industry, employment, economics and trade theory with focus on the forest sector peter lohmander
TRANSCRIPT
Industry, employment, economics and trade theory
with focus on the forest sector
Peter Lohmanderwww.Lohmander.com
IndustryEmployment Economics Trade theory
The forest sector
The optimal combination of forest industry investments, forest industry production and forest production may be determined.
The employment is strongly dependent on the activities in the forest sector.
Such dependences may be expressed via constraints in a forest sector model.
The economic result of all activities in the forest sector may be optimized.
Trade theoryIs one way to investigate how the activitites in different countries are linked and influence each other.
Trade theory
As presented by:
Colin Danby. http://faculty.uwb.edu/danby/bls324/trade/tradintr.html
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.
That’s 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/bls324/trade/tradintr.html
Secondly,
it would be nice to know about the effects of trade on the domestic economy.
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.
Here you may study trade theory and the international forest sector:
NA0061 The Forest Sector from an International View, 7.5 ECTSSkogssektorn i ett internationellt
perspektiv
http://www.slu.se/?id=371&Kurskod=NA0061&engelska=true&
Industry, employment, economics, trade and the forest sector
Can we optimize all of these things?
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 ?
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”.
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.
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.
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 2003-12-11www.Lohmander.com
! SMB2;! Peter Lohmander 2003-10-15;
Max = TProf;
TProf = - InkK - IntKostn + ForsI;InkK = PKTi*KTimmer + PKMav*KMav + PKFlis*KFlis
+ PReturpL*KReturpl + PReturpI*KReturpI; IntKostn = AvvK*Avv + TPKostTI*ETimmer + TPKostMA*EMav
+ CSV*ProdSV + CLiner*ProdLin;ForsI = PSV*ProdSV + PLiner*ProdLin + PSTi*STimmer
+ PSMav*SMav + PSFlis*SFlis;!Marknadspriser för råvaror samt ev. råvarurestriktioner
-------------------------------------------------------;PKTi = 380;PSTi = 330;
PKMav = 200;PSMav = 120;PKFlis = 250;PSFlis = 150;
PReturpL = 50;PReturpI = 730;
[LRetP] KReturpL <= 100;
!SMBs egen skog och avverkning -----------------------------;
AvvK = 70;AvvKap = 570;TimAndel = .5;
[KapAvv] Avv <= AvvKap;!SMAs egen virkestransport
-------------------------;TPKostTI = 60;TPKostMa = 70;
!SMBs eget sågverk
-----------------;PSV = 1500;CSV = 300;
SVKap = 80;TTimmer = ETimmer + KTimmer;
ProdSV = .5*TTimmer;ProdFl = .8*ProdSV;ProdSp = .2*ProdSV;
[KapSV] ProdSV <= SVKap;
!SMBs råvarubalanser gällande egna producerade råvaror och halvfabrikat-----------------------------------------------------------------;
EMav = (1-TimAndel)* Avv - SMav;ETimmer = Timandel*Avv - STimmer;
EFlis = ProdFl - SFlis;!SMBs egen linerfabrik
---------------------;PLiner = 4900;CLiner = 1200;
LinerKap = 400;TRetP = KReturpL + KReturpI;
TFiber = EMav + EFlis + KMav + KFlis; ProdLin = .25*TFiber + .95*TRetP;
[FFiberK] TFiber/TRetP >= 4;[KapLiner] ProdLin <= LinerKap;
end
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
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
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
Row Slack or Surplus Dual PriceLRETP 0.0000000 680.0000KAPAVV 0.0000000 160.0000KAPSV 0.0000000 600.0000FFIBERK 0.6043397E-09 -788.9547KAPLINER 0.0000000 2915.385
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.
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.
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.
Relevant result from 1981?
• The general finding that it may be optimal to use some of the wood for energy, still remains!
SVENSKA SKOGS- OCH MASSABOLAGET, SSM, 2000 - 2009 Praktikfallsuppgift i Kostnads - Intäktsanalys med OptimeringPeter Lohmander
SVENSKA SKOGS- OCH MASSABOLAGET, SSM, 2000 - 2009 Praktikfallsuppgift i Kostnads - Intäktsanalys med OptimeringPeter 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/ki99/SSM99/SSM994.htm
http://www-sekon.slu.se/~PLO/ki99/SSM99/SSM994.htm
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.
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.
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.
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.
The Option• A new generation of optimization models
is possible to construct.
• We should not hesitate to develop this generation!
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!
