understanding spatial multi criteria decision making...understanding spatial multi‐criteria...

An analytical demonstration of AHP‐based MCDM and how it is used in GIS

Understanding Spatial

Multi‐Criteria Decision Making

by: Rodrigo Nobrega “Sal”[email protected]

Memphis‐in‐May NCRST‐SEPP WorkshopMay 7th, 2009

M S U - N C R S T - S E P P M E M P H I S - I N - M A Y W O R K S H O P M a y 6 t h – 8 t h , 2 0 0 9 M e m p h i s - T N

UNDERSTANDING SPATIAL MULTI‐CRITERIA DECISION MAKINGan analytical demonstration of MCDM‐AHP and how to is used in GIS

• Multi‐Criteria: What it is? How does it works? Techniques available

• Analytical Hierarchy Process

• AHP GIS Spatial MCDMdeveloping numbers from input rankings

• Results and future implementations

Topics presented



Systematic way to select the best available alternatives based on different opinions and conflicting priorities and values.

What is MCDM ?

Haas & Meixner (2006) http://www.boku.ac.at/mi/

Why should we use it?

• MCDM enables multiple stakeholder preferences to be modeled

• MCDM offers improved coordination and collaboration

• MCDM can be implemented to integrate spatial information



How does MCDM works ?

GoalI‐269

Objectives1) Economy

2) Safety

3) Minimum environmental impact

Factors1) Desired distance from urban areas

2) Avoid wetlands and forest

3) Stay out (but not far) of ag fields

Criteria1) D < 1mi very high

2) 1mi < D < 2mi high

3) 2mi < D < 3mi med

4) 3mi < D < 4mi low

5) 4mi < D < 6mi med

6) D > 6mi high

Alternatives

1) B1

2) B2

3) B3

Problem Solving technique



• SAW (Simple Additive Weighing)

• TOPSIS (Technique for Order Preferences by Similarity to the Ideal Solution)

• AHP (Analytical Hierarchy Process)

and more...• ELECTRE (Elimination et Choice Translating Reality)• Bayesian Network Based Framework• SMART (Simple Multiple Attribute Rating Technique)• ANP (Analytic Network Process)

“Problem Solving” techniques



Analytic Hierarchy Process ‐ AHP

• It is a very robust problem solve technique based on pairwise comparisons, developed in early 70’s by Dr. Thomas Saaty as a method to help solve conflicts in ecomonic models.

• MCDM has been adapted from AHP to assist numerous corporate and govenment decision makers in different fields

• Problems are decomposed into a hierarchy of factors and criteria.



• AHP uses a hierarchical structure to solve problems Factors and criteria multi‐level

AHP flowchart

Adapted from Haas & Meixner (2006)



AHP – procedures



AHP – pair‐wise comparisons

Scale for pair‐wise comparison (Saaty 1980)

Pair‐wise comparisons should use the Saaty’s scale, which ranges from 1 (equal value) to 9 (extreme different)

Pair‐wise is applicable for all levels of the AHP process(concurrent factors and concurrent criteria as well)



AHP – normalization and consistency analysis

pair‐wise inputs normalized inputs



Normalization: “ behind the scene”

333231

232221

131211

CCCCCCCCC

For a matrix of pair-wise elements:

n

i ijij CC1

1) sum the values in each column of the pair-wise matrix

2) divide each element in the matrix by its column total to generate a normalized pair-wise matrix

n

i ji

ijji

C

CX

1

3) divide the sum of the normalized column of matrix by the number of criteria used (n) to generate weighted matrix

n

XW

n

j ji

ji 1

333231

232221

131211

XXXXXXXXX

13

12

11

WWW



Consistency analysis: “behind the scene” Consistency Vector is calculated by multiplying the pair‐wise matrix by the weights vector

333231

232221

131211

CCCCCCCCC

31

21

11

WWW

31

21

11

CvCvCv

* =

31332132113131

31

31232122112121

21

31132112111111

11

1

1

1

WCWCWCW

Cv

WCWCWCW

Cv

WCWCWCW

Cv

1

n

nCI RICICr

n

i jiCv1

Cr < 0.10Then it is is accomplished by dividing the weighted sum vector with criterion weight

