Industry, employment, economics and trade theory with focus on the forest sector

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Industry, employment, economics and trade
theorywith focus on the forest sector

• Peter Lohmander
• www.Lohmander.com

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Industry Employment Economics Trade theory The
forest sector
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The optimal combination of forest industry
investments, forest industry production and
forest production may be determined.
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The employment is strongly dependent on the
activities in the forest sector. Such
dependences may be expressed via constraints in a
forest sector model.
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The economic result of all activities in the
forest sector may be optimized.
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Trade theory Is one way to investigate how the
activitites in different countries are linked and
influence each other.
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Trade theory
As presented by Colin Danby. http//faculty.uwb
.edu/danby/bls324/trade/tradintr.html
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The first purpose of trade theory is to explain
observed trade.  That is, we would like to be
able to start with information about the
characteristics of trading countries, and from
those characteristics deduce what they actually
trade, and be right.   Thats why we have a
variety of models that postulate different kinds
of characteristics as the reasons for trade.
Colin Danby. http//faculty.uwb.edu/danby/bls32
4/trade/tradintr.html
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Secondly, it would be nice to know about the
effects of trade on the domestic economy.
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A third purpose is to evaluate different kinds of
policy.  Here it is good to remember that most
trade theory is based on neoclassical
microeconomics, which assumes a world of
atomistic individual consumers and firms.  The
consumers pursue happiness (maximizing utility)
and the firms maximize profits, with the usual
assumptions of perfect information, perfect
competition, and so on.  In this world choice
is good, and restrictions on the choices of
consumers or firms always reduce their abilities
to optimize.  This is essentially why this theory
tends to favor freer trade.
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Here you may study trade theory and the
international forest sectorNA0061 The Forest
Sector from an International View, 7.5
ECTSSkogssektorn i ett internationellt
perspektivhttp//www.slu.se/?id371KurskodNA00
61engelskatrue
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Industry, employment, economics, trade and the
forest sector Can we optimize all of these
things?
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Observation The raw material stock has been
increasing for a very long time. Central
Question What is the optimal stock level when
we consider the total present value of the
forest sector, employment and the environment ?
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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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• The same method applied to a smaller problem of
  the same type
• Såg och Massabolaget
• Ett praktikfall i Skogsindustriell Ekonomi
• http//www.lohmander.com/SkogIndEk1/SI1.html
• Peter Lohmander 2003-12-11
• www.Lohmander.com

