Download ca = 1/40*(kuw)^2

Optimal Economic Decision
Rules in the Biomass Supply
Chain with CO2 Considerations
Peter Lohmander
Professor Dr., SUAS, Umea, SE-90183, Sweden
[email protected]
ALIO-INFORMS International 2010
Buenos Aires, Monday, June 07, 08:30 - 10:00
1
Optimal Economic Decision Rules in the Biomass Supply
Chain with CO2 Considerations
Peter Lohmander
Abstract:
Decisions in the biomass supply chain influence the size of the
renewable energy feedstock. Indirectly, the use of fossil fuels,
CO2 uptake from the atmosphere, and emissions of CO2 to
the atmosphere are affected. CCS, carbon capture and
storage, is one method to limit total CO2 emissions. The total
decision problem of this system is defined and general
economic decision rules are derived. In typical situations, a
unique global cost minimum can be obtained.
2
The role of the forest?
• The best way to reduce the CO2 in the
atmosphere may be to increase
harvesting of the presently existing
forests (!), to produce energy with CCS
and to increase forest production in the new
forest generations.
• We capture and store more CO2!
3
Energy plant
CCS,
with CO2
capture and
Carbon
separation
Capture and
Storage,
has already
become
Oil field
the main
Coal
future
mine Natural
emission
gas
reduction
method of
the fossile
fuel energy
Permanent storage of CO2
industry
4
How to
reduce the
CO2 level in
the
atmosphere,
Energy plant
with CO2
capture and
separation
CO2
not only to
decrease the
emission of
CO2
Permanent storage of CO2
5
The role of the forest in the CO2
and energy system
• The following six pictures show that it is
necessary to intensify the use of the forest for
energy production in combination with CCS in
order to reduce the CO2 in atmosphere!
• All figures and graphs have been simplified as
much as possible, keeping the big picture
correct, in order to make the main point
obvious.
• In all cases, we keep the total energy
production constant.
6
The present
situation.
CO2
5
1
1
CO2 increase
in the
atmosphere:
5-1 =
4
4
0
Coal,
oil, gas
Permanent storage of CO2
7
CO2
CO2 increase
If we do not
in the
5
use the
1
atmosphere:
forest for
5-1 = 4
energy
production
but use it as
5
a carbon
sink. Before
the forest
Coal,
0
has reached
oil, gas
equilibrium,
this
happens:
Permanent storage of CO2
8
CO2
CO2 increase
If we do not
in the
5
use the
1
atmosphere:
forest for
1
5+1-1 = 5
energy
production
but use it as
5
a carbon
sink. When
the forest
Coal,
0
has reached
oil, gas
equilibrium,
this
happens:
Permanent storage of CO2
9
If we use
CCS with
80%
efficiency
and let the
forest grow
until it
reaches
equilibrium.
CO2
1
1
1
CO2 increase
in the
atmosphere:
1+1-1 =
1
5
4
Coal,
oil, gas
Permanent storage of CO2
10
If we use
CCS with
80%
efficiency
and use the
forest with
”traditional”
low
intensity
harvesting
and
silviculture.
CO2
1
1
1
CO2 increase
in the
atmosphere:
1-1 =
0
4
4
Coal,
oil, gas
Permanent storage of CO2
11
If we use
CCS with
80%
efficiency
and use the
forest with
increased
harvesting
and high
intensity
silviculture.
CO2
1
2
2
CO2 ”increase”
in the
atmosphere:
1-2 =
-1
3
4
Coal,
oil, gas
Permanent storage of CO2
12
General conclusions:
• The best way to reduce the CO2 in the
atmosphere may be to increase
harvesting of the presently existing
forests (!), to produce energy with CCS
and to increase forest production in the new
forest generations.
• We capture and store more CO2!
13
14
min C  Cu (u )  C f ( f )  Ca ( a  v)  Cw ( w)
u ,w
s.t.
u f K
 f  K u
wa  K
a  K w
vu
15
min C  Cu (u)  C f ( K  u)  Ca ( K  u  w)  Cw (w)
u ,w
16
17
C
 Cu (u )  C f ( K  u )  Ca ( K  u  w)  0
u
C
 Ca ( K  u  w)  Cw ( w)
0
w
Cu  C f  Ca
Ca  Cw
18
Observation 1
• In optimum, the marginal cost for forest
biomass utilization equals the marginal cost
of fossil fuel utilization plus the marginal
cost of global warming.
19
Observation 2
• In optimum, the marginal cost of global
warming equals the marginal cost of CCS.
20
C




