Methodology for optimization of continuous cover
forestry with consideration of recreation and the
forest and energy industries
Методология оптимизации непрерывного
неистощительного
лесопользования, как для обеспечения
рекреационных услуг, так и для
переработки в лесной и энергетической
промышленности
Peter Lohmander & Zazykina Liubov
FORESTS OF EURASIA - PODMOSKOVNY VECHERA
Moscow State Forest University
September 19 - 25, 2010
1
Профессор Петер Ломандер
Шведский университет
сельского хозяйства
(SLU), 90183 Умео, Швеция
Электронная почта:
[email protected]
[email protected]
http://www.Lohmander.com
Аспирантка Зазыкина Любовь
Московский государственный
университет
леса (МГУЛ)
1-ая институтская ул., Мытищи,
Московская обл., Россия
Электронная почта:
[email protected]
2
Professor Peter Lohmander
Department of Forest Economics,
Faculty of Forest Science,
Swedish University of
Agricultural Sciences (SLU),
SE – 901 83 Umea, Sweden
Профессор Петер Ломандер
Шведский университет
сельского хозяйства
(SLU),
90183 Умео, Швеция
[email protected]
[email protected]
[email protected]
[email protected]
Web: http://www.Lohmander.com
Web: http://www.Lohmander.com
[email protected]
[email protected]
3
Forests are used for many
different purposes. It is important
to consider these simultaneously.
A new methodological approach
to optimization of forest
management with consideration
of recreation and the forest and
energy industries has been
developed.
It maximizes the total present
value of continuous cover forest
management and takes all
relevant costs and revenues into
account, including set up costs.
Леса используются и могут
использоваться в разных
целях.
Важно учесть все эти цели
одновременно, разработан
новый методологический
подход к оптимизации
лесопользовании с учетом
обеспечения рекреационных
услуг, переработки в лесной и
энергетической
промышленности.
Он максимизирует общую
текущую дисконтированную
стоимость непрерывного
неистощительного
лесопользования и учитывает
все затраты будущего периода
и доходы, включая начальные
затраты.
4
In several regions, in particular
close to large cities, such as
Paris and Moscow, the economic
importance of recreation forestry
is very high in relation to the
economic results obtained from
traditional “production oriented”
forest management.
This does however not
automatically imply that
production of timber, pulpwood
and energy assortments can not
be combined with rational
recreation forestry.
В некоторых районах, в
особенности вблизи больших
городов, таких как Париж или
Москва, экономическая
важность рекреационного
лесопользования очень
высока, по сравнению с
экономическими результатами
полученными при
традиционным
лесопользовании.
Однако, это не означает
автоматически, что
рациональное рекреационное
лесопользование не может
быть скомбинировано с
производством
пиломатериалов, целлюлозы и
энергии.
5
The optimization model includes
one section where the utility of
recreation, which may be
transformed to the present value
of net revenues from recreation,
is added to the traditional
objective function of the present
value of the production of timber,
pulpwood and energy
assortments.
In typical cases, individuals
interested in recreation prefer
forests with low density.
Использование рекреационных
услуг , которое может быть
преобразовано в величину чистых
доходов, от этих услуг и обавлено
к традиционным целевым
доходам от производства
пиломатериалов, целлюлозы и
энергии.
В типичных случаях,
предпочитаются леса под
рекреацию с низкой плотностью
насаждений, это означает, что
лесопользование является
оптимальным, когда учитываются
все цели при осуществлении
более частых рубок ухода в
отличие от лесопользования,
которое направлено только на
производство пиломатериалов
целлюлозы и энергии.
6
This means that forest
management that is optimal
when all objectives are
considered, typically is
characterized by larger thinning
harvests than forest
management that only focuses
on the production of timber,
pulpwood and energy
assortments.
же влияние на
оптимизацию
лесопользования, как
увеличивающаяся
важность рекреационных
услуг в зонах близких, к
большим городам.
7
The results also show that large
set up costs have the same type
of effect on optimal forest
management as an increasing
importance of recreation, close
to large cities.
Both of these factors imply that
the harvest volumes per occation
increase and that the time
interval between harvests
increases.
Even rather small set up costs
imply that the continuous cover
forest management schedule
gives a rather large variation in
the optimal stock level over time.
Оба этих фактора
подразумевают, что объем
вырубок на ед.
времени увеличиваются , а так
же увеличивается сам
временной интервал между
вырубками.
Сравнительные малые
начальные затраты означают
что апланированное
непрерывное
неистощительное
лесопользование дает
относительно много вариаций
оптимального уровня запаса
древесины во времени.
8
Typical Forest Stock Development Without Harvesting
400
350
m3 / ha
300
250
200
150
100
50
0
0
20
40
60
80
100
120
Time (Years)
9
Growth