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! SMB2 ! Peter Lohmander 2003-10-15 Max
TProf TProf - InkK - IntKostn ForsI InkK
PKTiKTimmer PKMavKMav PKFlisKFlis
PReturpLKReturpl PReturpIKReturpI IntKostn
AvvKAvv TPKostTIETimmer TPKostMAEMav
CSVProdSV CLinerProdLin ForsI PSVProdSV
PLinerProdLin PSTiSTimmer PSMavSMav
PSFlisSFlis !Marknadspriser för råvaror samt
ev. råvarurestriktioner -------------------------
------------------------------ PKTi 380 PSTi
330 PKMav 200 PSMav 120 PKFlis
250 PSFlis 150 PReturpL 50 PReturpI
730 LRetP KReturpL lt 100
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!SMBs egen skog och avverkning
----------------------------- AvvK 70 AvvKap
570 TimAndel .5 KapAvv Avv lt
AvvKap !SMAs egen virkestransport
------------------------- TPKostTI
60 TPKostMa 70 !SMBs eget sågverk
----------------- PSV 1500 CSV 300 SVKap
80 TTimmer ETimmer KTimmer ProdSV
.5TTimmer ProdFl .8ProdSV ProdSp
.2ProdSV KapSV ProdSV lt SVKap
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!SMBs råvarubalanser gällande egna producerade
råvaror och halvfabrikat -------------------------
---------------------------------------- EMav
(1-TimAndel) Avv - SMav ETimmer TimandelAvv
- STimmer EFlis ProdFl - SFlis !SMBs egen
linerfabrik --------------------- PLiner
4900 CLiner 1200 LinerKap 400 TRetP
KReturpL KReturpI TFiber EMav EFlis KMav
KFlis ProdLin .25TFiber
.95TRetP FFiberK TFiber/TRetP gt
4 KapLiner ProdLin lt LinerKap end
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Local optimal solution found at step
10 Objective value
1373354.
Variable Value Reduced Cost
TPROF 1373354.
0.0000000 INKK
236846.2 0.0000000
INTKOSTN 563850.0
0.0000000 FORSI
2174050. 0.0000000
PKTI 380.0000
0.0000000 KTIMMER
160.0000 0.0000000
PKMAV 200.0000 0.0000000
KMAV 471.5128
0.0000000
PKFLIS 250.0000 0.0000000
KFLIS 0.0000000
50.00000 PRETURPL
50.00000 0.0000000
KRETURPL 100.0000 0.0000000
PRETURPI 730.0000
0.0000000 KRETURPI
105.1282 0.0000000
AVVK 70.00000
0.0000000 AVV
570.0000 0.0000000
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TPKOSTTI 60.00000
0.0000000 ETIMMER
0.0000000 10.00000
TPKOSTMA 70.00000
0.0000000 EMAV
285.0000 0.0000000
CSV 300.0000 0.0000000
PRODSV 80.00000
0.0000000 CLINER
1200.000 0.0000000
PRODLIN 400.0000
0.0000000 PSV
1500.000 0.0000000
PLINER 4900.000 0.0000000
PSTI 330.0000
0.0000000 STIMMER
285.0000 0.0000000
PSMAV 120.0000
0.0000000 SMAV
0.0000000 10.00000
PSFLIS 150.0000 0.0000000
SFLIS 0.0000000
50.00000 AVVKAP
570.0000 0.0000000
TIMANDEL 0.5000000
0.0000000 SVKAP
80.00000 0.0000000
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TTIMMER 160.0000
0.0000000
PRODFL 64.00000 0.0000000
PRODSP 16.00000
0.0000000 EFLIS
64.00000 0.0000000
LINERKAP 400.0000 0.0000000
TRETP 205.1282
0.0000000 TFIBER
820.5128 0.0000000

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Row Slack or Surplus Dual
Price LRETP 0.0000000
680.0000 KAPAVV 0.0000000
160.0000 KAPSV 0.0000000
600.0000 FFIBERK 0.6043397E-09
-788.9547 KAPLINER 0.0000000
2915.385
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Wood for energy in 1981

• Among these results, it was 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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SVENSKA SKOGS- OCH MASSABOLAGET, SSM, 2000 - 2009
Praktikfallsuppgift i Kostnads - Intäktsanalys
med Optimering Peter Lohmander
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SVENSKA SKOGS- OCH MASSABOLAGET, SSM, 2000 - 2009
Praktikfallsuppgift i Kostnads - Intäktsanalys
med Optimering Peter Lohmander Företaget står
i begrepp att utforma en 10- årsbudget
innefattande hela verksamheten inklusive
avverkning, rundvirkestransport, massa- och
pappersproduktion samt investeringar. Man har
för avsikt att ekonomiskt optimera två
femårsbudgetar simultant via lineär
programmering. http//www-sekon.slu.se/PLO/ki
99/SSM99/SSM994.htm
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http//www-sekon.slu.se/PLO/ki99/SSM99/SSM994.htm

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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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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 were 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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Detailed long term forest planning is not
optimal. Why should we make a detailed long
term plan based on future prices and other
conditions? Such things can not be perfectly
predicted!
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Stochastic Price
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Stochastic Price
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Economic Risk Management in Forestry and Forest
Industry and Environmental Effects in a Turbulent
World Economy
http//www-sekon.slu.se/plo/erm/ermtot8.htm
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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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Joint probability density function with
correlation 0.25 (which corresponds to the
prices of electricity and kraft paper)
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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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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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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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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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Where do we focus on optimization in the forest
sector? OR in the Forest Sector
2007 INFORMS International Meeting 2007 Puerto
Rico http//meetings.informs.org/PuertoRico2007/
http//www.lohmander.com/ORForSec07.doc
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Industry, employment, economics and trade
theorywith focus on the forest sector may be
optimized.It is our duty and pleasure to do
that!

• Peter Lohmander
• www.Lohmander.com