# Huff

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## WHAT IS IT?

A number of establishments that compete for regional customer exist or are contemplated in a particular geographic area. Given the several locations and attractivenesses of these establishments, we would like to predict the market share each will achieve. We are interested in deciding whether to build a number of new establishments as well as where to put any we do decide to build.

This problem falls under the category of **market area analysis**, addressing one of the category's main concerns: the location of prospective retail stores. The Huff model is used extensively for this purpose. The Huff NetLogo model constitutes a simple implementation of the Huff model.

The basic formula for the Huff model is

P(i,j) = (S(j)^{alpha} / T(i,j)^{beta}) / sum(i=1,n)[(S(j)^{alpha} / T(i,j)^{beta})]

where

- P(i,j) is the probability of a consumer at a given origin
*i*traveling to a particular shopping center*j*. - S(i) is the size of a shopping center
*j*(typically measured in terms of the square footage of selling area devoted to the sale of a particular class of goods). More generally, a measure of attractiveness of the shopping center (with higher values more attractive than lower values). T(ij) is the travel time or cost for customer

*i*to go to shopping center*j*.alpha is a parameter, to be estimated empirically but often simply set to 1, for scaling the importance of the attractiveness measure for the establishment, S(j).

- beta is a parameter, to be estimated empirically but often simply set to 2 (hence the literature often speaks of the "Huff
**gravity**model" for this class of models), reflecting the effect of travel time and other costs on various kinds of shopping trips. *n*is the number of establishments or shopping centers under consideration.

Further, it is presumed in using this model that there are *m* customers, that each customer has a known location, and that each of the establishments under consideration has a known location, real or hypothetical.

The expected traffic for a store *j* is

expected_traffic(j) = sum(i=1,m)[P(i,j)]

## HOW IT WORKS

Customers are represented by turtles and displayed as small gray circles. The setup procedure arrays them randomly. There is nothing in the implementation that makes them move. Stores are represented by patches whose `store-at?`

attributes are set to `true`

. The calculate-store-traffic procedure calculates P(i,j) for all customers *i* and stores *j* and reports to the output widget the expected traffic for each store in the model.

## HOW TO USE IT

Use the sliders to set the number of customers, *n* in the Huff formula, and alpha and beta in the Huff formula. Click the setup button to initialize the world. To add stores, click the add-drop-stores button and then click in the world on any patch that does not already have a store. If your click on a patch that already is a store, the store gets removed. Click the add-drop-stores button again when you are done adding or removing stores. Click on the calculate-store traffic to run the Huff formula on each of the customer-store combinations, and to report in the output widget the expected traffic for each store. Stores have a default size of 1 when they are added.

## THINGS TO NOTICE

Changing the size of a store can have a substantial affect on the level of its expected traffic, especially if alpha is much greater than 1. You can easily change the size of a store by inspecting it and editing the size attribute.

## THINGS TO TRY

You can work interactively with the program to try to find better positions for a given store. You can do this by clicking on the add-drop-stores button, deleting a given store, and adding a new store at a different location. The payoffs resulting from changes in position are often surprising, usually interesting.

You can use NetLogo commands to move the turtles/customers to non-random distributions. For example:

```
observer> ask turtles [set heading 180]
observer> ask turtles [fd 5]
```

Again, the payoffs resulting from changes in position are often surprising, usually interesting.

## EXTENDING THE MODEL

The Huff Turtles-Based NetLogo model represents a signficant extension to the Huff NetLogo model, as it affords individual and group searches by stores for better positions.

## NETLOGO FEATURES

The code uses the NetLogo table extension multiple times in its calculation of P(i,j) and expected traffic.

## RELATED MODELS

The coding methods here draw upon the Life NetLogo model, found in the Models Library.

The Huff model has an interesting relationship with Hotelling's spatial location models, which are implemented in the Hotelling's Law NetLogo model in the Models Library.

## HOW TO CITE

If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:

- Kimbrough, Steven O. (2014). Huff model. University of Pennsylvania, Philadelphia, PA. Huff.nlogo

## COPYRIGHT AND LICENSE

Copyright 2014 Steven O. Kimbrough.

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Steven O. Kimbrough at kimbrough@wharton.upenn.edu.

Version: $Id: Huff.nlogo 4336 2014-09-08 21:12:50Z sok $.

## Comments and Questions

extensions [table] globals[background-color the-stores stores-traffic] patches-own [store-at? store-size ] turtles-own [store-distances store-probabilities total-distance total-attractiveness store-attractivenesses] to setup clear-all set background-color white ask patches [set pcolor background-color set store-at? false set store-size 1] create-turtles customers ask turtles [setxy random-xcor random-ycor set color gray set shape "circle" set size 1 / 2] end to add-drop-stores let deleting? [store-at?] of patch mouse-xcor mouse-ycor while [mouse-down?] [ask patch mouse-xcor mouse-ycor [ifelse deleting? [delete-store] [put-store]] display ] end to delete-store ; You can't delete the last store. ; But actually, this isn't necessary. if count patches with [store-at? = true] > 1 [set store-at? false set pcolor background-color] end to put-store set store-at? true set pcolor black end to-report get-the-stores report patches with [store-at? = true] end to calculate-attractivness-statistics let stores get-the-stores let n count get-the-stores ask turtles [set store-distances [] set store-probabilities [] set store-attractivenesses []] ; Record the store distances for each turtle. ask turtles [ let the-turtle self ask stores [ let the-distance distance the-turtle let the-store self ask the-turtle [set store-distances fput (list the-distance the-store) store-distances] ] ] ; Not really needed: ask turtles [set store-distances sort-by [first ?1 < first ?2] store-distances] ; Record the store-attractivenesses for each turtle. ; The attractiveness of a store is the ; product of the size of the store powered ; to the value of alpha, times the ; reciprocal of ; distance to that store, powered to beta. ask turtles [set store-attractivenesses table:make set total-distance total-distances let td total-distance foreach store-distances [ let dist first ? let store last ? table:put store-attractivenesses (list [pxcor] of store [pycor] of store) ([store-size] of store) ^ alpha * (1 / dist) ^ beta ] ] ; Record the store-probabilities for each turtle. ask turtles [set store-probabilities table:make set total-attractiveness total-attractivenesses foreach table:keys store-attractivenesses [ table:put store-probabilities ? (table:get store-attractivenesses ? / total-attractivenesses) ] ] end to-report total-distances let answer 0 foreach store-distances [set answer (answer + first ?)] report answer end to-report total-attractivenesses let answer 0 foreach table:keys store-attractivenesses [set answer (answer + table:get store-attractivenesses ?)] report answer end to calculate-store-traffic calculate-attractivness-statistics set stores-traffic table:make let stores get-the-stores ask stores [ let x [pxcor] of self let y [pycor] of self let key (list x y) table:put stores-traffic key 0 ] ; set traffic-accumulator 0 let keys table:keys stores-traffic foreach keys [ ask turtles [table:put stores-traffic ? (table:get stores-traffic ? + table:get store-probabilities ?) ] ] ; Now display it clear-output output-print (word "Store Expected") output-print (word "Location Traffic") let listtable table:to-list stores-traffic set listtable sort-by [last ?1 > last ?2] listtable foreach listtable [let address (word first ?) let padding "" repeat (10 - length address) [set padding (word padding " ")] output-print (word address padding (round (100 * last ?) / 100))] end

There is only one version of this model, created about 8 years ago by Steven Kimbrough.

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