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Introduction Model Conclusions and Further work
A Stochastic Approach to Optimize EucalyptStand Management Scheduling, Under Fire Risk
Liliana FerreiraESTG*, Instituto Politecnico de Leiria
Joint work with:
M. ConstantinoCIO-DEIO, Faculdade de Ciencias da Universidade de Lisboa
J.G. Borges; J.Garcia-GonzalezCentro de Estudos Florestais, Instituto Superior de Agronomia
ALIOS-INFORMS Buenos Aires, Argentina 6-9 June*ESTG - Escola Superior de Tecnologia e Gestao
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Outline
1 Introduction
2 ModelStochastic Dynamic ProgrammingResultsSensitivity Analysis
3 Conclusions and Further work
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Outline
1 Introduction
2 ModelStochastic Dynamic ProgrammingResultsSensitivity Analysis
3 Conclusions and Further work
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Introduction
Forest Management:
Stand level;
Landscape level.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Introduction
Forest Management:
Stand level;
Landscape level.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Introduction
Forest Management:
Stand level;
Landscape level.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Concepts
Rotation length:
period of time since the stand is planted until it is clearcut;
Coppice cycle:
period of time since the stand regenerates until it is harvested;
Soil expectation value:
financial criterion used to make even-aged timbermanagement decisions;
present value of a perpetual series of even-aged rotations.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Concepts
Rotation length:
period of time since the stand is planted until it is clearcut;
Coppice cycle:
period of time since the stand regenerates until it is harvested;
Soil expectation value:
financial criterion used to make even-aged timbermanagement decisions;
present value of a perpetual series of even-aged rotations.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Concepts
Rotation length:
period of time since the stand is planted until it is clearcut;
Coppice cycle:
period of time since the stand regenerates until it is harvested;
Soil expectation value:
financial criterion used to make even-aged timbermanagement decisions;
present value of a perpetual series of even-aged rotations.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Research Aim
Development of an optimization forest management scheduling model:
at stand level;
with a stochastic element - wildfire risk;
Eucalyptus globulus Labill stand (even aged stand);
for short rotation coppice systems;
maximizes the soil expectation value;
finds the optimal harvest age in each cycle;
determines the optimal number of coppice cycles within a fullrotation.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Research Aim
Development of an optimization forest management scheduling model:
at stand level;
with a stochastic element - wildfire risk;
Eucalyptus globulus Labill stand (even aged stand);
for short rotation coppice systems;
maximizes the soil expectation value;
finds the optimal harvest age in each cycle;
determines the optimal number of coppice cycles within a fullrotation.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Research Aim
Development of an optimization forest management scheduling model:
at stand level;
with a stochastic element - wildfire risk;
Eucalyptus globulus Labill stand (even aged stand);
for short rotation coppice systems;
maximizes the soil expectation value;
finds the optimal harvest age in each cycle;
determines the optimal number of coppice cycles within a fullrotation.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Research Aim
Development of an optimization forest management scheduling model:
at stand level;
with a stochastic element - wildfire risk;
Eucalyptus globulus Labill stand (even aged stand);
for short rotation coppice systems;
maximizes the soil expectation value;
finds the optimal harvest age in each cycle;
determines the optimal number of coppice cycles within a fullrotation.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Research Aim
Development of an optimization forest management scheduling model:
at stand level;
with a stochastic element - wildfire risk;
Eucalyptus globulus Labill stand (even aged stand);
for short rotation coppice systems;
maximizes the soil expectation value;
finds the optimal harvest age in each cycle;
determines the optimal number of coppice cycles within a fullrotation.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Research Aim
Development of an optimization forest management scheduling model:
at stand level;
with a stochastic element - wildfire risk;
Eucalyptus globulus Labill stand (even aged stand);
for short rotation coppice systems;
maximizes the soil expectation value;
finds the optimal harvest age in each cycle;
determines the optimal number of coppice cycles within a fullrotation.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Research Aim
Development of an optimization forest management scheduling model:
at stand level;
with a stochastic element - wildfire risk;
Eucalyptus globulus Labill stand (even aged stand);
for short rotation coppice systems;
maximizes the soil expectation value;
finds the optimal harvest age in each cycle;
determines the optimal number of coppice cycles within a fullrotation.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Outline
1 Introduction
2 ModelStochastic Dynamic ProgrammingResultsSensitivity Analysis
3 Conclusions and Further work
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Dynamic Programming
Resolution of de subproblems, through a network, ina recursive form!
