# Decision-Aiding Evaluation of Public Infrastructure for Electric Vehicles in Cities and Resorts of Lithuania

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## Abstract

**:**

## 1. Introduction

## 2. Promotion of Electric Vehicles Policy Tools in Lithuania

## 3. Choosing Criteria of Evaluation

## 4. Eliciting of Weights of Criteria and Gauging the Level of Concordance of Opinions of Experts

_{i}, which express importance of each criterion (where i is an index for denoting criteria).

_{ik}, where i = 1, 2, …, m is the index for criteria (m is 8 in our case), while k = 1, 2, …, r is the index to denote responded experts (r—is also 8 in our case). The Kendall variable W, which is used in the chi-squared test statistics for gauging the level of concordance, depends on the squared deviations of sums of all ranks e

_{ik}by all experts (1):

_{max}, observed in the case of absolute concordance of opinions of experts, in terms of ranks of importance of criteria (4):

_{φ}denotes the number of equal ranks within a set within φ.

## 5. Weights Obtained Using Entropy

_{i}, for i = 1, 2, …, m for each criterion is calculated as follows (7):

_{i}, i.e., non-normalized values of the weights determined by the entropy method, are calculated for each criterion (9):

_{i}= 1 − E

_{i}.

_{i}are normalized values of d

_{i}calculated as follows (10):

## 6. A Combined COIN (COmpensating INfluences) Method of Obtaining Weights

## 7. Evaluation Using MCDM Methods

## 8. Evaluation by the EDAS Method

_{j}and NSN

_{j}(17) and (18):

## 9. Evaluation by the SAW Method

_{j}, similarly to all other MCDM methods considered in the paper, reflects attractiveness of each alternative by its magnitude: the larger is the criterion, the more attractive appears to be the alternative. Final values of the cumulative criterion S

_{j}are presented in Table 6.

## 10. Evaluation by the TOPSIS Method

_{1}is the set of indices of the maximizing criteria, I

_{2}is the set of indices of the minimizing criteria.

## 11. Evaluation by the PROMETHEE II Method

_{i}between values of criteria in pairs (A

_{j}, A

_{k}) compared. The method compares all such pairs and creates a cumulative criterion based on such comparisons. Choice of parameters q and s enhances the evaluation by providing more options and has influence on the result [34]. The cumulative criterion is calculated in two steps. First, for every alternative ${A}_{j}$ and all remaining alternatives ${A}_{k}$, two inward and backward aggregated preference indices $\pi ({A}_{j},{A}_{k})$ and $\pi ({A}_{k},{A}_{j})$ are calculated in accordance with the following Formula (27):

## 12. Results

_{cr}= 2.120 for the t-distribution for 16 degrees of freedom at the chosen 5% level of significance. Namely, the correlation coefficient between TOPSIS and SAW: 0.990 (test statistics 28.57 > 2.120); between TOPSIS and EDAS: 0.972 (test statistics 16.60 > 2.120); between SAW and EDAS: 0.973 (test statistics 16.98 > 2.120); between TOPSIS and PROMETHEE: 0.998 (test statistics 67.06 > 2.120); between EDAS and PROMETHEE: 0.973 (test statistics 16.72 > 2.120); and between SAW and PROMETHEE: 0.992 (test statistics 30.96 > 2.120) appeared to reveal a high degree of correlation.

_{f}are values of the aggregate criteria of a method f; ${\tilde{K}}_{f}$ are normalized values of the aggregate criteria of a method f.

## 13. Conclusions

_{cr}= 2.120 for the t-distribution for 16 degrees of freedom at the chosen 5% level of significance. Namely, the correlation coefficient between TOPSIS and SAW: 0.990 (test statistics 28.57 > 2.120); between TOPSIS and EDAS: 0.972 (test statistics 16.60 > 2.120); between SAW and EDAS: 0.973 (test statistics 16.98 > 2.120); between TOPSIS and PROMETHEE: 0.998 (test statistics 67.06 > 2.120); between EDAS and PROMETHEE: 0.973 (test statistics 16.72 > 2.120); and between SAW and PROMETHEE: 0.992 (test statistics 30.96 > 2.120) appeared to reveal a high degree of correlation. Thus, we can be more confident in the obtained results.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Normalised values of aggregate criteria of all four methods for 18 alternatives. Notes: Alternatives are cities of Lithuania: 1—Birštonas, 2—Druskininkai, 3—Alytus, 4—Jonava, 5—Kaunas, 6—Kėdainiai, 7—Klaipėda, 8—Marijampolė, 9—Mažeikiai, 10—Neringa, 11—Palanga, 12—Panevėžys, 13—Šiauliai, 14—Tauragė, 15—Telšiai, 16—Utena, 17—Vilnius, 18—Visaginas, authors’ calculations.

