3.2 Evaluation method

Regarding studies related to A, though the studies grasped the awareness of the local residents and awareness and behavior of users, as well as the actual condition of operation for nursing facilities, the location of the facilities was not considered. Regarding studies related to B, though the studies investigated the care services provided from nursing facilities, the location of the facilities was not considered. Regarding studies related to C, Nagashima et al. (2014) [19] and Munemasa et al. (2015) [21], respectively, considered EV power stations and business-andresidential distribution as their study subject and proposed a method to derive efficient locations. Though Segawa et al. (1996) [18] conducted simulations with the assumption that the facilities will be relocated, as there are currently many existing nursing facilities in cities of Japan, the above simulations cannot propose realistic solutions for such facilities. Additionally, though Tanaka et al. (2016) [27] and Furuta et al. (2017) [28] focused on the equity concerning the facility location evaluation method, it has only been applied to virtual cities and not to any actual cities. Therefore, with the results of the preceding studies mentioned above as a reference, the present study will demonstrate the originality by considering the lack of nursing facilities, which has become a serious social issue, and quantitatively

For the evaluation method of nursing facility locations, PostgreSQL Ver. 9.6.1 and ArcGIS Pro Ver. 2.0 of Environmental Systems Research Institute (ESRI) were

3.1.1 Creating the distribution maps of the aging population and nursing facilities as well

The distribution maps of the aging population and nursing facilities as well as a road network map are created in digital map form using GIS. These three types of digital maps are superimposed, and the closest road node from a representative point from each nursing facility and area (divided by town and street) is set on the

3.1.2 Calculating the specialization coefficient of the population aging rate and adding it

By applying the data obtained in section 3.1.2 to A\* algorithm, which is explained in the following section, the shortest route between each nursing facility

The specialization coefficient of the population aging rate is calculated using the aging population in addition to the total population data from each area, and the

used. The evaluation framework and process are as mentioned below:

evaluating current facility locations.

Geographic Information Systems and Science

3. Evaluation framework and methods

3.1 Evaluation framework and process

as a road network map

to the road network map

and each area is calculated.

26

results are added to the road network map.

3.1.3 Calculating the shortest route using A\* algorithm

road network map.

3.2.1 Creating the distribution maps of the aging population and nursing facilities as well as road network maps

#### 3.2.1.1 Distribution map of the aging population

The age group being evaluated in the present study is those over the age of 75. There are many cases where those over 65 can use nursing facilities. However, according to Hashimoto (2015) [29], the life expectancy and health span in Japan have become higher in recent year, with the latter being 71.19 for men and 74.21 for women. Therefore, assuming most users of nursing facilities are over 75, the age group was set for those over 75. As for the evaluation target area, in order to calculate evaluation points according to each area, GIS is used to display the distribution of the aging population on the digital map.

#### 3.2.1.2 Distribution map of nursing facilities

GIS is used to display the distribution of nursing facilities on the digital map. While nursing facilities include facility types such as admission type, commuter type, and other related facilities, the present study will only consider admission type of nursing facilities.

#### 3.2.1.3 Creating a road network map

As for the distance between nursing facilities and each area in the present study, the road network distance is used instead of the linear distance. This is because the linear distance may be extremely short compared to the distance when traveling along the roads to the nursing facilities, and this may cause the estimate of the travel distance of users to be shorter than it actually is.

First, GIS is used to display the road network map of the evaluation target area in digital map form. Next, the node closest to every nursing facility and the representative point in each area will be set up on the digital map. The representative point is the central point of the area, and the nodes are the intersections and endpoints of the roads. This is set up as the distance is calculated according to each node. In the present study, the node set as the representative point of the area is the start node, and the node set as the nursing facility is the end node.

### 3.2.2 Calculating the specialization coefficient of the population aging rate and adding it to the road network map

#### 3.2.2.1 Introducing the specialization coefficient of the population aging rate

In the present study, the distance is weighted so that the road distance of areas with a large demand is longer, while the road distance of areas with a small demand

Figure 1. Weighting pattern diagram.

is shorter, as shown in the weighting pattern diagram in Figure 1. If a user from a certain area selects a nursing facility that requires him or her to go through a transit area with a large demand, there is a high chance that there will be competition among users, as those from the transit area will most likely select the same nursing facility. Therefore, the weighting is conducted as mentioned above with the assumption that psychological distance of the users will be longer.

The specialization coefficient of the population aging rate is used as the weighting coefficient. The specialization coefficient of the population aging rate is the value indicating how high the population aging rate is in a certain area. Besides the specialization coefficient of the population aging rate, the population aging rate and the aging population can both be considered as a weighting coefficient. However, because the population aging rate is the ratio with the value always being 1 or less, the distance is always calculated to be shorter. Additionally, the difference in the aging population among the different areas is substantial enough to greatly affect the distance. On the other hand, the specialization coefficient of the population aging rate does not make the value too big or too small; hence, it is suitable as a weighting coefficient.

