**4. Methods**

In this study, two different methods were used. One of them was goal programming. The other one was the analytic network process. These two techniques will be briefly summarized below.

### *4.1. Goal Programming (GP)*

Goal programming is a kind of multi-criteria decision-making model. The model is established using both soft constraints and hard constraints. Soft constraints are used to model situations where deviations are acceptable to a desired goal value. Thus, more than one desired situation is provided approximately or fully. Goal programming is a mathematical programming method aiming at minimizing deviations from the goal values determined by turning aims to goals and ranking goals by importance ratings, or weighting each of them. In linear programming, while a single objective function is used, it is aimed to achieve the same goal by targeting multiple goals differently in the goal programming. In 1955, Charnes and his colleagues first worked on goal programming [67]. Later in 1961 and 1977, Charnes and Cooper developed this model [68,69]. Ignizio [70] describes goal programming as follows: Minimize the deviations in the aim thus that each target reaches as far as possible the given goals. The goal programming mathematical representation is as follows [71]:

$$\text{Minimize } Z = \sum\_{\mathcal{S}=1}^{\mathcal{C}} (d\_{\mathcal{S}}^{+} + d\_{\mathcal{S}}^{-}) \tag{1}$$

$$\sum\_{s=1}^{\mathcal{Y}} a\_{\mathcal{S}^s} \mathbf{x}\_{\mathcal{S}} - d\_{\mathcal{S}}^+ + d\_{\mathcal{S}}^- = b\_{\mathcal{S}} \tag{2}$$

$$d\_{\mathcal{X}}^{+} \; d\_{\mathcal{X}}^{-} \; \mathbf{x}\_{\mathcal{X}} \; \geq \; \mathbf{0} \tag{3}$$

$$\text{gg} = 1 \dots \text{~} \quad \text{s} = 1 \dots \text{~} \text{~} \dots \text{~} \text{~} \text{~} \text{~} \text{!} \text{\\
\text{Number of goals} \quad \text{s} \text{::} \text{!} \text{\\
\text{Number of devices variables} \quad \text{(4)}$$

*xs* : *s*th decision variable, *s* = 1... *y* (5)

$$a\_{\mathbb{S}^\S} \text{ : Coefficient of } g^{\text{th}} \text{ goal and } s^{\text{th}} \text{ decision variable } \quad \text{g} = 1 \dots \text{es} = 1 \dots \text{y} \tag{6}$$


### *4.2. Analytic Network Process (ANP)*

Analytical Networking (ANP) is a multi-criteria decision-making technique developed by Thomas L. Saaty as a more general approach than the Analytic Hierarchy Process (AHP) method and works with the dual comparative logic like AHP. The Analytical Networking Process can be used to model decision problems that need to take account of the relationships between factors and to achieve more effective results. In the ANP method, factors affecting a goal and a target are grouped according to their effects on each other and a suitable network is modeled [72]. The ANP differs from the AHP in that it uses a hierarchical structure (network / network form) instead of a hierarchical structure from top to bottom [73]. Furthermore, an important problem encountered in the AHP method is rank reversal. Order change; the alternative priorities determined by a particular set of factors change when a new alternative is added or removed [74]. This problem has been reduced by the ANP method [72]. Steps of the ANP method is like that [75]:

Step 1: Determining the Decision-Making Problem

Step 2: Determining Relationships: Interactions between criteria and sub criteria are identified.

Step 3: Performing Criteria Binary Comparisons

Step 4: Calculating of Consistency: The consistency ratio (CR) of each binary comparison matrix is calculated. For consistency, CR < 0.1.

Step 5: Creating Super Matrices in Order:


*Step 6:* Determination of the Best Alternative: Alternative priorities are obtained by selecting the highest alternative among these values by finding the limit super matrix and criterion weights.
