of all
future production. The production of
electricity and kraft paper in future periods is
affected by the product prices and the stock of
resources. The stock of resources is dynamically
optimized.
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The stochastic dynamic optimization problem
The optimal expected present value, f, as a
function of time, the stock level and the prices
electricity and kraft paper.
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The stochastic dynamic optimization problem
The profit in a particular period, t, as a
function of the production levels of electricity
and kraft paper, time, the stock level and the
prices of electricity and kraft paper.
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The stochastic dynamic optimization problem
The cost of the stock in a period as a function
of time, the stock level and the production
levels of electricity and kraft paper. (The
production in period t affects the stock level in
period t and in period t1.)
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The stochastic dynamic optimization problem
The production of electricity and kraft paper in
a period, t, is constrained by the production
capacities in the kraft paper mill and the energy
mill in that period and the entering resource
stock level.
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The stochastic dynamic optimization problem
The expected optimal objective function value of
period t1 is discounted to period t. The
probabilities of reaching different market state
combinations at t1 in the electricity market and
in the kraft paper market are conditional on the
prices in these markets at t.
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The stochastic dynamic optimization problem
The total optimization problem is found
above. Now, we will illustrate this with a
numerical program!
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General illustration why the marginal value of
production capacity increases with price risk
(and connection to heating plants)
X2
Production capacity 1
Production capacity 2
Total wood supply
X1
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The economic optimization problem
Along the iso profit line we have
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X2
Production capacity 1
Production capacity 2
Total wood supply
Isoprofit line
X1
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X2
Production capacity 1
Production capacity 2
Total wood supply
Isoprofit line
X1
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X2
Production capacity 1
Production capacity 2
Total wood supply
Isoprofit line
X1
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Link to the software

• http//www.lohmander.com/CDP5L.htm

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Results

• The expected economic value of one more unit of
  heating plant capacity is
• 17551 16461 1090.
• The economically optimal decision is this
• If the investment cost of an extra unit of
  capacity is less than 1090 Build this extra
  heating plant capacity!
• No other investment calculation method would give
  the correct rule.

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Conclusions from the numerical model

• It is possible to adaptively optimize all
  decisions over time including production of
  electricity, kraft paper and resource extraction.
• The approach makes it possible to determine the
  expected value of production capacity investments
  in heating plants and paper mills.
• The approach can be expanded to cover the
  complete energy and forest sector.

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Already in 1981

• World Bank Model to study the Swedish forest
  sector. (Nilsson, S.)
• In the model, timber, pulp wood and fuel wood
  could be produced and harvested in all regions.
• The energy industry was considered as an option
  in all regions. It was possible too burn wood,
  not only fuel wood but also pulp wood.

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Capacity investments

• The existing capacity in the saw mills, pulp
  mills and paper mills was investigated and used
  in the model. It was possible to invest in more
  capacity of different kinds in the different
  regions.

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Structure in 1981

• The forest sector of Sweden was modelled as a
  linear programming problem.
• The total economic result of all activities in
  the forest sector of Sweden was maximized.
• The wood based part of the energy sector was
  considered as a part of this forest sector.

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Wood for energy in 1981

• Among these results, we found that a large
  proportion of the pulpwood should be used to
  produce energy.
• This was particularly the case in the north, at
  large distances from the coast.

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Surprise? Not really!

• The cost of transporting pulpwood large distances
  is very high.
• If energy can be produced from pulpwood, far away
  from the coast and the pulp industry, it is not
  surprising that this may be the most profitable
  alternative.

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Relevant model in 1981?

• Of course, linear programming models are only
  models of reality. This is true with all models.
• Of course, linear programming models do not
  capture all nonlinear and other real properties
  of the real world such as risk and integer
  constraints.
• Better options exist today to handle
  nonlinearities, risk, integer constraints and all
  kinds of other properties of the real world.

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Relevant result from 1981?

• The general finding that it may be optimal to use
  some of the wood for energy, still remains!

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Questions today (1)

• Can we combine the forest sector and the energy
  sector in one modern optimization model for both
  sectors? The model should include relevant data
  for the heating and electricity plants and for
  all types of forest industry mills.

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President Lars Fritiof, E.ON (March 2006)

• During the next three years, the E.ON Group will
  invest about SEK 175 billion, of which SEK 155
  billion will be invested in plants.

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President Lars Fritiof, E.ON (March 2006)

• Secure energy supplies can no longer be taken
  for granted. Demand is increasing and European
  reserves of oil and gas are diminishing.The
  recently published EU Green Book reports that if
  nothing is done, Europes imports of energy will
  increase from 50 to 70 in the next 20 to 30
  years.

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Necessary Model Properties

• The model should be dynamic and include the
  options to invest in new production capacity.
  Such new capacity could, when it comes to
  investments in energy plants, have different
  properties with respect to technological choices,
  possible fuels and degrees of flexibility.

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Why flexibility?

• Prices and the availability of different fuels
  are impossible to predict over horizons of the
  economic life time of a heating plant. That is
  why flexibility is valuable. In the old type of
  optimization models, such things could not be
  analyzed at all. Now, economic optimization of
  flexibility is possible.

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Dynamic options

• In the model from 1981, one period was analysed.
  In a new dynamic model, the use of the forest
  resources can also be optimized over time.
• In the model from 1981, the capacities of
  different mills was constant. In the dynamic
  model, the capacity investments can be optimized
  over time.

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The Option

• A new generation of optimization models is
  possible to construct.
• We should not hesitate to develop this
  generation!

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Conclusions

• Optimal forest management under risk contains a
  large number of topics.
• The relevant general approach is stochastic
  dynamic programming.

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Conclusions

• Here you may read more about these things
• http//www.lohmander.com/Information/Ref.htm

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Conclusions

• Optimal forest management under risk contains a
  large number of topics.
• Here, you may instantly optimize some decisions!
• http//www.lohmander.com/Program/Program.htm

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Conclusions

• Here, you may study some courses
• http//www.lohmander.com/Kurser/Kurser.htm
• In particular
• Optimization in dynamic and stochastic decision
  problems (Graduate course)
• Forest Economics (Graduate course)
• Economic Forest Production (Advanced
  Undergraduate course)
• The Forest Sector from an International View
  (Advanced Undergraduate course)

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INFORMS The Institute for Operations Research and
the Management Sciences (INFORMS) is the largest
professional society in the world for
professionals in the field of operations research
(O.R.).  It was established in 1995 with the
merger of the Operations Research Society of
America (ORSA) and The Institute of Management
Sciences (TIMS).
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INFORMS 2007July 8-11, 2007INFORMS
International Puerto RicoWestin Rio Mar Beach
Resort SpaRio Grande, Puerto Rico O.R. in
the Forest Sector O.R. in the Forest Sector is
one of the clusters of INFORMS 2007. The sessions
in this cluster will include the most interesting
forest sector operations research applications
from all countries. Contact Cluster Chair
Professor Peter Lohmander, SLU, Faculty of Forest
Sciences, SE-901 83 Umea, Sweden. e-mail
peter.lohmander_at_sekon.slu.se
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Thank you for listening!Here you may reach me in
the future

• Peter Lohmander
• Professor of Forest Management and Economic
  Optimization,
• SLU, Swedish University of Agricultural Sciences,
  Faculty of Forest Sciences,
• Dept. Of Forest Economics, SE-901 83 Umea, Sweden
• http//www.Lohmander.com
• peter.lohmander_at_sekon.slu.se
• plohmander_at_hotmail.com
• Version 2007-02-18