C
(
u
)

C
(
K

u
)

C
(
K

u

w
)
u
f
a
2
u
2
C
 Ca ( K  u  w)
uw
2
C
 Ca ( K  u  w)
wu
2
C



C
(
K

u

w
)

C
a
w ( w)
2
w
2
21
Second order minimum
conditions:
C

0
2
u
2
C
2
u
2
C
wu
2
C
uw

0
2
C
2
w
2
22
Cu  C f   Ca  0

Cu  C f   Ca
 
Ca

 
Ca

Ca  Cw

0
23
Cu  C f   Ca  Cu  C f   Ca  0
C   C   C   C    C   C   C  C   C   C 





C  
C   C  
u
f
a
a
u
a
a
f
a
a
w
2
a
w
24
C   C   C  C   C    C  
u
f
a
a
w
a
2

   C C   C  
 CuCa  CuCw  C f Ca  C f Cw  Ca
2
a
w
2
a
 CuCa  CuCw  C f Ca  C f Cw  CaCw  0
25

Observations of the first and
second order conditions:
f ( x, y )
 fx  0

f

0
 y
df ( x, y )  f x dx  f y dy  0
26
d f ( x, y)  f xx (dx)  f xy dxdy  f yx dydx  f yy (dy)
2
2
2
f xy  f yx
d 2 f ( x, y )  f xx (dx) 2  f xy dxdy  f yx dydx  f yy (dy ) 2
d f ( x, y ) 
2
au
2

2huv

bv
2
27
d f  au  2huv  bv
2
2
2
h 
 2
2
d f  a  u  2 uv   bv
a 

2
 2
h
h 2
h 2
2
d f  a  u  2 uv  2 v   bv  v
a
a
a


2
2
2
28
2
h 

d f  au  v 
a 

2
 ab  h  2

v
 a 
2
f xx  a  a
f xx
f xy
f yx
f yy

a h
h b
 ab  h
2
29
 a  0    ab  h
2
 0  d f  0
2
h


2
 a  0    ab  h  0    u  v  0   d f  0
a


2
 a  0    ab  h
 a  0    ab  h
2
2
 0   v  0  d f  0
2
 0  u  0  v  0  d f  0
2
30
So, if
and
then
f xx  0
and
f xx
f xy
f yx
f yy
0
 dx  0  dy  0
or
 dx  0  dy  0
or
 dx  0  dy  0
d2 f  0
31
Then, the solution to
 fx  0

f

0
 y
represents a (locally) unique minimum.
32
33
A numerically specified
example:
1

Cu (u )  5  u
20
1
C f  ( f )  10 
f
300
1

Ca ( K  u  w)  0   K  u  w 
20
1

Cw ( w)  14 
w
100
34
35
Comparative statics analysis:
C
 Cu (u )  C f ( K  u )  Ca ( K  u  w)  0
u
C
 Cw ( w)  Ca ( K  u  w)
0
w
36

  

  


 
 C   C   C  du  C  dw  C   C  dK
f
a
a
f
a
 u


Ca du  Cw  Ca dw  Ca dK

37
 1
1
1 
1 
 1 
 1
 20  300  20  du   20  dw   300  20  dK


 