Subproblem 1
…Subproblem 2 Subproblem N‐1
Subproblem N
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Stochastic dynamic programming
Stages
States
Decisions
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Stochastic dynamic programming
Stages
States
Decisions
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Stochastic dynamic programming
Stages
States
Decisions
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Stochastic dynamic programming
Stages
States
Decisions
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Stage
Stage:
characterized by the cumulative number of harvests during thelifetime of a plantation (n)
0 1 st …
Stage 1 Stage 2 Stage 3
2 nd 3 rd
harvest harvest harvest
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
State
State:
characterized by the number of years since the stand was planted(Tn) 0 1 st …
Stage 1 Stage 2 Stage 3
2 nd 3 rd
harvest harvest harvest
TTn
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Decisions
Decisions:
definition of planned duration for coppice cycle (In);
number of selected sprouts by stool (Vn);
number of fuel treatments (Mn).
(Tn)
Início do estágio n
Início do estágio n+1
Crescimento / Incêndio
Estágio n
(Tn+1)
Corte talhadia ou finalLimpezas de mato (Mn)
Selecção de varasVn
3 anos
In
(Tn)
Beginningnth stage
Beginning(n+1)th stage
Growth / Fire
nth stage
(Tn+1)
Coppice or clear cutShrub cleaning (Mn)
Sprout selectionVn
3 years
In
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Decisions
Decisions:
definition of planned duration for coppice cycle (In);
number of selected sprouts by stool (Vn);
number of fuel treatments (Mn).
(Tn)
Início do estágio n
Início do estágio n+1
Crescimento / Incêndio
Estágio n
(Tn+1)
Corte talhadia ou finalLimpezas de mato (Mn)
Selecção de varasVn
3 anos
In
(Tn)
Beginningnth stage
Beginning(n+1)th stage
Growth / Fire
nth stage
(Tn+1)
Coppice or clear cutShrub cleaning (Mn)
Sprout selectionVn
3 years
In
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Decisions
Decisions:
definition of planned duration for coppice cycle (In);
number of selected sprouts by stool (Vn);
number of fuel treatments (Mn).
(Tn)
Início do estágio n
Início do estágio n+1
Crescimento / Incêndio
Estágio n
(Tn+1)
Corte talhadia ou finalLimpezas de mato (Mn)
Selecção de varasVn
3 anos
In
(Tn)
Beginningnth stage
Beginning(n+1)th stage
Growth / Fire
nth stage
(Tn+1)
Coppice or clear cutShrub cleaning (Mn)
Sprout selectionVn
3 years
In
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Dynamic Programming Network
E1 E2 E31st harvest 2nd harvest
Number of harvests
Timen
0
3rd harvest
10
S10
S16
S20
S21
S32 S48
E4 4st harvest
S40
S41
S64
11
S11
.
.
.
.
.
.
.
.
.
.
.
.
12
13
14
15
16
20
21
22
23
24
25
26
27
32
.
.
.
.
S30
S31
30
31
32
33
34
35
36
37
48
.
.
.
.
42
40
41
42
43
44
45
46
47
64
.
.
.
.
58
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Dynamic Programming Network
DP network nodes translate the possible states for each stage;
DP network arcs take into consideration the range of decisionsthat have to be taken for each state;
Aim: determine the optimal policy - a function that associatesto each state one set of management decisions (e.g. fueltreatment, sprout selection, coppice cycles and rotationlength).
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Dynamic Programming Network
DP network nodes translate the possible states for each stage;
DP network arcs take into consideration the range of decisionsthat have to be taken for each state;
Aim: determine the optimal policy - a function that associatesto each state one set of management decisions (e.g. fueltreatment, sprout selection, coppice cycles and rotationlength).
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Dynamic Programming Network
DP network nodes translate the possible states for each stage;
DP network arcs take into consideration the range of decisionsthat have to be taken for each state;
Aim: determine the optimal policy - a function that associatesto each state one set of management decisions (e.g. fueltreatment, sprout selection, coppice cycles and rotationlength).
