Gravity of Reilly, an American researcher (Kubis & Hartmann,

Gravity
models have been used as a solution to the retail store location problem by
researchers, analysts and marketing managers for many years now. These models emphasize on a customer’s perspective on availability and
accessibility of a given store. The development of the first version of a gravity
model was inspired in late 1930s by the work of Reilly, an American researcher (Kubis & Hartmann, 2007). Reilly suggested
that customers may make tradeoffs between the specific features of a store’s main product and the store’s location (Litz, 2014). In
1967, Wilson introduced a model for spatial distribution (A. G. Wilson, 1967) describing the
flow of money from population centroids to retail centers which was considered
a basis for retail locating and the prediction of retail center dynamics for
many years (A. G. Wilson & Oulton, 1983). In Wilson’s
model, survival of a retail center is dependent on its ability to compete for
the limited amount of available resources (customers) (Piovani, Molinero, & Wilson, 2017). He observed the
similarities between the factors applied to the gravity model and the partition
functions used in statistical mechanics, which led to a shift from a Newtonian
analogy to a Boltzmann statistical mechanics analogy (A. Wilson, 2010). Consequently,
Wilson introduced a new framework for spatial interaction modeling based on the
maximization of the entropy of urban and regional areas. In this framework, the
value of two parameters (one that scales attractiveness and floor-space and
another that depicts cost of moving), determine the survival chance of a retail
center.

Gravity models are usually
divided into two different general groups based on their type of approach;
qualitative and quantitative models. As it is suggested by their name, a
qualitative model uses non-numerical criteria to determine the best location
for a store. On the other hand, quantitative models take advantage of available
numerical information including the number of inhabitants, distances and so on. There are two types of
quantitative gravity models, deterministic and probabilistic. While
deterministic models usually calculate an estimation of accounting variables
such as turnover or return on investment to present to marketing managers to
decide upon, probabilistic models attempt to model the probability of a
consumer that lives at location i to purchase products
at location j. The later models are
based on the model of Huff (Kubis & Hartmann, 2007). 

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