Handbook of Market Area and Accessibility Models

Hansen Accessibility

Background

The Hansen Accessibility, named after him, was developed by Walter G. Hansen in the context of urban planning and land use[1]. Starting from a customer origin (e.g., place of residence), it represents the sum of all opportunities (e.g., jobs, shopping facilities, leisure activities, medical services), weighted by travel costs. It is a common formulation of spatial accessibility.

Model formulation

The Hansen Accessibility is formalized as follows[1]:

\[A_i = \sum_{j=1}^J O_j f(d_{ij})\]

where \(A_i\) is the weighted accessibility from origin \(i\), \(O_j\) is the number of opportunities at location \(j\) (\(j=1,2,...,J\)), and \(d_{ij}\) is the distance or travel time between \(i\) and \(j\).

The distance decay function \(f(d_{ij})\) is assumed to be a nonlinear function, e.g., power function.

Empirical application

Calculating the Hansen Accessibility involves the following steps:

  1. Define a study area and divide it into \(I\) customer origins (e.g., municipalities, ZIP code areas, census tracts)
  2. Identify the relevant \(J\) supply locations within the study area
  3. Collect the size values \(O_j\) (e.g., opportunities) of all \(J\) supply locations
  4. Calculate travel costs \(d_{ij}\) for all \(I \times J\) origin-destination combinations and store them in a travel cost matrix
  5. Define a distance decay function and the corresponding parameter(s) for \(t_{ij}\) (and, if required, define a weighting for \(O_j\) as well)
  6. Calculate \(A_i\) for all \(I\) origins

Further notes

The empirical application of the Hansen Accessibility has the same requirements as a Huff Model analysis, including the calculation of travel costs for all \(I \times J\) combinations of customer origins and supply locations. For more information on the calculation of a travel cost matrix, see the corresponding Huff Model section.

The Hansen Accessibility served as the model for incorporating cluster effects into the Competing Destinations Model.

Harris[2] developed a very similar indicator for market potential from the provider’s perspective:

\[M_j = \sum^I_{i=1} O_i d_{ij}^{-1}\]

where \(M_j\) is the market potential of supplier \(j\), \(O_i\) is the market potential at origin \(i\), \(d_{ij}\) is the distance or travel time between \(i\) and \(j\), and \(I\) equals the number of customer origins.

The principle of Hansen Accessibility (a weighted sum of all options) may be applied to more complex indicators parameterized using empirical-econometric market area or choice models[3].

References

[1] Hansen WG (1959) How Accessibility Shapes Land Use. Journal of the American Institute of Planners 25(2): 73-76. 10.1080/01944365908978307

[2] Harris CD (1954) The Market as a Factor in the Localization of Industry in the United States. Annals of the Association of American Geographers 44(4): 315–348. 10.1080/00045605409352140

[3] Rauch S, Wieland T, Rauh J (2025) Accessibility of food - A multilevel approach comparing a choice based model with perceived accessibility in Mainfranken. Journal of Transport Geography 128: 104367. 10.1016/j.jtrangeo.2025.104367