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Fire Risk
Fire risk was incorporated through wildfire and damage scenarios
A scenario defines a particular typeof fire, characterized by:
the time of fire occurrence;
its intensity.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Fire Risk
Fire risk was incorporated through wildfire and damage scenarios
A scenario defines a particular typeof fire, characterized by:
the time of fire occurrence;
its intensity.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Fire Risk
Set of all possible scenarios J = J1∪ J2
J1 includes:
the scenario where a fire does not occur during a stage;
all the scenarios involving the occurrence of wildfires withoutmortality, that allow the stand’s growth;
J2 includes:
the set of scenarios involving wildfires with death of trees thatforce a clearcut of the stand.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Fire Risk
Set of all possible scenarios J = J1∪ J2
J1 includes:
the scenario where a fire does not occur during a stage;
all the scenarios involving the occurrence of wildfires withoutmortality, that allow the stand’s growth;
J2 includes:
the set of scenarios involving wildfires with death of trees thatforce a clearcut of the stand.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Stochastic Dynamic Programming
Fire Risk
Set of all possible scenarios J = J1∪ J2
J1 includes:
the scenario where a fire does not occur during a stage;
all the scenarios involving the occurrence of wildfires withoutmortality, that allow the stand’s growth;
J2 includes:
the set of scenarios involving wildfires with death of trees thatforce a clearcut of the stand.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Model Building
Model Functions
G FunctionG Function
F FunctionS Function
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Model Building
Model
The model was defined as follows:
Determine Z = F1(0)− CP (1)
Fn(Tn) = maxIn ∈ ΨnVn ∈ ΘnMn ∈ Πn
{Gn(Tn, In, Vn,Mn), Sn(Tn)} , n = 1, ...,N (2)
FN+1(TN+1) = SN+1(TN+1) (3)
Gn(Tn, In, Vn,Mn) =∑
j∈J1pj (Tn, In, Vn,Mn)
[B jn(Tn, In, Vn)− CV j
n(Tn)− Ljn(Tn, In,Mn) + Fn+1(Tn + In)]
+∑
j∈J2pj (Tn, In, Vn,Mn)
[B jn(Tn, In, Vn)− CV j
n(Tn)− Ljn(Tn,Hj ,Mn) + Sn(Tn + H j )
](4)
Tn+1 = Tn + In, with n = 1, ...,N and T1 = 0 (5)
Sn(Tn) =F1(0)− CR
(1 + i)Tn, with n = 2, ...,N + 1 and S1(T1) = 0 (6)
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Model Building
Backward Method
Starts at the last stage;
Iterative process:
- to start the process it is necessary to use an estimate for the ”bareland nodes”(value of the rotations to perpetuity);
- Stopping condition: |Estimate value − solution| < small value;
- the convergence of the process can be proved using the fixed pointtheorem;
- the convergence is usually achieved after few iterations.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Model Building
Return Function
B jn(Tn, In,Vn) = R j
n(Tn, In,Vn) + Sal jn(Tn,Vn) (7)
R jn(Tn, In,Vn) =
P1
(1 + i)Tn+In× Vol(n, In,Vn) , j ∈ J1
P1
(1 + i)Tn+H j×(1− pmj
)× Vol(n,H j ,Vn), j ∈ J2
(8)
Sal jn(Tn,Vn) =
0 , j ∈ J1
P2
(1 + i)Tn+H j× pmj × Vol(n,H j ,Vn), j ∈ J2
(9)
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Model Building
Costs
Sprout selection cost:
CV jn(Tn) =
CV × NVn
(1 + i)Tn+3, if I jn > 3
0 , otherwise
(10)
CV = cost per sprout of doing sprout selection;
NVn = number of sprouts at nth stage.
