philadelphia, may 2–4, 2005 1 "geo-intelligent solutions for generating balanced, compact...

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Philadelphia, May 2–4, 2005

www.locationintelligence.net

"Geo-intelligent Solutions for "Geo-intelligent Solutions for Generating Balanced, Compact Generating Balanced, Compact

and Contiguous Territories"and Contiguous Territories"

Brady FoustBrady Foust

Senior Vice PresidentSenior Vice President

Proxix Solutions, Inc.Proxix Solutions, Inc.

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Territory OptimizationTerritory Optimization• Problem:Problem:

• Divide an area up into territories.Divide an area up into territories.

• Each should contain an equal amount of Each should contain an equal amount of some variable (balance).some variable (balance).

• Should not have islands or lakes Should not have islands or lakes (contiguity).(contiguity).

• Should be as compact as possible Should be as compact as possible (compactness).(compactness).

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Territory OptimizationTerritory Optimization

• Theoretical problem.Theoretical problem.

• Applied problem.Applied problem.

• GIS theory leads to solution of and GIS theory leads to solution of and important “business” problem.important “business” problem.

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• Smaller units aggregated and merged Smaller units aggregated and merged into larger units.into larger units.

• Block groups.Block groups.

• Census tracts.Census tracts.

• Zip codes.Zip codes.

• Up into larger territories.Up into larger territories.

• Can also be applied to point data.Can also be applied to point data.

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UsesUses

• Political redistricting.Political redistricting.

• Service territories (fire, police, school).Service territories (fire, police, school).

• Sales territories.Sales territories. Give every sales person an equal amount Give every sales person an equal amount

of potential sales.of potential sales. Performance based on effort.Performance based on effort. Not better territory.Not better territory.

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• All GIS operations are coordinate geometry All GIS operations are coordinate geometry operations.operations.

• Not a trivial coordinate geometry problem.Not a trivial coordinate geometry problem.• Most attempts are “add/subtract/evaluate” Most attempts are “add/subtract/evaluate”

operations.operations.• Should be embedded in a GIS as an Should be embedded in a GIS as an

operations research routine.operations research routine.• ““Run and Revise”.Run and Revise”.• Science, then art.Science, then art.

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Efficiency MeasuresEfficiency Measures

• Balance.Balance.

• Contiguity.Contiguity.

• Compactness.Compactness.

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BalanceBalance

• Take total of “x” in a study area.Take total of “x” in a study area.

• Divide total x by desired amount of x in Divide total x by desired amount of x in each territory.each territory.

• Yields # of territories.Yields # of territories.

• Decide on # of desired territories.Decide on # of desired territories.

• Divide total x by #.Divide total x by #.

• Yields amount of x per territory.Yields amount of x per territory.

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BalanceBalance

• Each resulting territory should contain the Each resulting territory should contain the same amount of X.same amount of X.

• Measure = Measure = • % deviation from desired amount of X.% deviation from desired amount of X.• Try to hold deviation to a few percentage Try to hold deviation to a few percentage

points.points.• Each congressional district should contain Each congressional district should contain

the same population (Constitution = basis the same population (Constitution = basis for US Census).for US Census).

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ContiguityContiguity• Each territory should be a single polygon.Each territory should be a single polygon.• No islands.No islands.• No lakes.No lakes.• Measure = # of polygons.Measure = # of polygons.• Should = 1.Should = 1.

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CompactnessCompactness

• Should be as “round” as possible.Should be as “round” as possible.

• ““Tile” space efficiently.Tile” space efficiently.

• Circle = theoretical ideal.Circle = theoretical ideal.

• Hexagon = practical ideal.Hexagon = practical ideal.

• How to measure.How to measure.

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CompactnessCompactness

• Calculate area = area A.Calculate area = area A.

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CompactnessCompactness• Calculate area.Calculate area.

• Calculate MBR.Calculate MBR.

