*2.2. TOPSIS*

This technique, developed by Hwang and Yoon [79], is based on the selection of the shortest distance from the positive ideal solution and the longest distance alternative from the negative ideal solution. The positive-ideal solution is the best possible combination of the criteria. The negative ideal solution consists of the worst criterion values that can be reached. The only assumption in this method is the assumption that each measure is either a monotone increasing or monotonously decreasing one-way benefit. The steps of the TOPSIS method will be shown on the handling problem.

TOPSIS is an approach for identifying an alternative that is closest to the ideal solution and farthest to the negative ideal solution [80]. It has numerous advantages such as a simple process and easy to use and programmable. The number of steps remains the same regardless of the number of alternatives and criteria [81]. This method has a wide range of application areas such as multi-criteria inventory planning [82], freight transport selection [83], selection of the scholarship with the AHP [84], selection of the service providers [85], performance evaluation [86], personnel selection [87], reverse logistics supplier selection [88].

In addition, ANP and TOPSIS methods have been used together in some studies. Ersoz and his colleagues determined the weights of the criteria that were effective in the course selection of graduate students by the ANP method and alternative courses were ranked by using the TOPSIS method [89]. ANP and TOPSIS methods have been used together to evaluate the supplier's selection process [90] and to rank strategies in the mining industry [91].

### **3. Using the ANP and TOPSIS Approach for Route Selection**

Firstly, the criteria and alternatives were identified for selection. Then, the interdependence between criteria, sub-criteria and alternatives was determined. The pairwise comparisons were carried out between these criteria and sub-criteria by using Super Decision program. The pairwise comparisons were made by expert opinions. By this way, weights of the criteria were found for TOPSIS method. In the other step, TOPSIS method were applied by using ANP weights. Then the negative and positive ideal solution and separation were calculated in the TOPSIS steps. At the end of the solution process, the best ranking was created among the alternative routes. This process:


### **4. An Application in ANKARA**

In this study, a route selection was applied for Ankara. Monorail is a new urban mass transportation system. It will be the first example of this system in urban transportation in Turkey with its implementation in Ankara. Ankara is a region covered with plains formed by confined the Kızılırmak and Sakarya rivers in the north-western part of Central Anatolia. The population of Ankara is 5,045,083 according to the results of the 2013 census using Address-Based Population Registration System. The largest districts of Ankara in terms of population are Cankaya, Keciören, Yenimahalle, Mamak, Sincan, Etimesgut, Altındag, Pursaklar and Polatli. The largest district in terms of surface area is Polatli. The main determinant of Ankara's socio-economic structure is the fact that the city of Ankara is the administrative center of the country at the same time. For this reason, the public service sector has an important place in Ankara's economic life. Economical, technological and political developments have initiated the population migration to Ankara from other settlements.

Due to the increasing population and migration, public transportation systems have to be used for urban transportation in Ankara. Public transportation services are provided municipal buses, private buses, minibuses, subways and suburban in this city. Efforts are continuing to establish the monorail system in Ankara.

### *4.1. Determination of the Alternatives*

Ankara is a big city and its population density is very high. For this reason, it has traffic problems. Therefore, municipal administrators have been producing projects for the solution of traffic problems. The first of their projects is urban mass transportation projects. Therefore, monorail technology, one of the types of public transportation, was considered. And 8 alternative routes were identified within the scope of this study.

Table 1 shows characteristic of the routes in terms of distance, number of stations, number of vehicles, number of series, total number of vehicles and approximate total cost of the routes. In this study eight monorail routes were used to determine the best route. These routes and their pictures are shown in Figure 2.


**Table 1.** Characteristic features of the routes.

Route\_1: AOÇ (Tema Park), Gstanbul road, Opera, K<sup>Í</sup>z<sup>Í</sup>lay, BakanlÍk, TBMM, Dikmen Street, Konya road 

Route\_2: Akay Junction, KuÂulupark, Atakule, YÍldÍz

Route\_3: Güvenpark,TBMM, EGM, Dikmen Valley, Hoódere Street, Atakule, Turan Güneó Boulevard, Panora AVM, Oran 

Route\_4: K<sup>Í</sup>z<sup>Í</sup>lay-YukarÍ Ayranc<sup>Í</sup>-Çankaya-YÍldÍz-Oran 

Route\_5: Opera, Ulus, ÇankÍrÍ Street, Grfan BaótuÂ Street, Turgut Özal Boulevard, AydÍnlÍkevler, Siteler, DoÂantepe 

Route\_6: Ulus, ÇankÍrÍ Street, <sup>D</sup>Íókap<sup>Í</sup>, Etlik Street, City Hospital Region, Etlik, Yükseltepe, 

Route\_7: Ulus-Kolej-SeyranbaÂlarÍ

Route\_8: Ulus- Kurtuluó-Türközü- Natoyolu

**Figure 2.** Alternative routes and their pictures in the map.

### *4.2. Determination of the Criteria*

Criteria and sub-criteria were determined by taking the expert opinions and as a result of the literature review. Some of the experts were personnel of Ankara Metropolitan Municipality and they were working in urban planning and traffic planning sections. Other experts were academicians studying in the related field. The determined criteria, sub-criteria and their explanations are shown in Table 2.