1 
 1 
 1
 1 

du  
  dw    dK



 20 
 100 20 
 20 
38
 31 
 1 
 16 
du

dw

dK






 300


 20 
 300 

  1  du   6  dw   1  dK






  20 
 100 
 20 
39
 16 


 300 
 1 
 
du
 20 

dK  31 


 300 
 1 
 
 20 
 1 
 
 20 
 6 


 100  0.0007

 0.189189189
0.0037
 1 
 
 20 
 6 


 100 
40
 31 


 300 
 1 
 
dw
 20 

dK  31 


 300 
 1 
 
 20 
 16 


 300 
 1 
 
0.0025
 20 

 0.675675675
0.0037
 1 
 
 20 
 6 


 100 
41
Explicit solution of the example
for alternative values of K
C
 Cu (u )  C f ( K  u )  Ca ( K  u  w)  0
u
C
 Cw ( w)  Ca ( K  u  w)
0
w
42
C 
1  
1
1
 

  5  u   10 
( K  u )    0  ( K  u  w)   0
u 
20  
300
20
 

C 
1  
1

 14 
w    0  ( K  u  w) 
0
w 
100  
20

43
C 31
15
16
1500

u
w
K
0
u 300
300
300
300
C
5
6
5
1400

u
w
K
0
w 100
100
100
100
44
 C

 0   31u  15w  16 K  1500  0

 u

 C

 0   5u  6 w  5 K  1400
0

 w

45
 C

 0   31u  15w  16 K  1500  0

 u

 C

 0   5u  6 w  5 K  1400
0

 w

46
 C

 0   31u  15w  1500  16 K

 u

 C

 0   5u  6w  1400  5 K

 w

47
48
1500  16 K
15
1400  5K
u
31 15
6
5

6 1500  16 K   15  1400  5 K 
 31 6    5 15 
6
30000  21K
u
111
49
31 1500  16 K
w
5
1400  5 K 31(1400  5 K )  5(1500  16 K )

31 15
 31 6    5 15 
5
6
50900  75K
w
111
50
Dynamic approach analysis
C
du





u




u
dt

C

dw
w 




w
dt


  1
51
 x  u  ueq

y

w

w
eq

52

 
  







x


C

C

C
x

C
y
u
f
a
a


 y   Ca x
 Cw  Ca y


53

x


m
x

m
y

xx
xy

 y   m yx x  m yy y


54
x(t )  Ae ;
kt
y(t )  Be
kt

 kAe  mxx Ae  mxy Be

kt
kt
kt
kBe


m
Ae

m
Be

yx
yy

kt
kt
kt
55
 kA  mxx A  mxy B

kB


m
A

m
B
yx
yy

56
k  mxx
 m
 yx
mxy   A 0






k  myy   B  0
57
• k is selected in way such that the two
equations become identical. This way,
the equations only determine the ratio
B/A, not the values of A and B. This is
necessary since we must have some
freedom to determine A and B such that
they fit the initial conditions.
• With two roots (that usually are different),
we (usually) get two different ratios B/A.
This makes it possible to fit the
parameters to the (two dimensional)
initial conditions (x(0),y(0)).
58
One way to determine the value(s)
of k is to use this equation:
k  mxx
mxy
myx
k  myy
  k  mxx   k  myy   mxy myx  0
59
mxy  myx
 k  mxx   k  myy    mxy 
2
0
k   mxx  myy  k  mxx myy   mxy   0
2
2
60
Another way to get to the same equation, is to
make sure that the two equations give the
same value to the ratio B/A.
 B   k  mxx  
  k  mxx  A  mxy B  0    A  m 
xy


mxy  myx

B
mxy 

mxy A   k  myy  B  0   
 A  k  myy  



61
  k  mxx 
B 
 
A 
mxy

k  m 
k  m k  m   m   0
k  m  m  k  m m  m 
mxy
yy
2
xx
yy
xy
2
xx
yy
xx
yy
xy
2
0
62
Lets us solve the equation!
m