Fuel treatment cost:
Ljn(Tn, Ijn,Mn) =
I jn∑l=1
L
(1 + i)Tn+l× PMn(l , I jn,Mn) (11)
PMn(l, I jn,Mn) =
1, if is carried out a fuel treatment, in lth year of jth scenario, with l = 1, ..., I jn
0, otherwise
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Outline
1 Introduction
2 ModelStochastic Dynamic ProgrammingResultsSensitivity Analysis
3 Conclusions and Further work
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
SDP model
Economic Parameters
Prices:
Timber stumpage price: 36 e/m3;Salvage price: 27 e/m3;Discount rate: 4%
Operational Costs:
( / )Operation Fixed cost (€/ha) Variable Cost
Shrub removal 167 ‐‐
l b f lPlantation cost 725 0.14€×number of plants
Sprout selection cost ‐‐‐ 0.15€×number of sprouts
i b f lConversion cost 1204 0.14€×number of plants
Table 1 ‐ Source: CAOF's Database of ANEFA
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
SDP model
States
Decision Possible values
Harvest age Ψn = {10, 11, …, 16}
Sprouts selected Θn = {1; 1.5; 2}
Shrub cleaning Πn = {1, 2, 3}
Table 2 ‐ Possible values for management decisions
Stage States
1 T = {0}
2 T = {1, 2, ..., 16}
3 T = {11, 12, ..., 32}
4 T = {21, 22, ..., 48}
5 T = {31, 32, ..., 64}
Table 3 ‐ Possible states for stochastic model
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
SDP model
Vegetation growth models
Globulus 3.0 - a growth and production model developed forPortuguese eucalypt stands (Tome et al.,2006);
Understory growth was estimated according to a modeldeveloped by (Botequim et al., 2009):
Biom = 17.745×(
1− exp−(0.085×understory age+0.004∗AB))
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
SDP model
Vegetation growth models
Globulus 3.0 - a growth and production model developed forPortuguese eucalypt stands (Tome et al.,2006);
Understory growth was estimated according to a modeldeveloped by (Botequim et al., 2009):
Biom = 17.745×(
1− exp−(0.085×understory age+0.004∗AB))
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
SDP model
Wildfire occurrence and damage models
1 Fire risk model: provides annual wildfire risk probability foreven aged eucalypt stands in Portugal
PfAge =1
1 + e−(−2.4368+0.0815×Biom−0.0671×Age−0.0671×AspSW+0.000613×N+0.0373×Dg)
2 Damage model: gives the proportion of dead trees in thestand, if mortality occurs
pam =1
1 + e−(0.8537+0.00244×Alt+0.0197×Slope−0.0851×AB+0.2246×Sd)
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
SDP model
Wildfire occurrence and damage models
1 Fire risk model: provides annual wildfire risk probability foreven aged eucalypt stands in Portugal
PfAge =1
1 + e−(−2.4368+0.0815×Biom−0.0671×Age−0.0671×AspSW+0.000613×N+0.0373×Dg)
2 Damage model: gives the proportion of dead trees in thestand, if mortality occurs
pam =1
1 + e−(0.8537+0.00244×Alt+0.0197×Slope−0.0851×AB+0.2246×Sd)
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
SDP model
Wildfire and damage scenarios probabilities
annual probabilities were assumed to be independent;
scenarios consider the probability of one wildfire occurrenceduring a cycle;
scenarios’ probabilities:
pj = Pij × (1− Pmort) , if j ∈ J1 − {0}pj = Pij × Pmort , if j ∈ J2
pj = 1−∑
j∈J1−{0}∪J2
pj , if j = 0
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
SDP model
Wildfire and damage scenarios probabilities
annual probabilities were assumed to be independent;
scenarios consider the probability of one wildfire occurrenceduring a cycle;
scenarios’ probabilities:
pj = Pij × (1− Pmort) , if j ∈ J1 − {0}pj = Pij × Pmort , if j ∈ J2
pj = 1−∑
j∈J1−{0}∪J2
pj , if j = 0
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
SDP model
Wildfire and damage scenarios probabilities
annual probabilities were assumed to be independent;
scenarios consider the probability of one wildfire occurrenceduring a cycle;
scenarios’ probabilities:
pj = Pij × (1− Pmort) , if j ∈ J1 − {0}pj = Pij × Pmort , if j ∈ J2
pj = 1−∑
j∈J1−{0}∪J2
pj , if j = 0
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Results
Deterministic case
DP algorithm was programmed with C++;
test problem was solved with a desktop computer(CPU Duo P8400 with 3GB of RAM);
Deterministic case
1st cycle 2nd cycle 3rd cycle 4th cycleNPL
1 cycle 2 cycle 3 cycle 4 cycleSEV (€/ha)In Mn Vn In Mn Vn In Mn Vn In Mn Vn
1111 15 1 ‐ 16 1 2 16 1 2 16 1 2 4390.12
1250 15 1 ‐ 16 1 2 16 1 2 16 1 2 4584.98
1667 14 1 ‐ 14 1 2 16 1 2 14 1 2 5153.99
NPL = Number of planted trees
