S.Chakhar & V.Mousseau - 58th MCDA Meeting - Moscow, October 9-11, 2003 1 Salem Chakhar and Vincent Mousseau LAMSADE University of Paris IX Dauphine

S.Chakhar & V.Mousseau

- 58th MCDA Meeting - Moscow, October 9-11, 2003

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Salem Chakhar and Vincent Mousseau

LAMSADE University of Paris IX Dauphine

www.lamsade.dauphine.fr

Towards a typology of spatial decision problems

58th MCDA Meeting . Moscow, October 9-11, 2003



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Plan

• Introduction

• Modes of handling temporal aspects of spatial problems

• Idea of the typology

• Poposed typology

• Problems implying complex alternatives

• Conclusion & Perspective



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Introduction

Spatial problems are of:

• multicriteria nature and are

• inscribed in a spatio-temporal dynamic context



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Modes of handling temporal aspects of spatial problems

• Static vision

• Temporal vision

• Dynamic vision

• Sequential vision



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Static vision

• Hypotheses: Unique decision + Static envi. + Punctual data

• Objective: Short-term decision-making

• Example : Selection of a trip itenerary

data available at t=t0

decision

tt0



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Temporal vision

• Hypotheses: Unique decision + Dynamic envi. + Evolving data

• Objective: Strategic decision-making

• Example: Location of a nuclear center

data at t=t0

decision

tt0

data at t=t1

t1

data at t=tn

tn

…



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Dynamic vision

• Hypotheses: Series of decisions + Dynamic envi. + Time pressure

• Objective: Control of dynamic spatial systems or phenomena

• Example : Forest fire fighting

data at t=ti

decision 1

ti

data at t=tj

data at t=tn

…

decision 2

decision 3

decision m

data at t=tk

…ttj tk tn



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Sequential vision

• Hypotheses: Series of decisions + Static envi.+ Uncertain data and/or

high costs • Objective: Sequential search for information

• Example : Planning of the implementation of a production unit

data period 1

decision 1

decision 2

decision n

t

decision 3

data period 2

data period 3

data period n



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Idea of the typology

The typology is based on a crossovering between:

• the types of spatial entities associated to spatial potential alternatives

• the different modes of handling temporal aspects of spatial problems



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Representing spatial potential alternatives

A spatial alternative may be represented with:

• an atomic spatial entity (i.e. point, line, polygon, network), or

• a collection of several spatial atomic entities



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Some examples

Point

Line

Polygon

Point-Polygon

School location: points represent potential sites

Highway corridor selection: lines represent potential corridors

Selection of a contruction zone: polygons represent different potential zones

School partitioning: points represent schools and polygons represent zones to serve

Network

Map

Selection of distribution policy: networks are different policies of good ditribution

Antipollution fight: each map represents the spatial pattern of a fighting policy



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Proposed typology

Point

Line

Polygon

Network

Static DynamicTemporal

Spatial problems with punctual alternatives

Spatio-temporal

problems

Spatio-dynamic

problems

Spatio-static

problems

Sequential

Spatial problems with

linear alternatives


polygon alternatives


network alternatives

Spatio-sequential

problems

spatio-static pbs with punctual alternatives

Vision of temporal aspects

Type of alterna.

spatio-static pbs with network alternatives

spatio-static pbs with polygon alternatives

spatio-static pbs with linear alternatives

spatio-temporal pbs with punctual alterna.

spatio-temporal pbs with network alterna.

spatio-temporal pbs with polygon alterna.

spatio-temporal pbs with linear alterna.

spatio-dynamic pbs with punctual alterna.

spatio-dynamic pbs with network alterna.

spatio-dynamic pbs with polygon alterna.

spatio-dynamic pbs with linear alterna.

spatio-sequential pbs with punctual alterna.

spatio-sequential pbs with linearl alterna.

spatio-sequential pbs with polygon alterna.

spatio-sequential pbs with network alterna.



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Spatio-static problems with puntcual alternatives

10;5 8;610;3 9;4 8;4

10;3

10;3

11;5

11;3

10;3 9;4 8;38;3

11;5

11;5 7;4

11;5 7;5

7;57;6

7;5

7;57;59;511;4

Implementation cost

avreage distance

Example : school location problem



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Proposed typology

Point

Line

Polygon

Network



Spatio-temporal

problems

Spatio-dynamic

problems

Spatio-static

problems

Sequential


linear alternatives





Spatio-sequential

problems



Type of alterna.


















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Spatio-temporal problems with linear alternatives

t1 tnt2

decision

….

O10;5

Implementation cost

8;5 8;59;3 9;4 O

10;4

9;3.5

10;5

D

8;5 9;4.5 8;38;4

11;6

10;5 8;5

10;5 7;6

7;410;6

8;5.5

7;57;510;611;4

8;610;3 9;4

10;3

10;3

11;5

D

10;3 9;4 8;38;3

11;5

11;5 7;4

11;5 7;5

7;57;6

7;5

7;57;59;511;4

10;5 9;610;4 9.5;4 O

8;4

11;5

10;3

D

11;3 8;4 9;38;3.5

10;5

9.5;6 7;5

10;5 9;5.5

6;410;6

7;4

8;510;68;511;4

Example : highway corridor selection problem

Impact on environment



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Towards an extension of multicriteria analysis

g(a) > g(b) aPb

gT(a) > gT(b) aPTb

with:

•T: planning horizon

•gT(.) AtT[ gt(.)] ; A : an aggregation mechanism

e.g. gT(.) = maxtT[ gt(.)]

punctual data

dispersed data



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Proposed typology

Point

Line

Polygon

Network



Spatio-temporal

problems

Spatio-dynamic

problems

Spatio-static

problems

Sequential


linear alternatives





Spatio-sequential

problems



Type of alterna.


















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Spatio-dynamic problems with polygon alternatives

decision 1

t

decision 2

decision 3

decision 4

...

team1 f1

xxxxxx

xx

xxxxx xxxxxx xx

xx

xxxxxxxxxxxxxxxxxxx

x

xxxx

team2 f2

f1

f2

f3

f1

f13

f4

team2 f3 team1 f4team1 f13

f13

f4...

Example: forest fire fighting problem



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Problems implying complex alternatives

Initial problemalt <e1,e2> ; spatial relation= {k}

Sub-problem 1 with alternatives of type e1

New decision space(s)

Sub-problem 2 with alternatives of type e2

Resolution of sub-problem1

Resolution of sub-problem 2 (with the consideration of

spatial relation k)

Step 0

Step 1

Step 2



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location-allocation initial problem

1 sub-problem of partitioning

n sub-problems of localization

Step 0 Step1 Step 2

zone 1 zone 2

zone 3

zone 5

zone 4

zone 6

1 problem with map alternatives

n problem with punctual alternatives

?Locale n

service points

alternative <point, map> spatial relation = {appartenance}

Problems implying complex alternatives



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Conclusion & Perspective

The typology:

1 characterizes temporal aspects of spatial problems

2 constitutes an adequate framework for developping tools for a specific class of problems

Perspective :

Detailed study of one class of problems: spatio-temporals problems with linear alternatives

Documents

S.Chakhar & V.Mousseau - 58th MCDA Meeting - Moscow, October 9-11, 2003 1 Salem Chakhar and Vincent Mousseau LAMSADE University of Paris IX Dauphine