dx
2
x
 ax  bx
dt
x  Stock
(m3 / ha)
Compare:
Verhulst, Pierre-François (1838). "Notice sur la loi que la population poursuit dans son accroissement".
Correspondance mathématique et physique 10: pp. 113–121.
10
Growth
6
m3/ha/year
5
4
3
2
1
0
0
50
100
150
200
250
300
350
400
450
Stock (m3/ha) = x

dx 1
1
2
Growth  x 

x
x
dt 20
8000
11
Stock = x(t)
400
350
m3 / ha
300
250
200
150
100
50
0
0
20
40
60
80
100
120
Time (Years) = t

dx 1
1
2
x

x
x
dt 20
8000
12
A separable differential equation

dx
2
x
 ax  bx
dt
1
dx

dt
2
ax  bx
13
1
dx  dt
2
ax  bx
c
D
1
1



2
x (a  bx) x(a  bx) ax  bx
c(a  bx)  Dx
1

2
x(a  bx)
ax  bx
14
c(a  bx)  Dx
1

2
x(a  bx)
ax  bx
ca  cbx  Dx  1
ca  (cb  D) x  1
1
c
a
b
D  cb 
a
15
1
dx  dt
2
ax  bx
c
D 
 
 dx  dt
 x (a  bx) 
1
b 
  
a
     a   dx  dt
(a  bx ) 
 x




1
b 
 
 dx  a dt
 x (a  bx) 
16
1
b 
 
 dx  a dt
 x (a  bx) 
1
b 

dx

a
dt


x  x (a  bx)  t
0
0
x1
t1
17


x1
t1
1
1 
x  x  a  dx  t a dt
0 
0
(  x) 

b


1
1 

dx

a
dt


x  x (h  x)  t
0
0
x1
t1
a
h
b
a
h
b
18
1
1 

dx

a
dt


x  x (h  x)  t
0
0
x1
t1
a
h
b
 LN ( x)  LN (h  x)x   at t
x1
t1
0
0
LN ( x1 )  LN (h  x1 )  LN ( x0 )  LN (h  x0 )  a(t1  t0 )
 x1 (h  x0 ) 
LN 
  aT
 x0 (h  x1 ) 
T  t1  t0
19
 x1 (h  x0 ) 
LN 
  aT
 x0 (h  x1 ) 
T  t1  t0
x1 (h  x0 )
aT
e
x0 (h  x1 )
aT
x0 e
x1

(h  x1 ) (h  x0 )
aT
x0 e
x1 
(h  x1 )
(h  x0 )
20
aT
x0 e
x1 
(h  x1 )
(h  x0 )

x0e 
x0e
x1 1 
h
(h  x0 )
 (h  x0 ) 
aT
aT
aT
x0 e
h
(h  x0 )
x1 
aT
x0 e
1
(h  x0 )
21
x0 e aT
h
(h  x0 )
x1 
x0 e aT
1
(h  x0 )
1
x1 
(h  x0 )  aT 1
e 
hx0
h
1
x1 
 1 1   aT 1
  e 
h
 x0 h 
22
x1 
1
1  1 1   aT
  e
h  x0 h 
23
Stock (m3/ha)
Time (Years)
24
Stock Development
140
120
m3 / ha
100
80
60
40
20
0
0
10
20
30
40
50
60
70
80
Time (Years)
25
The Present Value Function
c  ph1 (t , h0 ) 

