2.2.1. Defining Blank Service Areas and Candidate Facilities
A 300 m service area for each pre-existing PPP was created based on the road network. We assumed that in the region outside the above area, termed the “blank service area,” there were no PPP services, and all residents in this area required PPP service. Customers were located in the residential buildings within the blank service area. These residential buildings were termed “in-demand buildings.” As illustrated in
Figure 4, the green area represented the service area of the four pre-existing PPPs. The yellow areas represented the central points of each residential building in the blank service area and were designated as demand points.
According to our literature review, PPPs in France mainly depend on small local facilities, such as press kiosks, bars, florists, and tobacco shops [
16]. In the UK, PPPs have been established in frequently visited public facilities in urban areas, such as post offices, petrol stations, and small shops [
9]. In Guangzhou, the pre-existing PPP providers collaborate with retail shops (e.g., supermarkets, convenience stores) and service shops (e.g., car maintenance shops, real estate shops). Thus, in this study, we considered the following types of facilities as potential PPP facilities: supermarkets (including convenience stores), car maintenance shops, computer/phone repair shops, lottery shops, pharmacies, and real estate shops. Information on the location of these facilities in the blank service area was collected via Baidu coordinate system [
39]. On this website, the keywords for parcel pickup points were used as the search criteria; this immediately displayed all the relevant points, including information on latitude and longitude. Coordinate conversion is conducted before the points are added to ArcMap due to the BD-09 coordinate system used by Baidu maps. There are 35 facilities in the blank service area, of which three are located far from the location of the customers and, thus, are not considered.
In the subsequent step, the AHP method was applied in a pair-comparison of all candidate facilities to calculate their respective attractiveness indices. A high number of candidate facilities leads to a high computational cost of pair-comparison. In this study, for the cases where a location had multiple facilities, we selected one representative facility as a candidate facility to reduce the total number of facilities. We divided the 32 facilities into 12 groups according to their distribution and mutual aggregation that is represented by purple ellipses in
Figure 4. In each group, we only selected one facility, represented by a red triangle, as a candidate facility. If there was more than one facility in the group, we created a 300 m service area for each alternative using the ArcMap tool and, then, selected the facility with the largest population in the service area as the candidate facility. Ultimately, we selected 12 candidate facilities for analysis.
2.2.2. Estimating the Population of Residential Buildings
Population data at the building level is necessary for microanalysis. However, the minimum statistical unit of the Chinese census demographics data is a sub-district. Because detailed population data are scarce, estimations of the population play a crucial role.
Lwin and Murayama [
40] proposed a method of obtaining an accurate building population for micro-spatial analysis using the buildings’ volume and census tract data of the area.
The volumetric method is expressed mathematically as:
where BPi is the population in the building i, CP is the population of the census tract, BAi is the footprint area of building i, BFi is the number of floors of building i, i and k are summation indices, and n is the number of buildings that fall inside the CP polygon [
40].
Figure 5 illustrates the estimated population in the study area obtained using the volumetric approach. The population of the buildings in the urban villages is small because these buildings are low-rise buildings and cover a small area. The high-population buildings are the high-rise condominiums or apartments with large footprints.
2.2.3. Calculating the Attractiveness of Different Alternative Facilities Using AHP
AHP is an efficient approach for MCDA applications [
41], which combines qualitative and quantitative analysis with excellent reliability and an extensive range of applications [
42]. We carried out the following steps of the AHP method:
The selection of the criteria for the AHP method has been mainly based on the reviewed literature or expert recommendations [
43,
44]. However, this approach is not suitable for cases covered by only a few research studies. We attempted to carry out a survey of the residents in the research area to determine the factors influencing their judgment of the facility’s attractiveness. This method of determining the AHP’s criteria is one of the novel features of this work.
The selection of sample buildings in the resident preferences survey was based on the proportion of the three different types of residential buildings. We also ensured that the sample sites were spread throughout the blank service area. Questionnaires were administered to 212 residents who responded to queries about their attributes (gender, age, family composition), their willingness to use the PPP, their psychological characteristics, an acceptable distance to the PPP, and the factors affecting the location selection. Most of the questions required the selection of only one answer out of multiple choices provided except for the factors affecting the location selection for which respondents were allowed to select as many factors as were applicable.
Table 2 shows the results obtained for the factors affecting the attractiveness of the facility. It was found that 99% of the respondents would consider the operation hours of a facility, followed by the convenience and attributes of the PPP. Only 10% of the respondents considered the size of the staff. Thus, four critical factors determined the attractiveness of a facility: its operation hours, distance to bus stops, type of facility, and area.