**Figure 4.**The state of the public infrastructure for electric vehicles in cities and resorts of Lithuania. Notes: Alternatives are cities of Lithuania: 1—Birštonas, 2—Druskininkai, 3—Alytus, 4—Jonava, 5—Kaunas, 6—Kėdainiai, 7—Klaipėda, 8—Marijampolė, 9—Mažeikiai, 10—Neringa, 11—Palanga, 12—Panevėžys, 13—Šiauliai, 14—Tauragė, 15—Telšiai, 16—Utena, 17—Vilnius, 18—Visaginas, authors’ calculations.

Factor | Dimension | Reference |
---|---|---|

1. Streets in the city with the dedicated A lane for public transport allowed to be used also by electric vehicles | Part of all streets in the city | National legislation |

2. Parking places and areas exempt from the parking fee for electric vehicles | Number of parking places per 1000 inhabitants | National legislation |

3. Development of high-power charging posts | The number of access points for 1000 inhabitants | European Union legislation adopted in the national legislation |

4. Development of electric charging posts | The number of access points for 1000 inhabitants | European Union legislation adopted in the national legislation |

5. Investment of state institutions to the infrastructure for electric vehicles | Euro per 1000 inhabitants | Created by authors of this paper |

6. Investment of private institutions to the infrastructure for electric vehicles | Euro per 1000 inhabitants | Created by authors of this paper |

7. Integrated electric vehicle infrastructure development projects | Construction of access roads and its infrastructure, in euro per 1000 inhabitants | Created by authors of this paper |

8. Installation of high-power charge posts on roads of national importance within 50 km distance from major city center | The number of access points for 1000 inhabitants | European Union legislation adopted in the national legislation |

Experts | E_{1} | E_{2} | E_{3} | E_{4} | E_{5} | E_{6} | E_{7} | E_{8} | Final Weights ${\mathbf{\omega}}_{\mathbf{i}}$ | |
---|---|---|---|---|---|---|---|---|---|---|

Criteria | ||||||||||

1 | 0.15 | 0.2 | 0.08 | 0.06 | 0.11 | 0.2 | 0.3 | 0.13 | 0.154 | |

2 | 0.14 | 0.12 | 0.1 | 0.1 | 0.15 | 0.2 | 0.2 | 0.08 | 0.136 | |

3 | 0.11 | 0.1 | 0.2 | 0.25 | 0.16 | 0.1 | 0.02 | 0.14 | 0.135 | |

4 | 0.21 | 0.21 | 0.17 | 0.18 | 0.16 | 0.1 | 0.18 | 0.19 | 0.175 | |

5 | 0.09 | 0.09 | 0.06 | 0.18 | 0.09 | 0 | 0.19 | 0.11 | 0.101 | |

6 | 0.12 | 0.15 | 0.12 | 0.08 | 0.11 | 0.2 | 0.01 | 0.12 | 0.114 | |

7 | 0.11 | 0.08 | 0.13 | 0.05 | 0.13 | 0.1 | 0.1 | 0.13 | 0.104 | |

8 | 0.07 | 0.05 | 0.14 | 0.1 | 0.09 | 0.1 | 0 | 0.1 | 0.081 |

Criteria | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Weights | 0.001 | 0.079 | 0.019 | 0.132 | 0.162 | 0.341 | 0.212 | 0.053 |

Criteria | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Weights (entropy), ${\omega}_{i}^{en}$ | 0.001 | 0.079 | 0.019 | 0.132 | 0.162 | 0.341 | 0.212 | 0.053 |

Weights (elicited from experts), ${\omega}_{i}^{ex}$ | 0.154 | 0.136 | 0.135 | 0.175 | 0.101 | 0.114 | 0.104 | 0.081 |

Weights (COIN), ${\omega}_{i}^{C}$ | 0.078 | 0.108 | 0.077 | 0.154 | 0.132 | 0.227 | 0.158 | 0.067 |

