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Designing the alternatives
NRMNRMLec16Lec16
Andrea CastellettiPolitecnico di Milano
Gange Delta
2
ICT T
ools
yes
Final (political) decision
reasonable alternatives
2. Conceptualisation
3. Designing Alternatives
4. Estimating effectsS
takeh
old
ers
1. Reconnaissance
5. Evaluation
noMitigation,
and compensatio
n, Agreement
?
PIP procedure
PParticipatory and IIntegrated PPlanning procedure
6. Comparison or negotiation
3 A = A : A = (s, f ,d , p) with s ∈S , f ∈F ,d ∈D , p ∈P (s, f ,d){ }
Which alternatives to consider
Very often the alternatives considered in real world projects are only those proposed by the DM and/or the stakeholders or suggested by the Analyst’s experience.
It is suitable to consider for evaluation all the alternatives that can be obtained by combining in all the possible ways the actions identified in Phase 1.
Eg. Verbano project
• s storage disch. curve• f regulation range• d MEF value• p regulation policy
ACTIONS It is a 2-element finite set
Infinite sets
politicies
range
MEF
SDCcurr
politicies
range
MEF
SDC+600
Infinite alternatives
4
Design problemDesign problem
The design problem
Usually, even if not always infinite, the number of alternatives can be very high, therefore
one should identify the “most interesting” ones
“most interesting” according to the criteria expressed by the Stakeholders.
The indicators associated to such criteria are transformed into objectives and the alternatives which are efficient with respect to those objectives are identified.
5
Full rationality conditions
The solution of a design problem is usually complex because:
dealing with multiple, often conflicting, objectives a single criterion to select the aternatives is not available.
SIMPLIFICATION: full rationality
There exist only one project indicator
i =i x0 ,x1, ...,xh,u
P ,u0 ,u1, ...,uh−1,w0 ,w1, ...,wh−1, ε1, ε2 , ..., εh( )
This situation is not relevant if the aim is to apply a participatory paradigm to decision making, indeed:
• either only one Stakeholder exists, a very unlikely situation; • or the Analyst is considering only one objectives, thus ignoring
the Stakeholders (e.g. Cost Benefit Analysis): no participation.
!
6
Project indicator• The project indicator should be such that, given two
alternatives A1 and A2, if i(A1) < i(A2) then A1 is preferred over A2.
• The optimal alternative is the one for which i takes its minimum value.
• For example: i cannot be an indicator like the wet surface area S of a wetland
• In altre parole: i should reflect the satisfaction produced by the alternative, i.e. its Value.
V
S
7
ICT T
ools
yes
Final (political) decision
reasonable alternatives
2. Conceptualisation
3. Designing Alternatives
4. Estimating effectsS
takeh
old
ers
1. Reconnaissance
5. Evaluation
noMitigation,
and compensatio
n, Agreement
?
PIP procedure
PParticipatory and IIntegrated PPlanning procedure
6. Comparison or negotiation
OPTIMAL ALTERNATIV
E
It is required:• When two models
are used;• To validate the
results.
8
Complexity of the full rationality problem
Even with only one project indicator (full rationality) the problem can be particularly complex, because of
1. The existence of infinite alternatives;
2. The uncertainty of the effects induced by the presence of random disturbances;
3. The existence of recursive decisions.
9
Infinite alternatives
• With a finite (and small enough) number of alternatives:
exhaustive procedure for each alternative A compute
when i is a cost, the optimal alternative is the one that
i =i x0 ,x1, ...,xh,u
P ,u0 ,u1, ...,uh−1,w0 ,w1, ...,wh−1, ε1, ε2 , ..., εh( )min i
• With an infinite (or very big) number of alternatives a procedure should be used through which the optimal (or a nearby) alternative is singled out by analysing only a small number of alternatives.
10
Uncertainty of the effects
i =i x0 ,x1, ...,xh,u
P ,u0 ,u1, ...,uh−1,w0 ,w1, ...,wh−1, ε1, ε2 , ..., εh( )
The alternatives can not be ranked with respect to i
... random indicator (stochastic or uncertain)
random disturbances ---
Example
Project: construnction of bank on a river to protect from floods.
Decision: high uP of the bank
i = discounted future damage + construction costs
i changes with the trajectories of the level
This is not known (it is random!) when up has to be selected.
For a given up many values of i can occur.
What can we do?
11
Uncertainty of the effects
i =i x0 ,x1, ...,xh,u
P ,u0 ,u1, ...,uh−1,w0 ,w1, ...,wh−1, ε1, ε2 , ..., εh( )
The alternatives can not be ranked with respect to i
... random indicator (stochastic or uncertain)
random disturbances ---
Example
Project: construnction of bank on a river to protect from floods.
Decision: high uP of the bank
i = discounted future damage + construction costs
i changes with the trajectories of the level
This is not known (it is random!) when up has to be selected.
For a given up many values of i can occur.
What can we do?
The uncertainty must be filtered:
a deterministic value of i is associated to each uP.
1) If i is stochastic the probability distribution is identified,
if i is uncertian the corresponding set-membership.
2) Based on appropriate statistics the optimal alternative is selected
In our example:uP is selected such that the expected value of i is minimum (min E [i])
uP is selected s.t. the value is minimum in the worst case (min max i)
The uncertainty must be filtered:
a deterministic value of i is associated to each uP.
1) If i is stochastic the probability distribution is identified,
if i is uncertian the corresponding set-membership.
2) Based on appropriate statistics the optimal alternative is selected
In our example:uP is selected such that the expected value of i is minimum (min E [i])
uP is selected s.t. the value is minimum in the worst case (min max i)
disturbance filtering criteriadisturbance filtering criteria
12
Recursive decisions
i =i x0 ,x1, ...,xh,u
P ,u0 ,u1, ...,uh−1,w0 ,w1, ...,wh−1, ε1, ε2 , ..., εh( )
recursive decisions
They can be transformed into a planning decision by defining a management policy, which, in the simplest case, is a perodic sequence
p = m0(g),...,mT−1 (g),m0(g) ...{ }
of control laws mt(•)
ut=mt (xt )
How to define them?How to define them?
13
Reading
IPWRM.Theory Ch. 7