The results for the acceptable distance to PPP indicated by the residents are shown in
Table 3. Nearly half of the respondents could accept a distance range that was within 300 m, followed by 500 m and 1000 m, while all residents were opposed to a range that was greater than 1000 m. In the next analysis step, we will use these distances to determine the optimal facilities.
The general hierarchy structure of AHP consists of three fundamental levels. As illustrated in
Figure 6, the overall objective of AHP in this study is to quantify the attractiveness of the 12 candidate facilities. The four decision criteria are determined by the questionnaire described in the preceding section and the alternatives are the 12 candidate facilities. The overall decision matrix is expressed as:
where X denotes the overall attractiveness and
denotes the attractiveness of the facility i for criteria j.
The AHP creates a pairwise comparison matrix to determine the weights of the criteria. The relative importance scale with a numerical scale between one to nine derived from the psychophysical law of Weber–Fechner is the most widely used AHP scale [
45,
46]. To determine the consistency of the judgments from each pairwise comparison, the consistency index (CI) of the matrix was calculated and compared with a random index (RI) to obtain the consistency ratio (CR) [
41]. If the CR is less than 0.1, the judgments in the pairwise comparison matrix are considered to be consistent [
47]. We administered an AHP questionnaire among the potential customer representatives to obtain these data. Ten representative households that frequently shopped online were selected from different residential building types to fill the questionnaire: four from the condominium, four from the apartment, and two from the urban village. After collecting the data, we checked the consistency ratio (CR) and analyzed the data using a free online tool named the AHP Online Calculator— Business Performance Management Singapore (BPMSG) [
48]. Nine households’ data with a CR value that was below 0.1 qualified and one household’s data with a CR value of 0.29 was invalid. We then constructed the matrix w of the criteria and normalized the pairwise comparison data to obtain the weights using the online tool.
In this paper, with 12 alternatives and four criteria, the residents had to complete 264 questions to generate the weights of the alternatives. A comparison of the quantity data is tedious and inefficient, particularly in the cases with a high number of criteria and alternatives. Some researchers attempted to reduce the complexity of the preference eliciting process (i.e., by employing incomplete pairwise comparisons and a sparse structure) [
49,
50]. In this study, since the values of the alternatives in the criteria were mainly quantitive data, we suggested a simple approach for obtaining the relative importance scale in terms of one to nine, instead of a pairwise-comparison using a questionnaire. The equations are described below.
For example, the importance scale Bij was derived using the alternatives of Si and Sj, which are the matrix values in the interval [Max S, Min S]. If a larger value corresponds to better performance (such as size, business hour), and Si≥ Sj, Bij is calculated as:
If a smaller value corresponds to better performance (such as distance), and Si ≤ Sj, Bij is calculated as:
The attractiveness of each candidate facility is computed using the criteria matrices w and the alternative matrix S obtained in the preceding step:
2.2.4. Estimating the Number of Customers of the Potential Facilities Using the Huff Model
The Huff model assumes the flow between the facility and the demand to predict consumer spatial behavior. While in the previous study, the attractiveness was mainly based on the facility’s area, in this study, we imported the index of facility attractiveness calculated using the aforementioned steps. The probability (Pij) that a consumer living in i will select the facility j is calculated using the following formula:
where Pij is the possibility of a customer located in the building i selecting facility j, Aj is the attractiveness of facility j, Dij is the distance from i to j, λ is a parameter that considers the effect of distance on shopping, and n is the number of the facilities that can be accessed by the people living in building i.
The parameter estimated for Tajima, for which λ equals 2, was considered to be the most typical value for the attractiveness parameter [
51,
52]. This empirical parameter was used for the analyses conducted in this study.
The estimated number of consumers in the potential facility j is calculated using the following formula:
where Bj is the predicted number of residents visiting the facility j, Si is the total number of residents in the building i, and Pij is the probability that residents living in the building i will visit facility j.
Here, we consider the in-demand Building 1 in
Figure 7 as an example of the calculation in order to illustrate the method.
Figure 7 shows the allocation of PPP within 300 m and the routes from Building 1 to facilities in the road network analysis using ArcMap. The distance in network analysis in (b) is the same as the data in (a). This verifies that the allocation function in ArcMap is consistent with the calculation of the road network distance.
The estimated population of Building 1, the attractiveness of facilities J and H, and the distance between these facilities are used as input into the Huff model for verification. The predicted number of the residents living in Building 1 and visiting facilities J and H calculated using the Huff model formula is consistent with the data from the analysis results table produced using the network allocation function in ArcMap. In this study, we used this function after the Huff model to rapidly obtain accurate calculation results:
The result for the consumers predicted to use the facility depended on different acceptable distances. The ranking of the 12 candidate facilities changes according to the acceptable distance. A chart of the ranking fluctuation of each candidate facility with a distance ranging between 100 m and 1000 m was used for the analysis of the optimal location.