k 
xx
 myy     mxx  myy  
2

  mxx myy   mxy 

 
2
2


2
m

k 




m
m

m

2



xx
yy
xx
yy

   mxy 

 
2
2


2
63

No cyclical solutions!
• Observe that the expression within the
square root sign is positive.
• As a consequence, only real roots, k, exist.
• For this reason, cyclical solutions to the
differential equation system can be ruled
out.
64
mxx  Cu  C f   Ca
mxy  m yx  Ca


m yy  Cw  Ca
65
C   C   C   C   C      C   C   C    C   C    

k 
  C  



2
2


2
u
f
a
w
u
a
f
a
w
a
a





Cu  C f   Cw  2Ca   Cu  C f   Cw

k 
 
2
2

   C 

 

2
2
a

66
2
C   C   C   2C      C   C   C   


  C 
k 

 
 
2
2

2
u
f
w
a
u
f
w
2
a


• We may observe that



ABS Cu  C f   Cw  ABS Cu  C f   Cw

• As a consequence, both roots to to the equation are
strictly negative.
• Therefore, divegence from the equilibrium
solution is ruled out.
67
• With only strictly negative roots, we have a
guaranteed convergence to the equilibrium.
• However, this does not have to be monotone.
• With two different roots (k1 and k2) and with
parameters A1 and A2 with different signs
(and/or parameters B1 and B2 with different
signs), the sign(s) of the deviation(s) from the
equilibrium value(s) may change over time.
68
Derivation of the roots in the
example:
1
1
1 
 1

 
 
20 300 100 10  

k 

2
2
 1
1
1 
  20  300  100    1  2
 

 
2

  20 




69
49   13 
1
k 



600   600  400
2
k1  0.081667  0.054493
k1  0.13616
k2  0.081667  0.054493
k2  0.027174
70
 x(t )  A1e  A2e

k1t
k2 t
y
(
t
)

B
e

B
e

1
2
k1t
k2 t
71
We may determine the path
completely using the initial
conditions
 x(0), y(0)    x0 , y0 
72
We also use the earlier derived
results:
B

A
mxy
  k  mxx 

mxy
 k  myy 
73
Using the derived roots, we get:
  k1  mxx 
B1 
A1
mxy
A2 
 mxy
 k2  mxx 
B2
74
m

xy
k1t
k2t
x
(
t
)