λ is calculated by averaging the value of the Consistency Vector

CI measures the deviation



Real world needs: ranking instead pair‐wise inputs



AHP + GIS = Spatial MCDM



• Weights represent the resistance, friction or difficulty in crossing the cell which is expressed as cost

•Creation of accumulated-cost-surface grid from a cost-of-passage where friction values are stored

•Tracing a line of least cost from the accumulated-cost-surface (Douglas 1994)Wetlands




Data raster format (digital image)


Cells or Pixels



Study Area

The testbed used is a part of the I‐269

Around 30‐mile corridor that connects Hernando‐MS to Collierville‐TN

Spatial MCDM: case application



Spatial MCDM: case application (hypothetical values)Four factors:

• Drainage density (waterbodies + streams)• Developed areas• Wetlands• Slope

Criteria

Factors

Goal Least‐cost path

Drainagedensity

Avoidancedistances

Developed areas

Avoidance distances

Wetlands

Avoidance distances

Slope

Avoidance distances



Source: National Hydrography Dataset

Distance from Water Ranking

0 – 50 m 3

50 – 300 m 2

> 300 m 1

Hydrography



..0.65.3833.11637.01666.01428.01818.01666.01428.01818.0312/13/132972.03333.02857.02727.03333.02857.02727.02212/125389.05.05714.05455.05.05714.05455.013211

./321321

TotalsClDDClDDClDD

WtStdnClClClClassesDDDDDDClassesIIIStepIIStepIStep

Computing weights

1637.02972.05389.0.

12/13/13*212/12

3211321 WtsStd

DDDDDD

DDDDDDClassesIStep

4919.089405.06244.1Cv

columnthisAverageCvCvCv

IIStep

009.30048.31637.0/4919.00082.32972.0/89405.0

0142.35389.0/6244.1

3

2

1

0045.02

0.3009.3

CI 0077.0

58.00045.0Cr

Cr < 0.1Consistency ratio analysis:

3 = close2 = medium1 = far

Criteria inputs:



Distance from MPO Urbanized Limits

Source: Memphis MPO

Distance from MPO Ranking

0 – 2 Km 5

2 – 4 Km 4

4 – 6 Km 3

6 – 8 Km 2

> 8 Km 1



Computing weights


155.108333.60833.42833.20624.00.066 + 0.047 + 0.048 + 0.061 + 0.087066.0047.0048.0061.0087.015.0333.025.02.0UD50986.00.133 + 0.095 + 0.073 + 0.081 + 0.109133.0095.0073.0081.0109.0215.0333.025.0UD41611.00.200 + 0.190 + 0.146 + 0.122 + 0.146200.0190.0146.0122.0146.03215.0.333.0UD32618.00.266 + 0.285 + 0.292 + 0.244 + 0.219266.0285.0292.0244.0219.043215.0UD24162.00.333 + 0.381 + 0.439 + 0.489 + 0.438333.0381.0439.0439.0438.054321UD1

../UD5UD4UD3UD2UD1UD5UD4UD3UD2UD1

Totals

WeigthStdnClassesIIIStepIIStepIStep

0624.015.03333.025.02.050986.0215.03333.025.041611.0*3215.03333.032618.043215.024162.0543211.54321

UDUDUDUDUD

WtsStdUDUDUDUDUDClassesIStep

3140.04952.08150.03372.11291.2Cv

columnlastthisAverageCvCvCvCvCv

IIStep

5342.20345.50624.0/3140.00234.50986.0/4952.00603.52618.0/8150.01080.52618.0/3372.1

11.54162.0/1291.2

5

4

3

2

1

6165.04

0.55342.2

CI 1233.0

12.16165.0C r

5 = inner city4 = close3 = medium2 = far1 = so far

Criteria inputs:



Source: National Land Cover Database 2001

Distance from Wetlands

Ranking

0 – 50 m 3

50 – 200 m 2

> 200 m 1

Wetlands



Computing weights


..0.65.3833.11637.01666.01428.01818.01666.01428.01818.0312/13/132972.03333.02857.02727.03333.02857.02727.02212/125389.05.05714.05455.05.05714.05455.013211

./321321

TotalsWlWlWlWlWlWl

WtStdnClClClClassesWlWlWlClassesIIIStepIIStepIStep

1637.02972.05389.0.