Economic: Refers to the use of monetary resources. This criterion deal with construction costs, infrastructure investment, fuel costs. Social impact: This type of criteria refers to both benefits and negative impacts on society because of decisions made regarding the transport system such as the access to shopping-employment-resistant. In addition, the criterion deal with mobility, population density and visual impact for urban area. Engineering: These criteria are related with issues technical of transportation planning such as travel time, demand, accessibility, traffic capacity, ability to develop and to improve, the integration of transport. Environmental impact: This set of criteria is associated to the impacts on the natural environment and historical-cultural area. In this category, we find the sensitive areas and use of land. The attribute of criteria K14 influences criteria K15, the attribute of criteria K9 influences criteria K10, K11, K12 and K13, and criteria K3 influences criteria K4, K5, K7, K1, K2, K14, K15 and sub-criteria of engineering.

### *4.3. Determination of the Weights of the Criteria by ANP Technique*

One of the most important parts is to determine the criteria and measuring indicators in decision-making models. To be determined criteria and their interdependence for this purpose that the important aspects and characteristics of alternatives being measured. Therefore, the design for decision-making model has a direct impact on model efficiency. The criteria and sub-criteria affecting on selection processes differ based on objectives, in this study, we used expert opinion (academic and engineer planners) in order to identify criteria, with regard to municipality strategic goals. For evaluation of the monorail projects, we need quantitative data on environmental impact, engineering, economic and social impact main criteria. Since these projects are new and implemented for the first time in Ankara context, there is very limited quantitative data available, thereby making the evaluation process difficult. At the same time, these projects have ye<sup>t</sup> been considered and have in the process of being planned. To address this situation, a decision-making committee comprising of subject matter experts (4 academic researchers from industrial engineering and civil engineering, 2 transportation experts as rail system planner and transportation planner from Ankara Metropolitan Municipality) made qualitative ratings by using Saaty's 1–9 importance scale for assessing the alternatives and the criteria. In the TOPSIS method, the criterion values of the alternatives were found by using ANP with this scale according to expert opinions.

In this research, to be able to identify the relationship and degree of interdependency among the criteria, opinions of the experts from academia and from metropolitan municipality staff were consulted. Those experts were working and studying in the urban planning and traffic planning area. The relationship having interdependence among the four essential criteria and fifteen sub-criteria taken in this research is shown in Figure 3. There is an interdependence relationship among these criteria in the route selection problem. For example, population density criterion would result in an increase in public mobility and increase the demand level for the selection of alternative routes. All the criteria are linearly related to each other under the engineering criterion. And these criteria also related to the other essential 3 criteria. Likewise, sensitive areas increase the construction cost and these areas affect the current situation such as traffic capacity, ability to develop and to improve, the total travel time, the integration of transport. Thus, there is an interdependency among these criteria and sub-criteria, economy, environmental impact, social impact and engineering.

Comparing the structure of AHP hierarchy, there is the same level relationship among factors in the solution of ANP. At the same time, "Super Decision" program was used in this study.

In order to create pairwise comparisons in the direction of determining the relationships between criteria and alternatives and present them to the user, this program was used. In Table 3, the pairwise comparison of sub-criteria under the engineering factor is shown. This process was carried out for other criteria and sub-criteria. The interrelated criteria is made with ANP using 1–9 Saaty'scale to compare two alterative with respect to attribute.

**Figure 3.** Strategic decision framework.



This decision process is done for every pair of among the each other as shown in Table 3. A basic questionnaire has been prepared and feedback has been taken from academics and planner experts to find out the relative importance of the selected criteria. The pairwise comparison for population density is also shown in this table.

**Table 3.** Comparisons between population density and social impact.


Then, for each criterion, comparisons were carried out with each alternative. Prioritization of the weight of the criteria is ranked in Table 4. In the table, weights of the criteria found with ANP are seen. The criteria having the highest weight values are construction cost, sensitive area, land structure, population density, and ability to develop and to improve, respectively.


**Table 4.** Weights of the criteria.

### *4.4. Ranking Monorail Route Alternatives by Using TOPSIS*

The In this step, TOPSIS technique played role for ranking the routes. The weights were obtained by the ANP technique using Equations (1) and (2). Table 5 shows the normalized weighted matrix by using Equation (1).


**Table 5.** Normalized weighted matrix.

TOPSIS method was applied by using weights of the criteria that are results of the ANP method in the ANP-TOPSIS combine model. The used standard decision matrix in TOPSIS is found at the end of the comparisons of the alternatives with each criterion.