SEV = Soil expectation value
Table 4 ‐ Results for deterministic case
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Results
Deterministic case
DP algorithm was programmed with C++;
test problem was solved with a desktop computer(CPU Duo P8400 with 3GB of RAM);
Deterministic case
1st cycle 2nd cycle 3rd cycle 4th cycleNPL
1 cycle 2 cycle 3 cycle 4 cycleSEV (€/ha)In Mn Vn In Mn Vn In Mn Vn In Mn Vn
1111 15 1 ‐ 16 1 2 16 1 2 16 1 2 4390.12
1250 15 1 ‐ 16 1 2 16 1 2 16 1 2 4584.98
1667 14 1 ‐ 14 1 2 16 1 2 14 1 2 5153.99
NPL = Number of planted trees
SEV = Soil expectation value
Table 4 ‐ Results for deterministic case
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Results
Stochastic case
Stochastic case
NPL 1st cycle 2nd cycle 3rd cycle 4th cycle SEV
(€/ha)In Mn Vn In Mn Vn In Mn Vn In Mn Vn
1111 16 1 16 1 2 16 1 2 16 1 2 2387 131111 16 1 ‐ 16 1 2 16 1 2 16 1 2 2387.13
1250 16 1 ‐ 16 1 2 16 1 2 16 1 2 2498.68
1667 16 1 ‐ 16 1 2 16 1 2 16 1 2 2813.84
Table 5 ‐ Results for stochastic dynamic programming model
Stage States
1st cycle 10.7
2nd cycle 10.46
3rd cycle 10.86
4th cycle 11.12
Table 6 ‐ Expected rotation length for SDP model with NPL=1111model, with NPL=1111
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Sensitivity Analysis
Variations in discount rate
Stochastic case
Rate(%)
1st cycle 2nd cycle 3rd cycle 4th cycleSEV (€/ha)In Mn Vn In Mn Vn In Mn Vn In Mn Vn
2 16 1 ‐ 16 1 2 16 1 2 16 1 2 7307.97
4 16 1 ‐ 16 1 2 16 1 2 16 1 2 2387.13
6 15 1 ‐ 16 1 2 16 1 2 16 1 2 793.76
8 13 1 ‐ 14 1 2 14 1 2 16 1 2 73.08
Table 7 ‐ Sensitivity analysis for variations in discount rate, with NPL=1111
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Sensitivity Analysis
Variations in prices
Stochastic caseStochastic case
P1€/m³
P2€/m³
1st cycle 2nd cycle 3rd cycle 4th cycleSEV
(€/ha)I M V I M V I M V I M VIn Mn Vn In Mn Vn In Mn Vn In Mn Vn
28.8 21.6 16 1 - 16 1 2 16 1 2 16 1 2 1345.76
36 27 16 1 - 16 1 2 16 1 2 16 1 2 2387.13
43.2 32.4 16 1 - 16 1 2 16 1 2 16 1 2 3428.49
P1 = timber stumpage price
P2 = salvage price
Table 8 ‐ Sensitivity analysis for variations in prices (changes of 20%), with NPL=1111
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Outline
1 Introduction
2 ModelStochastic Dynamic ProgrammingResultsSensitivity Analysis
3 Conclusions and Further work
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Conclusions
In contrast to conventional deterministic DPapproaches, the solution by our formulationdoes not produce a predefined optimalprescription or an ”optimal path”;
It produces optimal stand managementpolicies, e.g. sprout selection, clearcut andfuel treatment options according to thestand state at any time;
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Conclusions
In contrast to conventional deterministic DPapproaches, the solution by our formulationdoes not produce a predefined optimalprescription or an ”optimal path”;
It produces optimal stand managementpolicies, e.g. sprout selection, clearcut andfuel treatment options according to thestand state at any time;
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Conclusions and further work
As a sequence of interrelated decisions ispresented, dynamic programming providesan efficient procedure to solve the problem;
The convergence of the stochastic model isquite good. Generally, not many iterationsare needed to get convergence;
Next step - examine the risk of fire and fueltreatment at landscape level.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Conclusions and further work
As a sequence of interrelated decisions ispresented, dynamic programming providesan efficient procedure to solve the problem;
The convergence of the stochastic model isquite good. Generally, not many iterationsare needed to get convergence;
Next step - examine the risk of fire and fueltreatment at landscape level.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
Introduction Model Conclusions and Further work
Conclusions and further work
As a sequence of interrelated decisions ispresented, dynamic programming providesan efficient procedure to solve the problem;
The convergence of the stochastic model isquite good. Generally, not many iterationsare needed to get convergence;
Next step - examine the risk of fire and fueltreatment at landscape level.
Liliana Ferreira IPL - ESTG
Eucalyptus Globulus
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