(.)   c  ph0  
rt
e 1
Profit from the
first harvest
Present value of an infinite
series of profits from
the later harvest
Stock Development
140
120
m3 / ha
100
80
60
40
20
0
0
10
20
30
40
Time (Years)
50
60
70
80
26
 c  ph0 
c  ph1 (t , h0 ) 


e 1
rt
Initial stock level
Rate of interest
Harvest interval
27
*
*
*
28
Present Value (SEK/ha)
y=250
y=200
y=150
y = First Harvest
Volume (m3/ha)
Harvest Interval (Years)
29
C = 500
Vertical Scale = Present Value (SEK/ha)
Harvest Interval (Years)
First Harvest Volume (m3/ha)
30
C = 500
First Harvest Volume
(m3/ha)
Vertical Scale = Present Value (SEK/ha)
Harvest Interval (Years)
31
C = 500
First Harvest Volume
(m3/ha)
Vertical Scale = Present Value (SEK/ha)
Harvest Interval (Years)
32
C = 500
First Harvest Volume
(m3/ha)
Vertical Scale = Present Value (SEK/ha)
Harvest Interval (Years)
33
Stock Level Directly
After Harvest (m3/ha)
C = 100
First Harvest Volume
(m3/ha)
34
C = 100
Vertical Scale = Present Value (SEK/ha)
Stock Level Directly
After Harvest (m3/ha)
Harvest Interval (Years)
35
C = 100
C = 500
36
Vertical Scale = Present Value (SEK/ha)
C = 100
C = 500
Stock Level Directly
After Harvest (m3/ha)
Harvest Interval (Years)
37
C = 2000
38
C = 2000
Stock Level Directly
After Harvest (m3/ha)
Vertical Scale = Present Value (SEK/ha)
Harvest Interval (Years)
39
Vertical Scale = Present Value (SEK/ha)
C = 100
C = 2000
Harvest Interval (Years)
Stock Level Directly
After Harvest (m3/ha)
40
Vertical Scale = Present Value (SEK/ha)
C = 100
C = 500
Harvest Interval (Years)
Stock Level Directly
After Harvest (m3/ha)
41
REM
REM CCF0403
REM Peter Lohmander
REM
OPEN "outCCF.dat" FOR OUTPUT AS #1
PRINT #1, " x1 t h1 PV"
FOR x1 = 10 TO 150 STEP 20
FOR t = 1 TO 31 STEP 5
c = 500
p = 200
r = .03
s = .05
x0 = 300
h0 = x0 - x1
x2 = 1 / (1 / 400 + (1 / x1 - 1 / 400) * EXP(-.05 * t))
h1 = x2 - x1
multip = 1 / (EXP(r * t) - 1)
pv0 = -c + p * h0
pv1 = -c + p * h1
PV = pv0 + pv1 * multip
PRINT #1, USING "####"; x1;
PRINT #1, USING "####"; t;
PRINT #1, USING "####"; h1;
PRINT #1, USING "#######"; PV
NEXT t
NEXT x1
CLOSE #1
END
42
x1
t h1
PV
90
90
90
90
90
90
90
1 4
6 23
11 44
16 67
21 91
26 116
31 141
48299
61906
62679
62441
61755
60768
59561
110
110
110
110
110
110
110
1
4
6 25
11 49
16 73
21 98
26 123
31 146
47561
60776
61115
60419
59276
57858
56266
130
130
130
130
130
130
130
1
4
6 28
11 52
16 77
21 102
26 125
31 148
46144
58919
58802
57656
56094
54309
52414
43
REM
REM OCC0403
REM Peter Lohmander
REM
OPEN "outOCC.dat" FOR OUTPUT AS #1
PRINT #1, " C X1opt topt PVopt h1opt x2opt"
FOR c = 0 TO 3000 STEP 100
FOPT = -999999
x1opt = 0
topt = 0
pvopt = 0
h1opt = 0
x2opt = 0
44
FOR x1 = 10 TO 150 STEP 5
FOR t = 1 TO 61 STEP 1
p = 200
r = .03
s = .05
x0 = 300
h0 = x0 - x1
x2 = 1 / (1 / 400 + (1 / x1 - 1 / 400) * EXP(-.05 * t))
h1 = x2 - x1
multip = 1 / (EXP(r * t) - 1)
pv0 = -c + p * h0
pv1 = -c + p * h1
PV = pv0 + pv1 * multip
IF PV > pvopt THEN x1opt = x1
IF PV > pvopt THEN topt = t
IF PV > pvopt THEN h1opt = h1
IF PV > pvopt THEN x2opt = x2
IF PV > pvopt THEN pvopt = PV
NEXT t
NEXT x1
PRINT #1, USING "######"; c; x1opt; topt; pvopt; h1opt; x2opt
NEXT c
CLOSE #1
END
45
X1opt(C)
Optimal Stock Level Directly
After Harvest (m3/ha)
90
80
70
X1opt
60
50
40
30
20
10
0
0
500
1000
1500
2000
C
2500
3000
3500
Set up Cost (SEK/ha)
46
Optimal Stock Level Directly
Before Thinning Harvest (m3/ha)