A
e

B
e
1
2

k

m

2
xx 



k

m

1
xx 
k1t
k2 t
 y (t ) 
A1e  B2e

m
xy

75
Let us use the initial conditions
and determine the parameters!
mxy

x

A

B
1
2
 0
k

m

2
xx 



k

m


1
xx
y 
A

B
0
1
2

m
xy

76

1


 k  m 
1
xx

mxy




 k2  mxx    A1   x0 
 


  B2   y0 

1

mxy
77
x0
A1 

mxy
 k2  mxx 
y0
1
  k1  mxx 
mxy
1

mxy
 k2  mxx 
 mxy

x0  
 y0
 k2  mxx  


k1  mxx 

1
 k2  mxx 
1
78
1
B2 
  k1  mxx 
mxy
1
  k1  mxx 
mxy

x0
y0
mxy
 k2  mxx 
  k1  mxx  
y0  
x0

 m

xy



k1  mxx 

1
 k2  mxx 
1
79
Using the figures from the
example, we get:
x0  0.6565 y0
A1 
1.431
y0  0.6565 x0
B2 
1.431
80
The solutions to the
numerically specified example
X(t) = -106.63·EXP(- 0.13612·t) + 6.61·EXP(- 0.02718·t)
81
Y(t) = - 69.95·EXP(- 0.13612·t) - 10.07·EXP(- 0.02718·t)
82
83
The cost function
from different
perspectives:
(based on the numerically
specified example)
84
85
86
Numerical solution of the
example problem using direct
minimization:
87
K = 600
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
model:
min = C;
k = 600;
C = cu + cf + ca + cw;
cu = 5*u+1/40*u^2;
cf = 10*f + 1/600*f^2;
ca = 1/40*(k-u-w)^2;
cw = 14*w+1/200*w^2;
f = k-u;
a = k-w;
@free(anet);
anet = a - u;
@free(eqw);
31*equ+15*eqw=1500 + 16*k;
5*equ+6*eqw = -1400+5*k;
end
88
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Variable
C
K
CU
CF
CA
CW
U
F
W
A
ANET
EQW
EQU
Value
8975.806
600.0000
4995.578
2516.909
1463.319
0.000000
358.0645
241.9355
0.000000
600.0000
241.9355
-53.15315
383.7838
Reduced Cost
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
1.903226
0.000000
0.000000
0.000000
0.000000
89
K = 800
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
model:
min = C;
k = 800;
C = cu + cf + ca + cw;
cu = 5*u+1/40*u^2;
cf = 10*f + 1/600*f^2;
ca = 1/40*(k-u-w)^2;
cw = 14*w+1/200*w^2;
f = k-u;
a = k-w;
@free(anet);
anet = a - u;
@free(eqw);
31*equ+15*eqw=1500 + 16*k;
5*equ+6*eqw = -1400+5*k;
end
90
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Variable
C
K
CU
CF
CA
CW
U
F
W
A
ANET
EQW
EQU
Value
13952.25
800.0000
6552.228
4022.401
2196.271
1181.353
421.6216
378.3784
81.98198
718.0180
296.3964
81.98198
421.6216
Reduced Cost
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
91
K = 1000
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
model:
min = C;
k = 1000;
C = cu + cf + ca + cw;
cu = 5*u+1/40*u^2;
cf = 10*f + 1/600*f^2;
ca = 1/40*(k-u-w)^2;
cw = 14*w+1/200*w^2;
f = k-u;
a = k-w;
@free(anet);
anet = a - u;
@free(eqw);
31*equ+15*eqw=1500 + 16*k;
5*equ+6*eqw = -1400+5*k;
end
92
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Variable
C
K
CU
CF
CA
CW
U
F
W
A
ANET
EQW
EQU
Value
19357.66
1000.000
7574.872
5892.379
2615.068
3275.339
459.4595
540.5405
217.1171
782.8829
323.4234
217.1171
459.4595
Reduced Cost
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
93
Numerical approximation of the
dynamics:
•
•
•
•
•
•
•
•
•
•
•
•
! dynsim;
! Peter Lohmander Valencia 20100222;
model:
sets:
time/1..100/:x,y,dx,dy;
endsets
cxx = 31/300;
cxy = 15/300;
cyx = 15/300;
cyy = 18/300;
x(1) = -100;
y(1) = -80;
94
• @FOR( time(t): dx(t)= -( cxx*x(t) + cxy*(y(t)) ));
• @FOR( time(t): dy(t)= -( cyx*x(t) + cyy*(y(t)) ));
• @FOR( time(t)| t#GT#1: x(t)= x(t-1) + dx(t-1) );
• @FOR( time(t)| t#GT#1: y(t)= y(t-1) + dy(t-1) );
•
•
•
•
@for(time(t): @free(x(t)));
@for(time(t): @free(y(t)));
@for(time(t): @free(dx(t)));
@for(time(t): @free(dy(t)));
• end
95
Conclusions
Global warming, forest policy, energy policy and CCS should be studied
as one system. This way, the economically most efficient solution can
be obtained.
General and optimal decision rules have been derived.
