© J.M. Piwowar 1Geog 409: Advanced Spatial Analysis & Modelling Gravity Models

Gravity Models

The 3 critical elements to a business' success:

LocationLocationLocation

© J.M. Piwowar 2Geog 409: Advanced Spatial Analysis & Modelling Gravity Models

Business Geographics

Trade areaThe geographic area from which a store

draws most of its customers.Applications:

New store location. Existing store promotional activities.

Delineation methods: Analog method. Proximal area method. Gravity model method.

© J.M. Piwowar 3Geog 409: Advanced Spatial Analysis & Modelling Gravity Models

Analog Trade Areas

Uses customer and sales data from an existing store(s) to predict sales in an anologous (i.e. similar) store.

Non-geographic.

© J.M. Piwowar 4Geog 409: Advanced Spatial Analysis & Modelling Gravity Models

Proximal Trade Areas

Defines proximal areas around each store based on the assumption that consumers will always shop at their nearest store.

Stores based: Trade areas are defined by Voronoi polygons around each store.

Customers based: Each customer is assigned to their nearest store. All the customers that share the same nearest stores are grouped to form that store's trade area.

But … what if there are other factors that attract customers to a store other than their nearest one?

© J.M. Piwowar 5Geog 409: Advanced Spatial Analysis & Modelling Gravity Models

Gravity Models

Gravity models define trade areas based on: Distance (or time) to a location; and A location's attraction.

The gravitational pull of a location (g) is in direct proportion to its attraction (S) and in inverse proportion to the square of its distance (d):

2

Sg

d

© J.M. Piwowar 6Geog 409: Advanced Spatial Analysis & Modelling Gravity Models

Reilly's Law

Consider 2 locations that are at a distance of d12 of each other and have attractions of S1 and S2, respectively. The breaking point that separates their trade areas is defined as:

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© J.M. Piwowar 7Geog 409: Advanced Spatial Analysis & Modelling Gravity Models

Huff Model A more general gravity model that defines trade

areas based on multiple locations. Defines a probability surface for each location

based on its attractiveness and distance. The probability (P) of an individual (i) selecting a

store (j) is found with:

Customers will usually visit the location that has the highest probability.

1

( )

j ijij n

k ikk

S dP

S d