Geographic Information Systems and Science

route in this example is indicated by the gray dotted line arrow, and the distance of the shortest route is 5. Though 1 was set as the distance when it was moved one cell over in the example of Figure 3, the distance can be changed according to each moved cell. In the present study, the distance of G is set as the product of the actual travel distance and the specialization coefficient of the population aging rate men-

3.2.4 Evaluation of nursing facility locations using the specialization coefficient of the

from the users to their closest facility is minimized, and this problem can be modeled as shown in Eq. (5). This model obtains the optimal location to reduce the

load of users in all areas to the extent possible by changing the value of Xij:

Z ¼ ∑ i ∑ j

min dij

> min Dij

4. Selection of evaluation target area and data processing

min Xij

Evaluation of Nursing Facility Locations Using the Specialization…

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

area i, and dij is the distance from area i to facility j.

The p-median problem is a facility location problem in which the total distance

where Xij∈f g 0; 1 : is the allocation for facility j in area i, wi is the demand in

In the present study, the evaluation method is developed based on the p-median problem. Eq. (5) is a model that obtains the suitable location to reduce the travel load of users in all areas as much as possible and is different to the purpose of the present study. Therefore, in order to match the purpose of the present study,

Zi <sup>¼</sup> widijAi <sup>¼</sup> p75i

where Zi is the evaluation point for area i, wi is the demand in area i, and dij is

Xij of Eq. (5) is removed in order for the facility location to stay the same, and by calculating the evaluation points according to each area, the facility location situation in each area can be quantitatively grasped. Additionally, as for the originality of the present study, distance dij is weighted by the specialization coefficient of the population aging rate as mentioned in Section 3.2.2. With Dij as the weighted

where, Zi is the evaluation point for area i, wi is the demand in area i, and Dijis

The evaluation points of each area is calculated after applying the aging population and the distance of shortest routes to nursing facilities of each area obtained in Sections 3.2.1 and 3.2.2, and the results are displayed on the digital map using GIS.

For the evaluation target area in the present study, Chofu City, Tokyo, was selected. Chofu City is located in the suburban area of Tokyo as shown in Figure 4.

pi

Zi ¼ wiDij (7)

widijXijAi <sup>¼</sup> p75i

pi

(5)

(6)

tioned in Section 3.2.2.

population aging rate

Eq. (5) is changed into Eq. (6):

the distance from area i to facility j (m).

distance, Eq. (6) can be expressed as Eq. (7):

the weighted distance of area i to facility j (m).

4.1 Selection of evaluation target area

31

#### Figure 3.

Example of shortest route calculation using A\* algorithm.

any direction is counted as 1. Additionally, for the estimate value of the shortest distance from the current cell to (5,5), H is set as the higher value of the difference between the x-coordinate and the y-coordinate of the two points.

The algorithm process is as follows:


The cells leading to the destination cell at this time is the shortest route, and the value of F obtained at the end is the distance of the shortest route. The shortest

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

route in this example is indicated by the gray dotted line arrow, and the distance of the shortest route is 5. Though 1 was set as the distance when it was moved one cell over in the example of Figure 3, the distance can be changed according to each moved cell. In the present study, the distance of G is set as the product of the actual travel distance and the specialization coefficient of the population aging rate mentioned in Section 3.2.2.

### 3.2.4 Evaluation of nursing facility locations using the specialization coefficient of the population aging rate

The p-median problem is a facility location problem in which the total distance from the users to their closest facility is minimized, and this problem can be modeled as shown in Eq. (5). This model obtains the optimal location to reduce the load of users in all areas to the extent possible by changing the value of Xij:

$$\min\_{X\_{\vec{\eta}}} Z = \sum\_{i} \sum\_{j} w\_{i} d\_{\vec{\eta}} X\_{\vec{\eta}} A\_{i} = \frac{\mathbf{P}\_{75i}}{\mathbf{P}\_{\vec{\imath}}} \tag{5}$$

where Xij∈f g 0; 1 : is the allocation for facility j in area i, wi is the demand in area i, and dij is the distance from area i to facility j.

In the present study, the evaluation method is developed based on the p-median problem. Eq. (5) is a model that obtains the suitable location to reduce the travel load of users in all areas as much as possible and is different to the purpose of the present study. Therefore, in order to match the purpose of the present study, Eq. (5) is changed into Eq. (6):

$$\min\_{d\_{\vec{y}}} Z\_i = w\_i d\_{\vec{y}} \mathbf{A}\_{\mathbf{i}} = \frac{\mathbf{P}\_{75\mathbf{i}}}{\mathbf{P}\_{\mathbf{i}}} \tag{6}$$

where Zi is the evaluation point for area i, wi is the demand in area i, and dij is the distance from area i to facility j (m).

Xij of Eq. (5) is removed in order for the facility location to stay the same, and by calculating the evaluation points according to each area, the facility location situation in each area can be quantitatively grasped. Additionally, as for the originality of the present study, distance dij is weighted by the specialization coefficient of the population aging rate as mentioned in Section 3.2.2. With Dij as the weighted distance, Eq. (6) can be expressed as Eq. (7):

$$\min\_{D\_{\vec{\eta}}} Z\_i = \ w\_i D\_{\vec{\eta}} \tag{7}$$

where, Zi is the evaluation point for area i, wi is the demand in area i, and Dijis the weighted distance of area i to facility j (m).

The evaluation points of each area is calculated after applying the aging population and the distance of shortest routes to nursing facilities of each area obtained in Sections 3.2.1 and 3.2.2, and the results are displayed on the digital map using GIS.

#### 4. Selection of evaluation target area and data processing

#### 4.1 Selection of evaluation target area

For the evaluation target area in the present study, Chofu City, Tokyo, was selected. Chofu City is located in the suburban area of Tokyo as shown in Figure 4.

any direction is counted as 1. Additionally, for the estimate value of the shortest distance from the current cell to (5,5), H is set as the higher value of the difference

between the x-coordinate and the y-coordinate of the two points.

2. Move to the cell with the value of F being the lowest.

as that of the current cell, it is moved to this cell.

1. Calculate the values of F, G, and H, surrounding the first cell.

3. Calculate the values of F, G, and H, surrounding the moved cell.

4.Among the cells newly calculated in the algorithm process 3, if the value of F is the same as or lower than that of the current cell, it is moved to that cell. If the value of F is higher than that of the current cell, the search on this route is discontinued. Then, among the value of cells already calculated, if the values of F, G, and H can be calculated and the value of F is the same or almost the same

5. The algorithm processes 3 and 4 are repeated until the destination cell is reached.

The cells leading to the destination cell at this time is the shortest route, and the value of F obtained at the end is the distance of the shortest route. The shortest

The algorithm process is as follows:

Example of shortest route calculation using A\* algorithm.

Geographic Information Systems and Science

Figure 3.

30

Chofu City was selected as the evaluation target area, as the aging population (age 65 or over) has already exceeded the youth population (under age 15), and the aging population is expected to increase in the future. According to the survey on the aging population in Chofu City [31], 23,545 people, equivalent to approximately 10% of the total population, fit in the current age range of the present study subject which is 75 and over. In the present study, evaluation will be conducted in the unit of 105 areas within Chofu City.
