Store Network Planning and Location-allocation Modeling

Retail chains are often concerned with selection of multiple store locations to serve a spatially dispersed population: that is, to allocate a given spatial distribution of demand to a specific number of retail outlets. This is achieved using location-allocation modeling, which is grounded upon the third law of location science: sites of an optimal multi-site pattern must be selected simultaneously rather than independently, one at a time (Church & Murray, 2009). In this chapter, the concepts of location-allocation are explained, and its operations in ESRI’s Network Analyst platform are illustrated with two case studies.

Location-allocation Modeling and Data Requirements

Location-allocation is used to select sites for a number of facilities simultaneously, from which sendees/goods are provided to a spatially dispersed population. It is suitable for spatial planning of both public and private service facilities. When used in store network planning, this method assists in determining how many stores are needed in the target market, how many stores can be supported, and where the stores should be located. Location-allocation modeling combines site selection and trade area delineation in the same process. Questions to be answered include: (1) how do all the outlets of a chain work together to efficiently serve the market? (2) if one store were to be added or closed, how would that change affect the performance of the other stores? (3) if some of the outlets are to be closed, which ones should be closed and which ones should remain open? Location-allocation modeling follows the deterministic approach in defining trade areas, which is different from the Huff Model.

Grounded upon the central place theory (Beaumont, 1987), the location-allocation method was first introduced in the 1960s by Cooper (1963). Since then, it has attracted a considerable amount of academic interest, especially in the 1970s and the 1980s, when related publications proliferated. A succinct explanation of locationallocation modeling is provided by Ghosh and McLafferty in their book Location Strategies for Retail and Service Firms, where they define location-allocation modeling as “a method for evaluating alternative network configurations and determining the sites that are most accessible to consumers” (Ghosh & McLafferty, 1987: 129). Location-allocation is not a single method, but a modeling procedure with several solutions, each using a different mathematical algorithm. It allows systematic evaluation of a large number of possible locational configurations, while meeting a set of user-defined criteria (or allocation rules), such as maximum cover, minimum travel distance, desired travel distance and time, and desired number of facilities.

Based on the objectives of particular problem solutions, locationallocation models can be differentiated into two general classes (Narula, 1984): cover models and mini-sum models. Cover models are concerned with locating facilities to maximize the number of clients to be served by them within a desired distance/time threshold by locating a fixed number of facilities (Church & ReVelle, 1974). They are commonly, but not necessarily only, applied to senices that are delivered to patrons (such as emergency sendees). Mini-sum models aim to minimize the distance traveled by patrons to facilities. More precisely, they aim to determine the locations of a number of facilities such that the total weighted distance to the closest facility is minimized (Kemp, 2008). Mini-sum models are typically applied to senices/businesses that patrons travel to, such as retail stores.

Description and explanation of the location-allocation models in mathematical terms is beyond the scope of this chapter. Fortunately, a number of easy-to-use “apps” are built into two of the many extensions of ESRI’s ArcGIS: Network Analyst and Business Analyst. Specifically, six location-allocation models are included in Network Analyst, of which three are included in Business Analyst (see Table 9.1). These apps spare the ordinary users from having to use the complex mathematical formulas to reiterate many rounds of calculations, and make computations and presentation of the results much easier and faster.

Table 9.1 Location-allocation Models in ESRI’s Network Analyst and Business Analyst

Model class

Model

In Network Analyst

In Business Analyst

Cover models

Maximum coverage

Maximum attendance

Maximum market share

Target market share

Maximum coverage

Maximum market share

Mini-sum models

Minimum impedance (/»-median) Minimum facility

Minimum impedance (/»-median)

The maximum coverage model locates facilities in such a way that all demand points, or the greatest possible number of them, within a specified impedance cutoff are allocated to the chosen facilities. The maximum attendance model uses the location of each demand site as an indicator, and tends to locate facilities closer to the areas with the highest density of demands; the proportion of demand allocated to the nearest facility decreases with increasing distance (ESRI, 2019). With the maximum attendance model, a set of facilities that maximize the total allocated demand is chosen; the demands that are further than the specified impedance cutoff do not affect the chosen set of facilities.

While the maximum coverage and the maximum attendance methods are deterministic (or spatial monopoly) methods of choosing new locations among all candidate sites in the study area, the maximum market share method chooses facilities in the presence of competitors, to maximize their captured market share (Lee & O’Kelly, 2011). Gravity model concepts are followed to determine the proportion of demand allocated to each facility, and the set of facilities that maximizes the total allocated demand is chosen. The target market share model is a variation of the maximum market share method: instead of maximizing the market share, it determines the minimum number of facilities and locates them to reach a specified market share that the business is content to capture, in accordance with the available company resources and the existing competitive market environment.

The minimum impedance model, also known as the /»-median model, chooses facility locations such that the sum of all weighted travel distance/time (i.e., the demand allocated to a facility multiplied by the distance between each demand point and the facility) is minimized for a given impedance cutoff (Gokbayrak & Kocaman, 2017). The main objective is to minimize the cost of transportation, which is an important component of the total shopping cost. In a variant method, a P power (or exponent) is used to amplify the effects of distance (Morrill, 1974). This calculation creates an effective distance value from each point of demand to each candidate site, and is generally used to limit the number of candidate sites with a larger distance from the given supply points. The minimum facility method, as its name indicates, chooses the smallest number of facilities needed to cover the greatest amount of demand within a specified impedance cutoff.

Goodchild (1984) distinguishes two types of corporate strategies that influence the choice of location-allocation models: the conservative strategy, and the aggressive strategy. The first strategy excludes from consideration the locations that are adjacent to established competitors, and favors locations in the “holes” of the existing market coverage. Associated with this strategy are market share models of locationallocation (both maximum market share and target market share). The second strategy looks for locations that are most accessible to customers, regardless of the presence of established competitors. With this strategy, the “competition-ignoring models” of location-allocation are used, and locations adjacent to competitors are also included in the list of candidate sites for consideration. If such locations are deemed “optimal”, the company may attempt to obtain them through business merger and acquisition.

Finally, readers should be aware that location-allocation models are subject to the effects of the modifiable areal unit problem (MAUP) (Chakrapani et al., 2006; Sedgwick, 2015). MAUP is one of the largest sources of statistical bias that can significantly impact spatial analysis. It is a result of varying geographies at differing scales, which can represent closely, or misrepresent, a target population in the market (Dark & Brain, 2007). In location-allocation modeling, the points of demand are usually represented by the centroids of the census geographies (such as census tracts or dissemination areas) from which distance to the location of facilities is calculated. The location-allocation results may vary depending on the scale of the census geography to be used to aggregate demands, and the market shares and population characteristics in the trade area of each facility can change as well. Because the minimum impedance model is based on reducing the weighted travel time or distance, it is more sensitive to the issues of MAUP.

Location-allocation modeling requires the use of three types of data:

  • (1) a list of census tracts or dissemination areas as points of demand;
  • (2) a list of candidate sites as potential facility locations; and (3) a road network that links the points of demand with the candidate sites, and is used to calculate travel distance/time. Two case studies are presented in the rest of this chapter to illustrate the location-allocation procedure and operations in the Network Analyst environment.
 
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