In typical situations, a unique global cost minimum can be obtained.
We should, in the optimally coordinated way:
-
Increase harvesting of the presently existing forests.
-
Use more biomass from the forests to produce energy.
-
Increase forest production in the new forest plantations.
-
Increase the use of CCS.
96
References
•
Lohmander, P., Adaptive Optimization of Forest Management in a Stochastic World, in
Weintraub A. et al (Editors), Handbook of Operations Research in Natural Resources,
Springer, Springer Science, International Series in Operations Research and Management
Science, New York, USA, pp 525-544, 2007
http://www.amazon.ca/gp/reader/0387718141/ref=sib_dp_pt/701-07349921741115#reader-link
•
Lohmander, P,. Energy Forum, Stockholm, 6-7 February 2008, Conference program with
links to report and software by Peter Lohmander:
http://www.energyforum.com/events/conferences/2008/c802/program.php
http://www.lohmander.com/EF2008/EF2008Lohmander.htm
•
Lohmander, P., Ekonomiskt rationell utveckling för skogs- och energisektorn i Sverige,
Nordisk Papper och Massa, Nr 3, 2008
•
Lohmander, P., Guidelines for Economically Rational and Coordinated Dynamic
Development of the Forest and Bio Energy Sectors with CO2 constraints, Proceedings
from the 16th European Biomass Conference and Exhibition, Valencia, Spain, 02-06 June,
2008 (In the version in the link, below, an earlier misprint has been corrected. )
http://www.Lohmander.com/Valencia2008.pdf
97
•
Lohmander, P., Economically Optimal Joint Strategy for Sustainable Bioenergy and Forest Sectors
with CO2 Constraints, European Biomass Forum, Exploring Future Markets, Financing and
Technology for Power Generation, CD, Marcus Evans Ltd, Amsterdam, 16th-17th June, 2008
http://www.Lohmander.com/Amsterdam2008.ppt
•
Lohmander, P., Ekonomiskt rationell utveckling för skogs- och energisektorn, Nordisk Energi, Nr. 4,
2008
•
Lohmander, P., Optimal resource control model & General continuous time optimal control model
of a forest resource, comparative dynamics and CO2 consideration effects, SLU Seminar in Forest
Economics, Umea, Sweden, 2008-09-18 http://www.lohmander.com/CM/CMLohmander.ppt
•
Lohmander, P., Tools for optimal coordination of CCS, power industry capacity expansion and bio
energy raw material production and harvesting, 2nd Annual EMISSIONS REDUCTION FORUM: Establishing Effective CO2, NOx, SOx Mitigation Strategies for the Power Industry, CD, Marcus
Evans Ltd, Madrid, Spain, 29th & 30th September 2008
http://www.lohmander.com/Madrid08/Madrid_2008_Lohmander.ppt
•
Lohmander, P., Optimal CCS, Carbon Capture and Storage, Under Risk, International Seminars in
Life Sciences, Universidad Politécnica de Valencia, Thursday 2008-10-16
http://www.lohmander.com/OptCCS/OptCCS.ppt
98
•
Lohmander, P., Economic forest production with consideration of the forest and energy industries, E.ON International
Bioenergy Conference, Malmo, Sweden, 2008-10-30 http://www.lohmander.com/eon081030/eon081030.ppt
•
Lohmander, P., Optimal dynamic control of the forest resource with changing energy demand functions and valuation
of CO2 storage, UE2008.fr, The European Forest-based Sector: Bio-Responses to Address New Climate and Energy
Challenges? Nancy, France, November 6-8, 2008 http://www.lohmander.com/Nancy08/Nancy08.ppt (See also later
versions 2009)
•
Lohmander, P., Optimal dynamic control of the forest resource with changing energy demand functions and valuation
of CO2 storage, The European Forest-based Sector: Bio-Responses to Address New Climate and Energy
Challenges, Nancy, France, November 6-8, 2008, Proceedings: (forthcoming) in French Forest Review (2009)
