Gravity Model – Huff Model of Spatial Allocation
Estimating flows from origins to destinations with no data on existing flows
You are planning on building three dollar
stores in an area encompassing 8 zip codes.
You are asked to make sales estimates for the
three stores by estimating the flow of dollars
from each zone to each store. You also want
to estimate sales if you build a fourth store in
zone 8
Data
Zone
Zone 1
Zone 2
Zone 3
Zone 4
Zone 5
Zone 6
Zone 7
Zone 8
Population
54,789
23,467
43,567
87,345
67,345
76,894
12,678
32,567
Annual
spending
at Dollar
Stores
$4,657,065
$1,994,695
$3,703,195
$7,424,325
$5,724,325
$6,535,990
$1,077,630
$2,768,195
Travel Times in Minutes
Zone
Zone 1
Zone 2
Zone 3
Zone 4
Zone 5
Zone 6
Zone 7
Zone 8
Store 3
Store 4
Store 6
15
9
4
10
8
30
22
24
10
17
10
4
9
25
14
18
17
20
30
25
35
4
12
27
Store
Store 3
Store 4
Store 6
Planned
Retail
Square
Footage
1,489,074
1,267,893
1,789,543
Steps
Calculate the probability of a dollar flowing to each of the three stores
The probability of a dollar being spent at a store is proportional to the size of the store and
disproportional to the distance to the store. In the absence of other knowledge, distance is squared.
The formula for the probability of a dollar going from zone i to store j is Rj/Dij2/∑Rj/Dij2
Allocate the dollars according to the probabilities
The flow of dollars from zone I to store j is the number of dollars originating in zone i times the
probability of a dollar flowing from zone i to store j.
Fij = Si * Rj/Dij2
∑Rj/Dij2
Open the Huff Model Spreadsheet