#### 3.2.2.2 Calculating the specialization coefficient of the population aging rate

The specialization coefficient of the population aging rate in each area is calculated. In order to calculate the specialization coefficient, the population aging rate must be calculated first. The population aging rate and the specialization coefficient of the population aging rate are, respectively, calculated using Eqs. (1) and (2):

$$A\_i = \frac{p\_{\text{75i}}}{p\_i} \tag{1}$$

rate. As a rule for addition, the specialization coefficient of the population aging rate is added if the nodes are in the same area as in nodes (i) and (ii) of Figure 2. However, if the nodes are in different areas as in nodes (ii) and (iii), the average value of the specialization coefficient of the population aging rate is added.

Example of specialization coefficient of the population aging rate added to the road network map.

The shortest route between each nursing facility and each area will be calculated using A\* algorithm. A representative search method for finding the shortest route is the Dijkstra method (Dijkstra, 1959) [30]. However, in the present study, the latitude and longitude are used for the coordinates of the representative points in each area as well as the nursing facilities, and the estimate value of the shortest routes between the two points are available in advance. Therefore, A\* algorithm, which is the improved version of the Dijkstra method that can effectively calculate

In general, when considering the shortest route which starts at the start node, goes through node n, and ends at the end node, the route is expressed as shown in Eq. (3):

ð Þþ <sup>n</sup> <sup>h</sup><sup>∗</sup>

ð Þ <sup>n</sup> is the shortest route distance (m), <sup>g</sup><sup>∗</sup>ð Þ <sup>n</sup> is the shortest distance

ð Þ <sup>n</sup> can be easily obtained if the values of <sup>g</sup><sup>∗</sup>ð Þ <sup>n</sup> and <sup>h</sup><sup>∗</sup>

where f nð Þ is the estimate value of the shortest route, g nð Þ is the estimate value of the shortest route from the start node to n, and h nð Þ is the estimate value of the

An example of actually searching for the shortest route using A\* algorithm on a computer is shown in Figure 3. In this example, the shortest route from coordinates (2,2) to (5,5) is obtained. The gray cells are set as impassable, while F, G, and H correspond to f nð Þ,g nð Þ, and h nð Þ of Eq. (4). However, G is the actual travel distance from (2,2) to the current cell, and the distance for moving one cell over in

∗

ð Þ n (3)

ð Þ n are impossible to obtain beforehand.

ð Þ n are already

ð Þ n is the shortest distance from n to the end

ð Þ n with the estimated f nð Þ is called A\* algo-

f nð Þ¼ g nð Þþ h nð Þ (4)

3.2.3 Calculating the shortest route using A\* algorithm

Evaluation of Nursing Facility Locations Using the Specialization…

DOI: http://dx.doi.org/10.5772/intechopen.81364

f ∗ ð Þ¼ <sup>n</sup> <sup>g</sup><sup>∗</sup>

the shortest routes, is used.

∗

from the start node to n (m), and h<sup>∗</sup>

Therefore, the method of replacing f

shortest route from n to the end node.

known, in reality, the values of <sup>g</sup><sup>∗</sup>ð Þ <sup>n</sup> and <sup>h</sup><sup>∗</sup>

rithm, and it is expressed as shown in Eq. (4):

where f ∗

node (m). Though f

29

Figure 2.

where Ai is the population aging rate of area i (%), p75<sup>i</sup> is the population of those over 75 in area i (people), and pi is the total population of area i (people).

$$\text{SC}\_{i} = \frac{\text{A}\_{i}}{\text{A}} \tag{2}$$

where SCi is the specialization coefficient of the population aging rate in area i, Ai is the population aging rate of area i (%), A is the population aging rate of all areas (%).

#### 3.2.2.3 Adding the specialization coefficient of the population aging rate to the road network map

The specialization coefficient of the population aging rate calculated in Eq. (2) is added to the road network map using PostgreSQL. This is done by multiplying the distance between nodes by the specialization coefficient of the population aging

Evaluation of Nursing Facility Locations Using the Specialization… DOI: http://dx.doi.org/10.5772/intechopen.81364

Figure 2. Example of specialization coefficient of the population aging rate added to the road network map.

rate. As a rule for addition, the specialization coefficient of the population aging rate is added if the nodes are in the same area as in nodes (i) and (ii) of Figure 2. However, if the nodes are in different areas as in nodes (ii) and (iii), the average value of the specialization coefficient of the population aging rate is added.
