Reilly's law of retail gravitation

`Reilly's law of retail gravitation states that larger cities will have larger spheres of influence

than smaller ones, meaning people travel further to reach a larger city.

The law presumes the geography of the area is flat without any rivers, roads or mountains to alter

a consumer's decision of where to travel to buy goods. It also assumes consumers are indifferent

between the actual cities.

The law was developed by William J. Reilly in 1931.

A plain English paraphrase would be that the balance or Break Point (BP) is equal to the

Distance (d) between two places, divided by the following: Unity or Total (1) plus the Square

Root of, the size of Place One (p1) divided by the size of Place Two (p2).

d is distance and p1 and p2 are the sizes of the places between which the distance exists; the

answer will give the distance from p2, also called a break-point. What is the break-point? As an

example: after leaving a store a you remember something that you wanted to buy; it just so

happens that you are headed towards an alternative store b. The break-point can be thought of as

the point after which you would travel towards store b instead of store a because of its notional

"gravity". This would happen sooner, for example, if store b is an equivalent store but with

greater square footage, suggesting that you are more likely to go to store b for greater available

utility. This notional gravity can be influenced by a number of things, but square footage is

simple and effective.

In 1931, William J. Reilly was inspired by the law of gravity to create an application of the

gravity model to measure retail trade between two cities. His work and theory, The Law of Retail

Gravitation, allows us to draw trade area boundaries around cities using the distance between the

cities and the population of each city.

Reilly realized that the larger a city the larger a trade area it would have and thus it would draw

from a larger hinterland around the city. Two cities of equal size have a trade area boundary

midway between the two cities. When cities are of unequal size, the boundary lies closer to the

smaller city, giving the larger city a larger trade area.

TRADE AREA ANALYSIS AND MAPPING

Trade Area Analysis, Development and Mapping

Trade area analysis and mapping describe the characteristics of the area around a store or

network of stores. Without accurate trade area definitions, you cannot measure the key statistics

that impact a store's performance.

Use trade area analysis to aid site selection and target marketing.

Trade area analysis and mapping tell you:

Where a store's customers are coming from

How many customers you have in a trade area

Where to look for more customers

Benefits of Trade Area Analysis

Identify gaps or overlaps in the market coverage of your existing store network, and

make corrections by opening, closing or moving stores

Make better site selection decisions by using characteristics of existing trade areas to

predict trade areas around potential locations

Define a geographic area to analyze for market potential, market penetration, and

competitive threats

Become more efficient and effective at target marketing by reaching out only to those

customers and prospects in a store's trade area

Use as a key input into customer profiling

Factors that Impact Trade Areas

Analyzing trade areas should be performed regularly to provide key metrics for improving sales

and marketing performance.

Adding new stores to your network will cause the trade area of nearby stores to change. In a

saturated market, or if stores are placed too close to one another, cannibalization can occur.

A change to product offerings will impact the trade area, as will shifts in population and

demographics, the existence of competitors, changes to highways and roads, and the addition of

other businesses that attract people to the area.

Choosing a retail site in the absence of sound trade area analysis is a lot like flying an airplane

with blinders: It forces a business to commit itself to a course in the absence of vital information

such as store patronage, local market opportunities, competing businesses, and barriers that

would dissuade consumers from visiting the site.

Geographic Information System technology is a fundamental tool for analyzing retail trade areas

today. This technology removes site selection "blinders" because it identifies and illustrates the

crucial factors for site selection within a geographic framework.

Essentially, trade area analysis is a methodology, process or technique that provides a basis for

understanding, visualizing and quantifying the extent and characteristics of known or

approximated trade areas.

Trade area analysis provides the foundation for:

Understanding the geographic extent and characteristics of store patronage

Spatially assessing performance

Performing competitive analysis

Evaluating market penetration and market gap analysis.

Target marketing

Merchandising.

Identifying/quantifying effects of cannibalization

Developing and exploiting demographic profiles.

Site suitability and site selection studies.

Trade area analysis also employs theoretical techniques that are used to approximate the

potential patronage area. These techniques are used in cases where customer level data is not

available. Three types of theoretical approaches are commonly employed in trade area analysis,

including:

A. Radial (ring) studies

B. Gravity models

C. Drive time analyses

Spatial Distribution Analysis: Definitions

There are, actually, several forms of the gravity model as it is applied to the spatial distribution

of people.

The simplest, or "pure," gravity model expresses the relationship:

Attraction = K {(Pop. 1) * (Pop. 2)} / Distance**2

This formula says that the force of attraction is proportional to the size of two locations (as

measured by population) divided by the square of the distance between them, and scaled to some

"constant" value (or "fudge factor"), K.

The impact of distance is squared to reflect the perception that movement is discouraged with

greater impact as distance increases. In other words, if the store is out of cigarettes and you have

to walk an additional block to find some, you might think twice about it but you would probably

go. If you had to walk two additional blocks, your resistance to going would more than double; if

you had to go three more blocks you might decide to give up smoking for awhile unless you

were really addicted. The resistance you feel does not increase in equal increments, but seems to

grow by leaps and bounds.