MBR

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CompactnessCompactness• Calculate area = area A.Calculate area = area A.• Determine radius of circle of Area A = radius XDetermine radius of circle of Area A = radius X• Calculate MBR.Calculate MBR.• Calculate greatest extent of MBR.Calculate greatest extent of MBR.

MBR

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CompactnessCompactness• Calculate area = area A.Calculate area = area A.• Determine radius of circle of Area A = radius Determine radius of circle of Area A = radius

XX• Calculate MBR.Calculate MBR.• Calculate greatest extent of MBR.Calculate greatest extent of MBR.• Take ½ = radius Y.Take ½ = radius Y.

MBR

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CompactnessCompactness• Calculate area = area A.Calculate area = area A.• Determine radius of circle of Area A = radius XDetermine radius of circle of Area A = radius X• Calculate MBR.Calculate MBR.• Calculate greatest extent of MBR.Calculate greatest extent of MBR.• Take ½ = radius Y.Take ½ = radius Y.• Compare radius X to radius Y.Compare radius X to radius Y.

MBR

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Optimize EngineOptimize Engine

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# of Territories# of Territories

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Territory ResultsTerritory Results

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Weighted Mean CentersWeighted Mean Centers

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Reported ResultsReported Results

TERRITORY UNITS % OF TOTAL CONTIGUITY COMPACTNESS1 140,213 6.29% 100.00% 96.00%2 141,968 6.37% 100.00% 91.00%3 138,000 6.19% 100.00% 96.00%4 138,057 6.19% 100.00% 92.00%5 138,725 6.22% 100.00% 93.00%6 139,057 6.24% 100.00% 89.00%7 138,104 6.20% 100.00% 91.00%8 138,550 6.22% 100.00% 95.00%9 139,159 6.24% 100.00% 87.00%

10 138,094 6.19% 100.00% 98.00%11 140,007 6.28% 100.00% 85.00%12 140,944 6.32% 100.00% 88.00%13 138,507 6.21% 100.00% 97.00%14 138,441 6.21% 100.00% 98.00%15 138,052 6.19% 100.00% 90.00%16 143,392 6.43% 100.00% 91.00%

TOTAL 2,229,270

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Balance Variable SelectionBalance Variable Selection

• Creation/selection of a “Balance” variable is Creation/selection of a “Balance” variable is a very important part of Territory a very important part of Territory Optimization. Optimization.

• Territories have significance only if the Territories have significance only if the balance variable clearly defines the problem. balance variable clearly defines the problem.

• Sophisticated measures are required for Sophisticated measures are required for retail, financial, service, and office territory retail, financial, service, and office territory optimization. optimization.

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Balance VariableBalance Variable

• Raw variable.Raw variable.

• Computed variable.Computed variable.

• Can account for existing locations, Can account for existing locations, competitors, and barriers.competitors, and barriers.

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Example: Insurance ProblemExample: Insurance Problem

• Risk concentration (policy density). Risk concentration (policy density).

• Market penetration.Market penetration.

• Market potential.Market potential.

• Run scenarios.Run scenarios.

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Risk ConcentrationRisk Concentration

• Optimize on total risk.Optimize on total risk.• Ever polygon has same amount of risk.Ever polygon has same amount of risk.• Small areas = high concentrations.Small areas = high concentrations.• What are they near?What are they near?• How can the risk be spread around?How can the risk be spread around?

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Market Penetration and PotentialMarket Penetration and Potential

Scenario NameHousehold Penetration

Rate

Policies per Household

1New Markets 20% 2.25

2 Emerging Markets

25% 2.25

3 Moderately Mature Markets

30% 2.25

4 Mature Markets

35% 2.75

5User Defined ??% ?.??

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QUESTIONSQUESTIONS

philadelphia, may 2–4, 2005 1 "geo-intelligent solutions for generating balanced, compact...

Documents

desired territories

sales territories

larger territories

territory optimization

total of x

total x

service territories

gis operations