x2opt(C)
180
160
140
x2opt
120
100
80
60
40
20
0
0
500
1000
1500
2000
C
2500
3000
3500
Set up Cost (SEK/ha)
47
h1opt(C)
Optimal Thinning Harvest Volumes per occation (m3/ha)
140
120
h1opt
100
80
60
40
20
0
0
500
1000
1500
2000
C
2500
3000
3500
Set up Cost (SEK/ha)
48
Optimal Harvest Interval (Years)
topt(C)
45
40
35
topt
30
25
20
15
10
5
0
0
500
1000
1500
2000
C
2500
3000
3500
Set up Cost (SEK/ha)
49
Optimal Present Value (SEK/ha)
PVopt(C)
66000
65000
PVopt
64000
63000
62000
61000
60000
59000
0
500
1000
1500
2000
C
2500
3000
3500
Set up Cost (SEK/ha)
50
What happens to the optimal forest
management schedule if we also
consider the value of recreation?
51
Alekseevskiy forest
•Source: Zazykina, L., Lohmander, P., The utility of recreation as a function , of site
characteristics: Methodological suggestions and a preliminary analysis, Proceedings of the
II international workshop on Ecological tourism, rends and perspectives on development in
the global world, Saint Petersburg Forest Technical Academy, April 15-16, 2010 ,
http://www.Lohmander.com/SPb201004/Zazykina_Lohmander_SPbFTA_2010.pdf
http://www.Lohmander.com/SPb201004/Zazykina_Lohmander_SPbFTA_2010.doc
52
•
Source: Zazykina, L., Lohmander, P., The utility of recreation as a function , of site characteristics: Methodological suggestions and a
preliminary analysis, Proceedings of the II international workshop on Ecological tourism, rends and perspectives on development in the
global world, Saint Petersburg Forest Technical Academy, April 15-16, 2010 ,
http://www.Lohmander.com/SPb201004/Zazykina_Lohmander_SPbFTA_2010.pdf
http://www.Lohmander.com/SPb201004/Zazykina_Lohmander_SPbFTA_2010.doc
53
Interpretations and
observations:
#1: Several alternative interpretations are
possible!
#2: Furthermore, the results are most likely
sensitive to local conditions, weather
conditions etc..
54
Assumptions:
The ideal average forest density, from a recreational point of view, is 0.5.
Directly before thinning, the density is 0.8 .
As a result of a thinning, the density in a stand is reduced in proportion
to the harvest volume.
The density of a stand is a linear function of time between thinnings.
The value of recreation is a quadratic function of average stand density
in the forest area.
The recreation value is zero if the density is 0 or 1.
Under optimal density conditions, the value of recreation, per individual,
hectare and year, is 30 EURO. (The value 30 has no empirical
background.)
55
Annual Value of Recreation per Visitor
35
30
EURO / Hectare
25
20
15
10
5
0
0
0,2
0,4
0,6
0,8
1
1,2
Stand Density
Approximation in the software:
•
•
•
•
•
D = .8 * ((x1 + x2) / (2 * x2))
IF D < 0 THEN D = 0
IF D > 1 THEN D = 1
U = 120 * D - 120 * D * D
PVtotU = n / r * U
56
Forest visitors seem to prefer forests with
rather high basal area levels during hot periods.
N(Y) Regression curve
25
N = Pers
20
15
10
5
0
-5 0
20
40
60
80
Y = m2perha
N(Y) = Number of persons per 100 m2 a function of
Y = Basal Area (m2/ha), Moscow
DURING THE VERY HOT SUMMER OF 2010
57
N   29.6  1.52 Y  0.0148 Y
2
N(Y) Regression curve
25
N = Pers
20
15
10
5
0
-5 0
20
40
60
80
Y = m2perha
N  Number of persons per 100 m 2
Y  Basal area (m2 / ha)
58
59
60
What was the most popular basal area
during the hot summer of 2010 from a
recreational point of view?
61
Scenic Beauty, SB, as a function of basal area, BA. The
