from the pip procedure to modsss mnrl03 andrea castelletti politecnico di milano
TRANSCRIPT
From the PIP procedure to MODSSs
MNRMNRL03L03
Andrea CastellettiPolitecnico di Milano
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Planning actions and management actions
Planning actionsPlanning actions:: decided once forever or over a long time horizon.
Management actionsManagement actions: decided frequently or even periodically, often on a daily basis.
Planning actionsPlanning actions:: by means of a Project, i.e. by evaluating different alternatives (i.e. mix of planning actions) with the aim of individuating those that better satisfy the DM and/or Stakeholders’ point of views.
Management actionsManagement actions: taken on the basis of the Regulator’s experience, i.e. somehow empirically.
Does not work!!!Does not work!!!
How are they taken?
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t
infl
ows
t
leve
ls
G D t
rele
ases
capacity
Planning a new reservoir
Deciding to build the reservoir does require deciding how it will be daily regulated, otherwise it is not possible to evaluate if and how the farmers are satisfied.
The management must be always considered when either the planning requires it or it change the context in which the current managemt is performed.
Planning the managementPlanning the managementPlanning the managementPlanning the management
.......
tin
flow
s
t
leve
ls
G D t
rele
ases
capacity
Planning decision:Planning decision: to build the reservoir
Management decisionManagement decision:: water volume to be released in the next 24 hours
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Planning the management
Simplification: when the system is a periodic one, only 365 management decisions have to be defined.
IDEA: we can define the management decision for each day of the Project horizon (N years) by specifying the sequence of decisions (N*365) over that horizon. This sequence constitutes a
planning decisionplanning decision..
Release plan
Is this the best solution?
To reply let’s consider the management only, i.e. let’s assume the reservoir has
already been built.
Is this the best solution?
To reply let’s consider the management only, i.e. let’s assume the reservoir has
already been built.
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Taking decisions in full rationality
model
Cabora Bassa
MOZAMBIQUE
irrigationDecision:volume of water to release every day from the dam in order to satisfy the farmers’ demand
ut
st
at+1
6
catchment
reservoir
+ users
st+1
wt+1
ut
It
at+1
The release plan
m0 … m364
?
7
a*t+1
m0 … m364
catchment
reservoir
+ users wt+1
ut
It
The rule curve
st+1
t
s*
s*t+1
8
a*t+1
m0 … m364
catchment
reservoir
+ users wt+1
ut
It
The rule curve
t
s*
s*t+1
?
s
t
s*
9
The rule curve
Rule curve for Cabora Bassa
Actual path
10
m0 … m364
catchment
reservoir
+ users wt+1
ut
It
The control policy
t
s*
t
s*
p= {mt(•) t = 0,1,…,h}
delay
mt(st)
a*t+1
s*t+1
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st+1
m0 … m364
catchment
reservoir
+ users wt+1
ut
It
at+1at+1
The control policy
mt(st)
delay
mt(st,wt)mt(st,wt,It,at)
forecaster
â t+1
mt(st ,wt ,ât+1)
delay
mt(st ,wt ,It ,at)
delay
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st+1
m0 … m364
catchment
reservoir
+ users wt+1
ut
It
at+1at+1
The control policy
mt(st)
delay
mt(st,wt)mt(st,wt,It,at)
forecaster
â t+1
mt(st ,wt ,ât+1)
delay
mt(st ,wt ,It ,at)
delay
Why a single decision ut? It’s more rational a whole set Mt !
Mt
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st+1
m0 … m364
catchment
reservoir
+ users wt+1
ut
It
at+1at+1
The control policy
mt(st)
delay
mt(st,wt)mt(st,wt,It,at)mt(st ,wt ,at+1)
delay
delay
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performance indexes
comparison & generation of policies
catchment
reservoir + users
st+1
wt+1
at+1
utmanag. policy
model of the
physical
system
It
scenario choice
ANALYST
manag. policy
Simulation
delay
delay
delay
model of the
manag. system
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performance indexes
catchment
reservoir + users
st+1
wt+1
at+1
manag. policy
model of the
manag. system
model of the
physical system
It
scenario choice
ANALYST
Set-valued simulation
delay
delay
delay
utset valued manage policy
Mt DM
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In a deterministic world
Let’s introduce a simplification:
We are dealing with deterministic inflows
We know {a1,…,ah} for any time horizon {1,…,h}
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3. Designing policy
Single-Objective control problem
xt+1= ft (xt, ut, at+1)
p = {mt(•) t = 0,1,…,h}
ut= mt(xt)
utUt (xt)
at+1 ~ t (•)
Design Procedure
2. Conceptualisation
Defining criteria and indicators
Identifying the model
1. Reconnaissance
Defining actions
(measures)
* *
Problem formulation
MOZAMBIQUE
B*mz. = utopia
p*mz.
