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.

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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?

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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

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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