The potential attractiveness of one location is the sum of its attractiveness to all possible

locations:

Attraction = K * Sum {Population[n] / Distance[n]**2}

where n = each of all the possible locations

The pure gravity model is reflected in "Reilly's Law of Retail Gravitation" (Reilly, 1929), which

is used to calculate market areas. In its simplest form, it assumes two market centers (towns,

shopping malls, etc.) which will divide the market between themselves. In this simplified

schema, customers will shop only at one center or the other (or, what amounts to the same thing,

any crossover from one market will be exactly offset by crossovers from the other). The division

of the market can then be expressed as the product of the ratio of the sizes of the centers and the

ratio of their distances from the boundary:

Attraction = (Pop.1 / Pop.2 ) * ({Distance2 **2}/ {Distance1**2})

In this form, the equation presents the structure of the model. In actual use, the true distances are

usually unknown, in which case the calculating formula takes the form:

Distance to loc.1 = Total Distance / (1 + {Pop.2 / Pop.1}**.5)

where Attraction = 1

The derivation of the calculating formula from the structural formula is given in Krueckeberg &

Silvers (1974). It comes from the fact that the total distance between the two centers is divided

into two market ranges (or, Total Distance = Distance 1 + Distance 2) and the total attraction of

the two centers is 100 per cent (unity, or 1) of the resident population.

The pure gravity model returns surprisingly good predictions, considering the simplifications

assumed by the model. Recent work has refined the model, redefining the key variables to allow

greater specification. These more recent gravity models approach the problem not as predicting

the behavior of population aggregates, but as estimating the probability of an individual's

behavior. Rather than measuring attraction, they estimate the attractiveness of a location. This

measure of attractiveness ("attraction potential," if you will) can then be applied to a population

pool to return an estimate of the attraction which will be realized. The distinction is a subtle one,

and holding everything else equal the two families of models would return roughly the same

results. The advance was, rather, a conceptual breakthrough: by redefining the problem it opened

up new strategies for solving it.

The simplest of the probability models is the "unconstrained" gravity model. It takes the form:

Trips1-2 = K {(Pop.1**a) * (Opportunities2**b)} / Distance**c

The similarity to the pure gravity model should be apparent; the differences are equally

instructive. The unconstrained gravity model no longer speaks of "attraction"; attraction is now

expressed in behavior--number of trips. Notice that it also specifies that the trips go from

location 1 to location 2. The fudge factor (constant) remains, as doe’s population at center 1 and

the distance between the two centers

But notice that there is a variable exponent ("a" and c, respectively) attached to each. The pure

gravity model is retained if the population exponent is "1" and the distance exponent is "2"; but

the formula allows the exponents to be adjusted to reflect theoretical assumptions or (depending

on the use to which the model is being put) to model observed events. This is a slight change, but

one that allows the model to be more finely tuned than the pure gravity model. The third term,

population at center 2, is transformed into "opportunities at center 2," also with a variable

exponent. Again, this is an important conceptual shift. If the opportunities at center 2 are

measured by the population at that location, the pure gravity model is approximated. But the

model lays the groundwork for mixing the terms of the analysis. It is possible to measure the

impact on people of, say, sales volume or floor area or labor pool; with the pure gravity model,

both center 1 and center 2 had to be measured in the same terms.

In the unconstrained gravity model, the total number of trips is the sum of the trips generated by

all the centers. In other words, the available opportunities will determine the total number of

trips. There is some merit to this--if the opportunities do not present themselves, it will be

difficult to make a trip to use them. But it is also true that people will not necessarily use every

opportunity which presents itself; after all, how many cars will you buy in a year? The

unconstrained gravity model has a tendency to overestimate the number of trips which will be

generated.

The problem of overestimation was resolved with the "constrained gravity model." This model

specifies that the sum of the trips to each center is limited by the pool of total trips possible.

Substituting this constraint into the unconstrained model leads, eventually, to the calculating

formula:

Trips1-2 = Trips[1] * {(Opportunities[2]**b) / (Distance[1-2]**c)} / Sum

{(Opportunities[all]**b) / (Distance[all]**c)}

The complete derivation can be seen in Krueckeberg & Silvers (1974).

The constrained gravity model states that the trips generated from location 1 to location 2 is a

proportion of the total trips generated by location 1 ("Trips[1]"). That proportion is the ratio of

the attractiveness of location 2 to the total attractiveness of all locations (including location 2). In

other words, people will distribute their trips (for shopping, recreation, or any other activity)

among the potential locations based on the relative attractiveness of each location.

SOURCE URL’S:

http://krypton.mnsu.edu/~tony/courses/609/Gravity/defs.html

http://www.directionsmag.com/

http://www.mappinganalytics.com/

http://en.wikipedia.org/wiki

http://www.about.com/

http://www.applet-magic.com/