The weights of the evaluation criteria using ANP is shown in Table 6. In addition, the weighted normalized decision matrix by TOPSIS is shown in Table 7. The vector normalization technique is used for computing the element (*aij*) of the normalized decision matrix, which is given as:

$$a\_{ij} = \frac{r\_{ij}}{\sqrt{\sum\_{i=1}^{m} r\_{ij}}} \tag{1}$$

The weighted normalized decision matrix can be calculated by multiplying each row (*rij*) of the normalized decision matrix with its associated attribute weight *ND*. The weighted normalized value *vij* is calculated as below:

$$V\_{i\bar{j}} = N\_D \* r\_{i\bar{j}} \qquad \text{where } \bar{j} = 1, 2, \dots, n; \; i = 1, 2, \dots, m. \tag{2}$$


**Table 6.** The weights of the evaluation criteria using ANP.


**Table 7.** The weighted normalized decision matrix.

Then, using Equations (3) and (4) positive and negative ideal solutions were obtained. The obtained results are shown in Table 8. Compute the positive ideal solution (PIS/A+) and the negative ideal solution (NIS/A−) for each criterion:

$$A^{+} = \left\{ (\max X\_{i\bar{i}} | j \in I^{\*}), (\min X\_{i\bar{i}} | j \in I^{-}) \right\} = \left\{ X\_{1}^{+}, X\_{2}^{+}, \dots, X\_{n}^{+} \right\} \tag{3}$$

$$A^- = \left\{ (\min X\_{i\bar{j}} | j \in I^\*), \left( \max X\_{i\bar{j}} | j \in I^- \right) \right\} = \left\{ X\_1^-, X\_2^-, \dots, X\_n^- \right\} \tag{4}$$

where *J*\* is the set of benefit attributes and *J*− is the set of cost attributes.


**Table 8.** The ideal solution and negative solution.

The ideal solution which maximizes the benefit criteria (criteria of K3, K4, K5, K6, K7, K8, K9, K11 and K12 in this study) and minimizes the cost criteria (criteria of K1, K2, K10, K14 and K15 in this study), whereas the negative ideal solution criteria in this study maximizes the cost criteria/attributes and minimizes the benefit criteria/attributes. The negative ideal solution consists of the worst performance values whereas the best alternative is the one that is nearest to the ideal solution.

The next step of TOPSIS technique is to calculate the Euclidean distance of each alternative. For the positive and negative ideals, the Euclidean distance of each alternative was calculated by using Equations (5) and (6). The distance (*di*+, *di*−) of each weighted alternative *i* = 1, 2 ... , m from the PIS(*d*+*i*) and the NIS(*d*<sup>−</sup>*i*) is computed as follows:

$$d\_i^+ = \left\{ \sum\_{j=1}^n \left( X\_{ij} - X\_j^+ \right)^2 \right\}^{0.5} i = 1, 2, \dots, m; \ j = 1, 2, \dots, n \tag{5}$$

*Mathematics* **2019**, *7*, 16

$$d\_i^- = \left\{ \sum\_{j=1}^n \left( X\_{i\bar{j}} - X\_{\bar{j}}^- \right)^2 \right\}^{0.5} i = 1, 2, \dots, m; \ j = 1, 2, \dots, n \tag{6}$$

In the final stage, relative closeness of suppliers to ideal solution was obtained by using Equation (7) and the results were ranked in terms of relative approximately descending order of routes. Table 9 presents the ranking of alternative routes based on combination of ANP and TOPSIS techniques. The closeness coefficient *CL*+*i* represents the distances to the positive ideal solution (*A*+) and the negative ideal solution (*A*−) simultaneously. The closeness coefficient of each alternative is calculated as:

$$\text{CL}\_{i}^{+} = \frac{d\_{i}^{-}}{(d\_{i}^{+} + d\_{i}^{-})^{\prime}}, \qquad 0 \le \text{CL}\_{i}^{+} \le 1, \; i = 1, 2, \dots, m \tag{7}$$


**Table 9.** Final ranking in two-phase ANP-TOPSIS approaches.

As it is shown in Table 9, route R1 can give the best score among all alternative routes. The order of alternative monorail routes according to the obtained closeness coefficients is R1 > R8 > R4 > R3 > R6 > R5 > R7 > R2. According to this ranking, the best monorail route is "Route\_1(R1): AOÇ (Tema Park), ˙ Istanbul road, Opera, Kızılay" which has the highest closeness coefficient. The results are also shown graphically in Figure 4.

**Figure 4.** Alternatives' rank.

In the study, the criteria with the highest importance levels are sensitive areas, land structure, population density, ability to expand and develop, and construction cost. As a result, this line, which was selected first, became the foreground in terms of being the longest route and having high population.