Alternatives | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

EDAS | 0.462 | 0.208 | 0.051 | 0.063 | 0.220 | 0.243 | 0.300 | 0.023 | 0.004 |

Rank | 2 | 6 | 15 | 13 | 5 | 4 | 3 | 17 | 18 |

Alternatives | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

EDAS | 0.906 | 0.195 | 0.184 | 0.196 | 0.061 | 0.080 | 0.034 | 0.206 | 0.075 |

Rank | 1 | 9 | 10 | 8 | 14 | 11 | 16 | 7 | 12 |

Alternatives | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

SAW | 0.175 | 0.037 | 0.015 | 0.019 | 0.045 | 0.036 | 0.080 | 0.014 | 0.012 |

Rank | 2 | 7 | 15 | 13 | 5 | 9 | 3 | 16 | 18 |

Alternatives | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

SAW | 0.329 | 0.042 | 0.030 | 0.036 | 0.020 | 0.022 | 0.013 | 0.057 | 0.017 |

Rank | 1 | 6 | 10 | 8 | 12 | 11 | 17 | 4 | 14 |

Alternatives | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

TOPSIS | 0.431 | 0.124 | 0.041 | 0.082 | 0.153 | 0.107 | 0.223 | 0.061 | 0.063 |

Rank | 2 | 8 | 18 | 13 | 6 | 9 | 3 | 15 | 14 |

Alternatives | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

TOPSIS | 0.749 | 0.163 | 0.100 | 0.124 | 0.095 | 0.096 | 0.048 | 0.186 | 0.052 |

Rank | 1 | 5 | 10 | 7 | 12 | 11 | 17 | 4 | 16 |

Alternatives | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

${F}_{j}^{+}$ | 6.641 | 1.287 | 0.240 | 0.612 | 1.717 | 0.887 | 2.643 | 0.356 | 0.359 |

${F}_{j}^{-}$ | 1.634 | 1.766 | 2.444 | 2.106 | 1.831 | 1.806 | 1.581 | 2.221 | 2.263 |

${F}_{j}$ | 5.007 | −0.479 | −2.204 | −1.494 | −0.114 | −0.919 | 1.062 | −1.865 | −1.904 |

Rank | 2 | 7 | 18 | 13 | 6 | 9 | 3 | 14 | 16 |

Alternatives | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

${F}_{j}^{+}$ | 10.989 | 2.024 | 0.820 | 0.981 | 0.714 | 0.771 | 0.260 | 2.294 | 0.357 |

${F}_{j}^{-}$ | 0.710 | 1.440 | 1.885 | 1.856 | 2.069 | 2.048 | 2.239 | 1.798 | 2.256 |

${F}_{j}$ | 10.279 | 0.584 | −1.065 | −0.875 | −1.355 | −1.277 | −1.979 | 0.496 | −1.899 |

Rank | 1 | 4 | 10 | 8 | 12 | 11 | 17 | 5 | 15 |

Alternatives | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

Average rank | 2.0 | 7.0 | 16.5 | 13.0 | 5.5 | 7.8 | 3.0 | 15.5 | 16.5 |

The final rank of the evaluation | 2 | 7 | 16.5 | 13 | 5 | 8.5 | 3 | 15 | 16.5 |

Alternatives | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

Average rank | 1.0 | 6.0 | 10.0 | 7.8 | 12.5 | 11.0 | 16.8 | 5.0 | 14.3 |

The final rank of the evaluation | 1 | 6 | 10 | 8.5 | 12 | 11 | 18 | 4 | 14 |

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**MDPI and ACS Style**

Palevičius, V.; Podviezko, A.; Sivilevičius, H.; Prentkovskis, O.
Decision-Aiding Evaluation of Public Infrastructure for Electric Vehicles in Cities and Resorts of Lithuania. *Sustainability* **2018**, *10*, 904.
https://doi.org/10.3390/su10040904

**AMA Style**

Palevičius V, Podviezko A, Sivilevičius H, Prentkovskis O.
Decision-Aiding Evaluation of Public Infrastructure for Electric Vehicles in Cities and Resorts of Lithuania. *Sustainability*. 2018; 10(4):904.
https://doi.org/10.3390/su10040904

**Chicago/Turabian Style**

Palevičius, Vytautas, Askoldas Podviezko, Henrikas Sivilevičius, and Olegas Prentkovskis.
2018. "Decision-Aiding Evaluation of Public Infrastructure for Electric Vehicles in Cities and Resorts of Lithuania" *Sustainability* 10, no. 4: 904.
https://doi.org/10.3390/su10040904