Introduction
Gravity models are models that investigate the catchment areas of commercial activities and other activities at an urban and regional level. The Huff model is one of the prominent models in this field, which calculates the probability of customer attraction for existing commercial locations and the catchment areas of commercial locations. In Huff's original model to calculate the catchment area of cities’ commercial places, two factors of distance and size of the commercial place are used as influencing factors. The travel time index or the distance between business locations and customers was used for the distance factor, and the size of the business location, the area index was used. During the different years, this model was used in studies modified and adjusted by different researchers. Using network distance instead of Euclidean distance and calculating the attraction power of commercial places or other studied places are among these modifications. In all the research conducted in this field, despite the modifications made in Huff's model, no evaluation was done on the output and results of this model. In this research, the main goal is to provide a method to evaluate the results and outputs of the modified Huff model. The secondary goal of this research is to investigate the spatial distribution of stores and their catchment areas from the point of view of urban planning and to identify the strengths and weaknesses of the existing pattern.
Materials and Methods
The methods used in this research are theoretical and subjective. In the theoretical method, after studying the sources (related books and articles), the theoretical foundations and structure of this model were built. In the next step, a map of chain store catchment areas in Buein Zahra city was determined based on Huff's theoretical model and using spatial analysis and network analysis tools in Arc GIS software. The indicators used to measure the attractiveness of the stores (shopping center size) include the size of the store, the number of employees, the variety of products, and the presence of marginal parking around the store. In the next stage, using the questionnaires completed by the residents of the city, their priority of visiting chain stores in the city was questioned. In this stage, the sample was determined using the Morgan method and random spatial sampling, and about 430 residential units were selected as samples. After determining the priority of residents to visit chain stores, the actual catchment area of these stores draws on the map of Buein Zahra city. Finally, two methods were used for evaluation. In the first method, overlaying theoretical and actual map layers, then average, maximum, and minimum indices are extracted based on the theatrical catchment area pixel values in order to determine the degree of correspondence between the actual and theoretical store catchment areas. In the second method, the evaluation was done using the Kappa agreement index.
Findings
In Buein Zahra city, nine chain stores exist that are not uniformly distributed and most of them are concentrated in the central area of the city (Imam, Taleghani, and Valiasr streets). In the first stage, using the modified model of Huff, the chain store catchment area was determined. Generated maps show the probability of residents visiting chain stores. These probabilities varied based on the distance between the store and the attractiveness index. To create a final map of the theoretical catchment area based on the highest probability of residents visiting the stores, the probability maps produced for the stores overlaying and draw break lines. With this method, a map of the areas with the highest probability of visiting each store create. Some spaces of the city are placed in the catchment area of two or more stores according to their location about the stores, according to the equal probability of visiting the stores. In the second stage, the actual catchment area of chain stores was produced based on the questionnaires completed by 430 sample households. Findings of this stage show the city area divided into areas where in each area the majority of households have chosen a store as their priority. Based on the findings of this stage, nine catchment areas were identified for chain stores. To evaluate the modified Huff model used in this research, two methods were used: in the first method, the layers of the actual and the theoretical chain store catchment areas overlaid in the ArcGIS software, and using spatial analysis functions, the average, and minimum and maximum values of the pixels were extracted separately. Based on the findings obtained from this stage, the actual and theoretical chain store catchment areas in Buein Zahra city are compatible, although the degree of compatibility is higher for some stores and less for some of them. The highest degree of compatibility and coordination is dedicated to store number 8 (Korush, branch 1). The second method to evaluate the results is to calculate Cohen's kappa coefficient. To calculate this coefficient, the map of the sample points that used to calculate the actual catchment area (the location of 430 sample households) and the final map of the theoretical absorption area overlaid in ArcGIS software and then calculate Cohen's kappa coefficient. Examining the level of agreement using the calculated Cohen's kappa coefficient shows that the accuracy level in the absorption areas of all stores is above 90%, and this indicates the excellent accuracy of the Huff model in determining the catchment area and its proper matching with the actual catchment area.
Conclusion
In this research, the main goal is to evaluate the effectiveness of the modified Huff model for identifying the chain store catchment areas in small cities. The results of this research are expressed in two parts: the first part, which is based on the main objective of the article, i.e. the evaluation of the modified Huff model, shows that this model is superior in identifying the locations of chain stores in small cities. Results from methods for evaluating the modified huff model (statistical indicators, as well as Cohen's Kappa coefficient); show that the model outputs are close to the pattern of residents' visits to stores in the city. The second part of the results presented is in line with the secondary goal of the research, which is to investigate the distribution of stores and the formation of their catchment areas in the city of Buein Zahra. The research findings indicate the formation of asymmetric catchment areas with different areas in parts of the city. In the central part of the city, the catchment area is smaller, and with the distance from the city center, the catchment area becomes larger.