Facility Dependent Distance Decay in Competitive Location
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Facility Dependent Distance Decay in Competitive Location Tammy Drezner1 · Zvi Drezner1
· Dawit Zerom1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper we propose a simple general framework for obtaining facility dependent distance decay function in competitive location models. As the distance increases, the decay in patronage by more attractive facilities is slower than the decay by less attractive facilities. This implies that by using only the distribution patterns of neighborhoods from which facility’s patrons originated, the facility dependent decay approach implicitly accounts for the varying degrees of facilities’ attractiveness. No modifications are required in order to apply existing solution algorithms to the new model. The effectiveness and accuracy of the new approach is demonstrated using a real data set. Keywords Competitive facility location · Gravity model · Huff model
1 Introduction There are several models for estimating the buying power attracted by competing facilities. The most widely used approach, which is investigated in this paper, is the gravity model sometimes called the Huff model. The gravity model was proposed almost a century ago by Reilly (1931) and refined more than half a century ago by Huff (1964) and Huff (1966). According to the gravity model, the probability that a customer patronizes a facility is proportional to its Zvi Drezner
[email protected] Tammy Drezner [email protected] Dawit Zerom [email protected] 1
Steven G. Mihaylo College of Business and Economics, California State University-Fullerton, Fullerton, CA 92834, USA
T. Drezner et al.
attractiveness and declines according to a distance decay function. Scores of papers analyze variations on the basic gravity model (Reilly (1931) and Huff (1964) were each cited over 1,500 times). It is assumed in all of these papers that the distance decay function for a specific retail category is the same regardless of the attractiveness of the facility. If, for example, the probability of patronizing a facility of average attractiveness at 4 miles is half the probability of patronizing it at 3 miles, this ratio of one half is the same regardless of the attractiveness of the facility. However, in reality, the proportion of customers coming from farther away is larger for more attractive facilities. This observation was confirmed by analyzing a real data-set of seven shopping malls in Orange County, California. If customers come from farther communities to patronize a facility, the facility is more attractive. In this paper we refine the gravity model by assigning different decay functions to different facilities. Customers patronize a more attractive facility from greater distances. A more attractive facility has a flatter decay function. The multiplicative attractiveness values are replaced by different decay functions. This approach is easier to implement because there is no need for public opinion surveys. It yielded more accurate results on a real data set. Applying
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