Abstract: Page 65 of: http://www.gip-ecofor.org/docs/34/rsums_confnancy2008__20081105.pdf
Presentation as pdf: http://www.gipecofor.org/docs/nancy2008/ppt_des_presentations_orales/lohmander_session_3.1.pdf
Conference: http://www.gip-ecofor.org/docs/34/nancy2008englishprogramme20081106.pdf
•
ECOFOR, (in French) Summary of results by Peter Lohmander (on page 8) in “Evaluation du developpement de la
bioenergie”, in Bulletin d’information sur les forets europeennes, l’energie et climat, Volume 157, Numero 1, Lundi 10
novembre 2008 http://www.gip-ecofor.org/docs/34/nancy2008synthseiisd.pdf
•
IISD, Summary of results by Peter Lohmander (on page 6) in “Evaluation of Bioenergy Development”, in European
Forests, Energy and Climate Bulletin, Published by the International Institute for Sustainable Development (IISD)
http://www.iisd.org/ , Vol. 157, No. 1, Monday, 10 November, 2008
http://www.iisd.ca/download/pdf/sd/ymbvol157num1e.pdf
99
•
Lohmander, P., Integrated Regional Study Stage 1., Presentation at the E.ON Holmen - Sveaskog - SLU Research Meeting, Norrköping, Sweden, 2008-12-10
– 2008-12-11, http://www.lohmander.com/NorrDec08/NorrDec08.ppt ,
http://www.lohmander.com/NorrDec08/NorrDec08.pdf ,
http://www.lohmander.com/NorrDec08/NorrDec08RawData.xls
•
Lohmander, P., Öka avverkningen och hjälp Sverige ur krisen, VI
SKOGSÄGARE, Debatt, Nr. 1, 2009
http://www.lohmander.com/PLdebattVIS2009nr1.pdf
•
Lohmander, P., Economic Forest Production with Consideration of the Forest
and Energy Industries (SLU 2009-01-29),
http://www.lohmander.com/SLU09/SLU09.pdf
http://www.lohmander.com/SLU09/SLU09.ppt
•
Lohmander, P., Rational and sustainable international policy for the forest sector
with consideration of energy, global warming, risk, and regional development,
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•
Lohmander, P., Strategic options for the forest sector in Russia with focus on
economic optimization, energy and sustainability
(Full paper in English with short translation to Russian), ICFFI News, Vol. 1,
Number 10, March 2009
http://www.Lohmander.com/RuMa09/RuMa09.htm
100
•
International seminar, ECONOMICS OF FORESTRY AND FOREST
SECTOR: ACTUAL PROBLEMS AND TRENDS, St Petersburg, Russia,
March 2009, http://www.lohmander.com/RuMa09/ProgramRuMa09.pdf
•
Lohmander, P., Satsa på biobränsle, Skogsvärden, Nr 1, 2009
http://www.Lohmander.com/PL_SV_1_09.jpg
•
Lohmander, P., Stor potential för svensk skogsenergi, Nordisk Energi,
Nr. 2, 2009
http://www.Lohmander.com/Information/ne1.jpg
http://www.Lohmander.com/Information/ne2.jpg
http://www.Lohmander.com/Information/ne3.jpg
http://www.Lohmander.com/PL_SvSE_090205.pdf
http://www.Lohmander.com/PL_SvSE_090205.doc
•
Lohmander, P., Strategiska möjligheter för skogssektorn i Ryssland
Nordisk Papper och Massa, Nr 2, 2009
http://www.Lohmander.com/PL_NPM_2_2009.pdf
http://www.Lohmander.com/PL_RuSwe_09.pdf
http://www.Lohmander.com/PL_RuSwe_09.doc
101
• Lohmander, P., Economic forest production with consideration of
the forest- and energy industries, Project meeting presentation,
Stockholm, Sweden, 2009-05-11,
http://www.lohmander.com/EON_090511.ppt
• Lohmander, P., Derivation of the Economically Optimal Joint
Strategy for Development of the Bioenergy and Forest Products
Industries, European Biomass and Bioenergy Forum,
MarcusEvans, London, UK, 8-9 June, 2009,
http://www.lohmander.com/London09/London_Lohmander_09.p
pt & ttp://www.lohmander.com/London09.pdf
• Lohmander, P., Rational and sustainable international policy for
the forest sector - with consideration of energy, global warming,
risk, and regional development, Preliminary plan, 2009-08-05,
http://www.lohmander.com/ip090805.pdf
102