# Huff model

The Huff model is a commercial gravitation model that seeks to estimate the level of demand that a commercial establishment could reach considering its geographic location and surface.

The Huff model calculates the probability that customers make their purchases in a certain commercial area, considering that one of the fundamental determinants is the distance that the consumer must travel to reach it.

The model was created by David Huff, Emeritus Professor of Marketing and Geography at the University of Texas at Austin. Huff developed his doctoral thesis on the modeling of transfers (trips) to shopping centers and stores. The study was published in 1963, and the following year he developed the so-called Huff Model that relates geography to business (sales and marketing).

## Huff model objective

The Huff model is a tool for companies to make better decisions regarding their strategic location and thus attract more customers.

To make optimal location decisions, companies must know that distance is a highly relevant variable for consumers. The further away a commercial establishment is, the less attractive it will be, so there must be some other valued variable so that it is worth making the effort to relocate.

## How the Huff Model Works

Huff's model was one of the first models to include a consumer utility function to study consumer behavior. In it, it is assumed that consumers always value their available alternatives and their decision about where to buy not only considers the location, but also other characteristics of the commercial establishments.

The model, in its simplest version, considers that the surface (meters) of the establishment is a variable that increases the attractiveness for consumers, while the distance is a variable that reduces it. In this way, the utility that the consumer obtains from visiting a certain establishment is given by the formula:

Where:

Sj: Area of the establishment j measured in square meters.

Dij: Distance traveled by consumer (i) to reach the establishment (j), measured in minutes it takes him to travel that distance.

α, β: Sensitivity parameters

Then, the probability that a consumer goes to a certain shopping center is the quotient between the utility of said shopping center divided by the utility that the available alternatives could provide (other shopping centers)

Or what is the same:

Where:

Pij: Probability that consumer i visits commercial establishment j

## Huff model example

In this example we will calculate the probability that Torrellano consumers will go to Alicante to make their purchases, considering that they also have the possibility of buying in Elche or Santa Pola.

The data is as follows:

- Alicante has 601,671 square meters of surface and is 9 minutes from Torrellano.
- Elche has 424,455 square meters and is 6 minutes
- Santo Pola has 46,380 square meters and is 10 minutes
- α = 1 and β = 2

P T a A = (601,671 / 9 2) / (601,671 / 92 + 424,455 / 62 + 46,380 / 102) = 37.74%

Ansoff matrix

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