Part 1: Understanding the idea

Imagine you live in a neighbourhood and want to buy groceries.

There are several supermarkets nearby. Some are large, some are small. Some are close, some are further away.

When choosing where to shop, most people think about two main things.

Store attractiveness

Large supermarkets often attract more customers because they offer more products, wider variety, and sometimes lower prices.

Distance

People generally prefer shops that are closer to them. Travelling further requires more time and effort.

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A simple example

Suppose people in a neighbourhood spend £10,000 per week on groceries.

Nearby there are three stores:

Even though Tesco is the biggest store, Aldi is much closer. This means Aldi might still attract many customers.

Instead of assuming everyone goes to one store, the spatial interaction model assumes that spending is shared between all stores depending on their attractiveness and distance.

Example distribution:

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Part 2: Key components of the model

To estimate how spending is distributed, the model needs three types of information.

1 Demand

Demand represents the total spending from each residential area.

Example:

This represents the origin of spending.

2 Store attractiveness

Stores are not equally attractive.

Larger stores usually attract more customers.

In this practical, attractiveness is represented by floorspace.

Example:

3 Distance

Customers are more likely to shop at stores that are nearby.

Distances are measured between postal sector centres and store locations using their coordinates.

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Part 3: How the model works conceptually

The model works in three steps.

Step 1: Calculate store attraction

A store becomes more attractive when it is larger and closer.

Step 2: Compare all stores

For each residential area, the model compares the attraction of every store.

Step 3: Allocate spending

Total spending from each area is divided between the stores according to these attraction levels.

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Part 4: Mathematical version of the model

Once the logic is understood, we can express the model mathematically.

Variables

• i = residential zone
• j = store

Distance decay

Distance influence is represented by

$$d_{ij}^{-\beta}$$

In this exercise

$$\beta = 0.8$$

Store attraction

The attraction of store $j$ for zone $i$ is:

$$W_j d_{ij}^{-\beta}$$

Spatial interaction model

$$T_{ij} = O_i \frac{W_j d_{ij}^{-\beta}}{\sum_k \left( W_k d_{ik}^{-\beta} \right)}$$

$T_{ij}$ represents spending flowing from zone $i$ to store $j$.

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Balancing factor

$$A_i = \frac{1}{\sum_j \left( W_j d_{ij}^{-\beta} \right)}$$

The model can also be written as

$$T_{ij} = A_i O_i W_j d_{ij}^{-\beta}$$

This ensures

$$\sum_j T_{ij} = O_i$$

meaning all spending from each zone is allocated across stores.

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Part 5: How the Excel model implements this

Distance sheet

Calculates distances between zones and stores ($d_\{ij\}$).

Calc sheet

Calculates $W_j d_{ij}^{-\beta}$ and the balancing factor $A_i$.

Flows sheet

Calculates final retail flows:

$$T_{ij} = A_i O_i W_j d_{ij}^{-\beta}$$

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Key idea

The spatial interaction model predicts where people shop based on:

• how attractive stores are
• how far away they are Bigger and closer stores attract more spending, while smaller and distant stores attract less.

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Questions to think about

The model is useful because it is simple, but that simplicity also hides assumptions. When interpreting the results, it is worth asking:

1. Is the way distance is calculated reasonable? Straight-line distance is easy to compute, but real shopping journeys follow roads, public transport routes, and everyday travel patterns.
2. Are people living near the edge of a postal sector also influenced by stores just across the boundary? Administrative zones are convenient for analysis, but people do not make decisions based on those boundaries.
3. Does floorspace capture attractiveness well enough? Larger stores often offer more choice, but price, brand, parking, product quality, and opening hours may also shape behaviour.
4. Do all customers respond to distance in the same way? Some people may be highly sensitive to travel time, while others are willing to travel further for a preferred store.
5. Is one distance-decay parameter appropriate for every place? Dense urban areas and more rural areas may show very different travel behaviour.
6. Are there stores that should not be treated as direct competitors? For example, a premium supermarket and a discount supermarket may attract overlapping but not identical customer groups.
7. Does the model assume shopping demand is fixed? In reality, the opening of a new store may change how much people buy, not just where they buy it.

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Further readings

Related tutorials on this site:

• Part 1: Different distance measures in spatial interaction models: the wider discussion of what the distance term can mean.
• Part 2: Coordinate systems and Euclidean distance: how the spreadsheet distance values are actually calculated.
• Part 3: Network distance, shortest paths, and routing algorithms: how route-based accessibility differs from straight-line distance.
• Using the retail spatial interaction app: the interactive version of the teaching workflow. External resources:
• How Huff Model works: a concise GIS-oriented explanation of the Huff model.
• Huff Gravity Model: Store Customer Predictions: a simpler and more intuitive explanation of the model.
• Developing a Huff retail gravity model in R: an example of implementing the model in code.