12/13/13*212/12

3211321 WtsStd

WlWlWl

WlWlWlClassesIStep

4919.089405.06244.1Cv


IIStep

009.30048.31637.0/4919.00082.32972.0/89405.0

0142.35389.0/6244.1

3

2

1

0045.02

0.3009.3

CI 0077.0

58.00045.0Cr

3 = close2 = medium1 = far

Criteria inputs:



Slope Ranking

< 5% 1

5‐20% 3

> 20% 6

Topography



Computing weights


..0.1033.541.10935.01.00625.01182.01.00625.01182.0313/16/132216.03.01876.01773.03.01876.01773.02314/126865.06.07504.07092.06.07504.07092.016411

./321321

TotalsLDSCLDSCLDSC

WtStdnClClClClassesSCSCSCClassesIIIStepIIStepIStep

0935.02216.06865.0.

13/16/13*314/12

6411321 WtsStd

SCSCSC

SCSCSCClassesIStep

2816.06737.01339.2Cv


IIStep

0532.30117.30935.0/2816.00401.32216.0/6737.01083.36865.0/1339.2

3

2

1

0266.02

0.30532.3

CI 045.0

58.00266.0Cr

6 = Rugged 3 = medium1 = flat

Criteria inputs:



7 = develope area 4 = drainage density1 = slope3 = wetlands

Combining multiple scenarios (hypothetical values)



Combining multiple scenarios

0.4667*(UD) + 0.2667*(DD) + 0.2*(WL) + 0.0667*(SC)

Factor Rank WeightUD 7 0.4667DD 4 0.2667WL 3 0.2000SC 1 0.0667

In multiple layer cases,assigned numerical valuesthat provide relative weights are also normalized.

In this approach, each stakeholder may select weights that match their personal and professional perspective and values to create a unique cost surface and cost path!



Least‐Cost Path

Cumulative cost surface and the least‐cost path Least‐cost path visualized using Google Earth



SENSITIVE ANALYSIS USING MCDM



Putting together different scenarios

INPUT rankingsOUTPUT least‐cost path

Scenario 1 Scenario 2 Scenario 3



Results

Path 1 Path 2 Path 3



ADDING MORE FACTORS



FACTOR Ranking

MPO urban limits 9 criteria: dist from 0 – 7 Km

Wetlands 5avoidance

Forest 5avoidance

Agriculture 3High cost

Hydrography 2criteria: dist from 0 – 300 m

Roads 1Reuse existing roads

Slope 10‐ 20% , >20%

Increasing the complexity of the analysis

High weight for the avoidance areas

The system forces to follow existing roads away from avoid areas

Prefferentially don’t use prime ag fields nor intersect/follow streams/ponds



Experimenting Aditional Factor and ScenariosOverlaying : MPO urban + Ag + wetlands + forest + existing roads

Note how the existing roads are reused and avoidance areas are considered



• Feb 2009 ‐MSU Transportation WorkshopPoster presentation: NOBREGA et al. Environmental sensitive corridor planning using MCDM

• March 2009 – ASPRS Annual ConferencePaper/Oral presentation: SADASIVUNI et al. A transportation corridor case study for multi‐criteria decision analysis.

• April 2009 – Management of Environmental Qualify International JournalJournal paper (submitted): NOBREGA et al. Bridging decision making process and environmental needs in transportation corridor planning

• Journal papers in progress:MCDM and non‐traditional remote sensing data inputs (in collaboration with MTRI)

An innovative MCDM approach for corridor planning based on integrated multi‐scale data and AHP method

MCDM Research Results



That’s it!Next presentation: application & results

understanding spatial multi criteria decision making...understanding spatial multi‐criteria...

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