From the PIP procedure to MODSSs

MNRMNRL03L03

Andrea CastellettiPolitecnico di Milano

2

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?

3

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

4

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.

5

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

11

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

12

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

13

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

14

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

15

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

16

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

20

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

22

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

25

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

26

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

28

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.

29

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 ….

30

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

31

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

32

planning

management

analyst DM

stakeholders

DMusers

operational control

models and policies

release decision

TwoLe/P

TwoLe/M

TwoLe: a 2 level MODSS