graph has been constructed using equation
SB = 5.663 – 4.086 BA/t + 16.148 ln (BA), which is found in
Hull & Buhyoff (1986).
62
Optimization of present value of
roundwood production and
recreation
63
•
•
•
•
•
REM OP100409
REM Peter and Luba
REM
OPEN "outOP.txt" FOR OUTPUT AS #1
PRINT #1, " n x1opt topt h1opt x2opt
pvopt
optPV opttotU"
•
•
•
•
•
•
•
•
•
•
FOR n = 0 TO 550 STEP 55
pvopt = -9999999
optpv = -9999999
x1opt = 0
topt = 0
h1opt = 0
x2opt = 0
c = 50
p = 40
r = .03
64
• FOR x1 = 10 TO 150 STEP 5
• FOR t = 1 TO 100 STEP 1
• x0 = 158
• h0 = x0 - x1
• x2 = 1 / (1 / 316 + (1 / x1 - 1 / 316) * EXP(-.0848 * t))
• h1 = x2 - x1
• multip = 1 / (EXP(r * t) - 1)
• pv0 = -c + p * h0
• pv1 = -c + p * h1
• PV = pv0 + pv1 * multip
65
•
•
•
•
•
D = .8 * ((x1 + x2) / (2 * x2))
IF D < 0 THEN D = 0
IF D > 1 THEN D = 1
U = 120 * D - 120 * D * D
PVtotU = n / r * U
•
TPV = PV + PVtotU
•
•
•
•
•
•
•
IF TPV > pvopt THEN x1opt = x1
IF TPV > pvopt THEN topt = t
IF TPV > pvopt THEN h1opt = h1
IF TPV > pvopt THEN x2opt = x2
IF TPV > pvopt THEN optpv = PV
IF TPV > pvopt THEN opttotU = PVtotU
IF TPV > pvopt THEN pvopt = TPV
• NEXT t
• NEXT x1
66
Annual Value of Recreation per Visitor
35
30
EURO / Hectare
25
20
15
10
5
0
0
0,2
0,4
0,6
0,8
1
1,2
Stand Density
Approximation in the software:
•
•
•
•
•
D = .8 * ((x1 + x2) / (2 * x2))
IF D < 0 THEN D = 0
IF D > 1 THEN D = 1
U = 120 * D - 120 * D * D
PVtotU = n / r * U
67
• PRINT #1, USING "######"; n; x1opt; topt;
• PRINT #1, USING "######"; h1opt; x2opt;
• PRINT #1, USING "########.##"; pvopt; optpv;
opttotU
• NEXT n
• CLOSE #1
• END
68
Optimal results:
(outOP.txt)
69
x1opt
Optimal stock level directly after harvest
80
cubic metres per hectare
70
60
50
40
30
20
10
0
0
100
200
300
400
500
600
Visitors per hectare and year
70
x2opt
Optimal stock level directly before harvest
cubic metres per hectare at the time of harvest
180
160
140
120
100
80
60
40
20
0
0
100
200
300
400
500
600
Visitors per hectare and year
71
h1opt
Optimal thinning volume per occation
cubic metres per hectare and occation
140
120
100
80
60
40
20
0
0
100
200
300
400
500
600
Visitors per hectare and year
72
topt
Optimal time interval between thinnings
25
20
years
15
10
5
0
0
100
200
300
400
500
600
Visitors per hectare and year
73
Present values of forest harvesting and recreation
600000
EURO per hectare
500000
400000
pvopt
300000
optPV
opttotU
200000
100000
0
0
100
200
300
400
500
600
Visitors per hectare and year
In forest areas with many visitors, close to large cities, the present value
of recreation may be much higher than the present value of timber production.
74
Upper and lower optimal stock levels as a function
of time and the number of visitors
180
160
cubic metres per hectare
140
120
x0_1
100
x0_2
x55_1
80
x55_2
60
40
20
0
0
50
100
150
200
250
300
Time (years)
75
The case with no visitors
76
The case with many visitors that
prefer low density forests
77
Conclusions:
A new methodological approach to optimization of
forest management with consideration of recreation
and the forest and energy industries has been
developed.
It maximizes the total present value of continuous
cover forest management and takes all relevant
costs and revenues into account, including set up
costs.
Optimal solutions to empirically investigated cases
have been analysed and reported.
78
Thank you for listening!
Questions?
79