Stochastic Price PE Price of Electricity, Large Industrial
Consumers (li) 70 000 MWh (Source: Statistics Sweden)
0,0
10,0
20,0
30,0
40,0
50,0
60,0
70,0
-12,0 -10,0 -8,0 -6,0 -4,0 -2,0 0,0
Year - 2007
CS
EK
/kW
h
Stochastic Price Export Price of Kraft Paper and Kraft Board
(Source: Statistics Sweden)
0,0
1000,0
2000,0
3000,0
4000,0
5000,0
6000,0
1996 1998 2000 2002 2004 2006
Year
SE
K/T
on
PP
PP minus 4500
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
Low Correlation between Energy Prices and Pulp Prices
(Source: Statistics Sweden)
0,0
500,0
1000,0
1500,0
2000,0
2500,0
3000,0
3500,0
1996 1998 2000 2002 2004 2006
Year
Pri
ces
in d
iffe
ren
t sc
ales
PP minus 4500
PE times 50
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
Joint probability density function with correlation 0.25 (which corresponds to the prices of electricity and kraft paper)
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)
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.
X1
X2
Production capacity 2
Production capacity 1
Total wood supply
General illustration why the marginal value of production capacity increases with price risk (and connection to
heating plants)
The economic optimization problem
1 1 2 2max PX P X
1 1 2 2
1 1
2 2
a X a X R
X Cap
X Cap
1 1 2 2 0d PdX P dX
2 1
1 2
dX P
dX P
Along the iso profit line we have:
X1
X2
Production capacity 2
Production capacity 1
Total wood supply
Isoprofit line2 1
1 2
1dX P
dX P
X1
X2
Production capacity 2
Production capacity 1
Total wood supply
Isoprofit line 2 1
1 2
1dX P
dX P
X1
X2
Production capacity 2
Production capacity 1
Total wood supply Isoprofit line
2 1
1 2
1dX P
dX P
Stochastic dynamic example with heating and pulp plants
P1
P2
P1
P2
P2 Time
The prices of electricity and kraft paper are not known many years in advance.
P1
Stochastic dynamic example with heating and pulp plants
Time
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.
Stock level
Stochastic dynamic example with heating and pulp plants
P1
P2
P1
P2
P2 Time
Time
Stock level
P1
The stochastic dynamic optimization problem
1 2 1, 1 2, 1
1 2 1 2
1, 2, 1 2 1, 2, 1 2 1, 1 2, 1 1, 2, 1 1, 1 2, 1,
( , ) ( , , , )
( , , , ) ( , ; , , , ) ( , , , ) ( , , ) ( 1, , , )maxt t
t
r tt t t t t t t t t t t t t t
X X P P
X X S t i Cap Cap
f t i P P X X t i P P h t i X X e P P P P f t i P P
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.
The stochastic dynamic optimization problem
1, 2,( , , , )t t tf t i P P
The optimal expected present value, f, as a function of time, the stock level and the prices electricity and kraft paper.
The stochastic dynamic optimization problem
1 2 1, 2,( , ; , , , )t t tX X t i P PThe 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.
The stochastic dynamic optimization problem
1 2( , , , )th t i X XThe 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 t+1.)
The stochastic dynamic optimization problem
1 2 1 2( , ) ( , , , )tX X S t i Cap Cap
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.
The stochastic dynamic optimization problem
1, 1 2, 1
1, 1 2, 1 1, 2, 1 1, 1 2, 1( , , ) ( 1, , , )t t
r tt t t t t t t
P P
e P P P P f t i P P
The expected optimal objective function value of period t+1 is discounted to period t.
The probabilities of reaching different market state combinations at t+1 in the electricity market and in the kraft paper market are conditional on the prices in these markets at t.
The stochastic dynamic optimization problem
1 2 1, 1 2, 1
1 2 1 2
1, 2, 1 2 1, 2, 1 2 1, 1 2, 1 1, 2, 1 1, 1 2, 1,
( , ) ( , , , )
( , , , ) ( , ; , , , ) ( , , , ) ( , , ) ( 1, , , )maxt t
t
r tt t t t t t t t t t t t t t
X X P P
X X S t i Cap Cap
f t i P P X X t i P P h t i X X e P P P P f t i P P
The total optimization problem is found above.
Now, we will illustrate this with a numerical program!
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.
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.
Where do we focus on optimization in the forest sector?
OR in the Forest Sector 2007INFORMS International Meeting 2007
Puerto Ricohttp://meetings.informs.org/PuertoRico2007/
http://www.lohmander.com/ORForSec07.doc
Industry, employment, economics and trade theory
with focus on the forest sector
may be optimized.
It is our duty and pleasure to do that!
Peter Lohmanderwww.Lohmander.com