history
optimization
Single-Objective control problem
Design Procedure
Inte
gra
ted
Mod
ellin
g Fra
mew
ork
3. Designing policy
2. Conceptualisation
Identifying the model
1. Reconnaissance
Defining actions
(measures)
Defining criteria and indicators
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Full rationality
xt+1= ft (xt, ut, at+1)Cabora Bassa
MOZAMBIQUE
irrigation
Kafue
Kariba
Cabora Bassa
MOZAMBIQUE
ZIMBABWE
ZAMBIA
irrigation
hydropower
Taking decisions in partial rationality
Partial rationality Many interests
Many DMs
Many interests
Many DMs
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BZim
BMoz
BZam
(BZamopt;BZim
opt) today
BMozcon
Present situation
21
BZim
BMoz
BZam
(BZamott;BZim
ott) today utopia
BMozcon BMoz
ott
D
F
E
The optimal solution for Mozambique
BMoz
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BZim
BMoz
BZam
(BZamott;BZim
ott) today
BMozcon BMoz
ott
D
F
E
The Pareto frontier
Pareto frontier
utopia
23
BMoz
BZam
BZim
BZam
BMoz
utopia today
alternative
The Pareto frontier
24
Multi-objective control problem
xt+1= ft (xt, ut, at+1)
p = {mt(•) t = 0,1,…,h}
ut= mt(xt)
utUt (xt)
at+1 ~ t (•)
* *
Pareto frontier
mozambique
zim
babw
e
zam
bia
Formulation
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In an uncertain world
Considering the inflows as deterministic is an unrealitsic assumption.
However, we can not simply say that future inflows are unknow
Rational decision Evaluation Prediction
Predicting the future requires some past characteristic of the process to keep in the future:
modelling the inflow as a random process (stochastic).
THE STEADY STATE PARADIGMTHE STEADY STATE PARADIGMTHE STEADY STATE PARADIGMTHE STEADY STATE PARADIGM
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Decision-making in uncertain condition - example
Knowing exactly what will happen, we would select alternative A2 that returns 1500 €.
Indicator value
Occurrence 1
Decisions
A1 1490
A2 1500
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Risk aversion
Laplace criterion provide alternative A2 as the best choice.
And you, what would you select?
Maybe the worst case: min
Indicator value
Occurrences 1 2
Alternatives A11490 1490
A20 7500
Probability of occurrence j 0,8 0,2
Ej[iij]
1490
1500
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Partial rationality + Uncertain worldThe Multi-Objective Control
problem
BZim
BMoz
BZam
Generating the whole Frontier is not always possible.
In some cases, interacting with the Stakeholders is more appropriate, thus generating the Front point by point. NEGOTIATIONS.
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Negotiations
BZim
BMoz
BZam
05
10152025303540
BMoz BZim BZam
0
50
100
150
200
250
300
350
400
450
500
15/03/76 22/03/76 29/03/76 05/04/76 12/04/76 19/04/76 26/04/76
flow
[m3/s
]
afflussi
domanda irrigua
Just showing the value of the objectives could be not enough, in some cases showing the associated trajectories can be more useful ….
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no
Mitigation and
compensation,
Multi-objective control problem
5. Evaluation
6. Comparison and negotiations
Agreement?
reasonable alternative
s
3. Policy design
2. Conceptualisation
1. Reconnessaince
4. Estimating the effects
Design ProcedurePareto frontier
mozambique
zim
babw
e
zam
bia
3. Designing policy
2. Conceptualisation
5. Evaluation
6. Comparison and negotiations
Agreement?
4. Estimating effects
yes
Final decision
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MO
DS
S
6. Comparison or negotiation
reasonable alternatives
2. Conceptualisation
3. Designing alternatives
4. Estimating effects
Sta
keh
old
ers
1. Reconnaissance
5. Evaluation
noMitigation and
compensation
Agreement? yes
Final (political) decision
Tw
oLe
Daily management
Planning
Management
Tw
oLe/P
TwoLe/M
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planning
management
analyst DM
stakeholders
DMusers
operational control
models and policies
release decision
TwoLe/P
TwoLe/M
TwoLe: a 2 level MODSS