# Hybrid Group MCDM Model to Select the Most Effective Alternative of the Second Runway of the Airport

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- The development of a flexible MCDM model that helps decision makers to choose the best alternative based on a set of parameters for specific problem-solving goals;
- The hybrid group MCDM model to select the most effective choice of the second runway of the airport approach for the planning of strategy.

- The law permits it (only alternatives that are allowed or may be allowed by law may be potentially applied);
- Physically feasible (depending on plot size, shape, topography, and other features);
- Financially sound (the efficient and best use of assets must be economically viable, use of the building must ensure an adequate income to justify construction costs and investor returns, the remaining economic life is evident; in the case of growth, the issue of commercial viability becomes the most problematic issue of local use);
- The logic of rational use: content and procedure, macro and micro, long-term and short-term effects.

- The results of problem solutions—known or unknown;
- The consequences occurrence period—one or more;
- The number of alternatives—finite or infinite;
- The alone decision maker or group of decision makers;
- The indirectly assessed and modelled competitive response.

## 3. Problem-Solving Model

#### 3.1. Research object

- Identify potential critical airplanes;
- Identify the most demanding airplanes;
- Determine method;
- Select the recommended runway length;
- Describe available alternatives;
- Assess the feasible options and rank them;
- Analyze solution results;
- Implement the selected choice.

#### 3.2. Setting the Criteria Values

#### 3.3. Determination of Criteria Weights By Ranking Method

_{k}– k is the number of related ranks; number of equal grades k; h

_{l}—the number of ranks in a group of related ranks, in terms of k expert; the grade assigned to a criterion of an expert; r—the number of experts; n—the number of evaluated criteria.

#### 3.4. Task-Solving by the MULTIMOORA-F Method

#### 3.4.1. Calculation of Relative Sizes, the Fuzzy Ratio System of the MOORA Method

_{i}for each i-th alternative. Normalized values express aggregation or subtraction of fuzzy numbers.

#### 3.4.2. The Fuzzy Reference Point Part of the MOORA Method

#### 3.4.3. Part of the Multiplicative Form of the MOORA Method

## 4. Practical Problem Solving Using the MULTIMOORA-F Method

**x**has the most significant impact on the final solution in this particular matrix (approximately 14%). Criterion

_{2}**x**and

_{4}**x**are considered to be in the second and third places to influence the final decision (approximately 12.5% or approximately the same influential as the second criterion). The difference between the most important criterion

_{7}**x**and the least essential criterion

_{2}**x**is approximately 4%. Besides, the relative impact of the most important criterion is approximately thirty-five per cent higher than the least influential criterion.

_{5}## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Fuzzy element $\tilde{f}$, which has a dependency function ${\mu}_{\tilde{f}}\left(x\right)$.

Rank | Country | Airport | 2017 | 2012 | 2007 | 2004 |
---|---|---|---|---|---|---|

1 | Latvia | Riga International | 6,097,765 | 4,767,764 | 3,160,945 | 1,060,426 |

2 | Lithuania | Vilnius International | 3,761,837 | 2,208,096 | 1,717,222 | 964,164 |

3 | Estonia | Tallinn | 2,648,361 | 2,206,791 | 1,728,430 | 997,941 |

4 | Lithuania | Kaunas International | 1,186,081 | 830,268 | 390,881 | 27,113 |

Direction | Length (m) | Surface | Number of Passengers (2017) | Aircraft Movements |
---|---|---|---|---|

01/19 | 2515 | Asphalt/Concrete | 3,761,837 | 39,253 |

Verbal rates | Scale |
---|---|

Poor (B) | 0.1; 0.1; 0.5 |

Moderate (P) | 0.5; 0.75; 1 |

Good (G) | 0.75; 1; 1 |

Criteria | A_{1} | A_{2} | A_{3} | A_{4} |
---|---|---|---|---|

Use with prevailing winds | Poor | Moderate | Good | Good |

Airspace compatibility | Moderate | Good | Good | Good |

Flight field capacity increase | Moderate | Poor | Moderate | Good |

Need for investment and new infrastructure | Poor | Good | Poor | Poor |

Environmental impact | Poor | Good | Moderate | Moderate |

Noise reduction | Moderate | Moderate | Moderate | Moderate |

Earth demand | Poor | Good | Poor | Poor |

Interruptions to construction work | Good | Poor | Good | Good |

Cost efficiency | Poor | Poor | Poor | Poor |

Experts | Use for Dominant Winds | Airspace Compatibility | Increase in Flight Field Capacity | Need for Investment and New Infrastructure | Environmental Impacts | Noise Reduction | Earth Demand | Obstacles to Construction Work | Cost Efficiency |
---|---|---|---|---|---|---|---|---|---|

x_{1} | x_{2} | x_{3} | x_{4} | x_{5} | x_{6} | x_{7} | x_{8} | x_{9} | |

E_{1} | 7 | 5 | 8 | 6 | 3 | 4 | 9 | 1 | 2 |

E_{2} | 8 | 2 | 9 | 5 | 6 | 4 | 7 | 1 | 3 |

E_{3} | 8 | 4 | 7 | 5 | 3 | 6 | 9 | 1 | 2 |

E_{4} | 1 | 5 | 7 | 3 | 6 | 8 | 9 | 2 | 4 |

E_{5} | 7 | 5 | 8 | 6 | 3 | 4 | 9 | 1 | 2 |

E_{6} | 8 | 2 | 9 | 5 | 6 | 4 | 7 | 1 | 3 |

E_{7} | 2 | 1 | 7 | 8 | 4 | 5 | 6 | 3 | 9 |

E_{8} | 8 | 4 | 7 | 5 | 3 | 6 | 9 | 1 | 2 |

E_{9} | 1 | 5 | 7 | 3 | 6 | 8 | 9 | 2 | 4 |

E_{10} | 4 | 2 | 8 | 6 | 5 | 3 | 9 | 1 | 7 |

Σ | 54 | 35 | 77 | 52 | 45 | 52 | 83 | 14 | 38 |

w | 0.12 | 0.08 | 0.17 | 0.12 | 0.1 | 0.12 | 0.18 | 0.03 | 0.08 |

Concordance factor 0.59; $W>0.5$ (expert opinions harmonized) |

x_{1} | x_{2} | x_{3} | x_{4} | x_{5} | x_{6} | x_{7} | x_{8} | x_{9} | |
---|---|---|---|---|---|---|---|---|---|

Weight | 0.12 | 0.08 | 0.17 | 0.12 | 0.10 | 0.12 | 0.18 | 0.03 | 0.08 |

Opt | min | Max | max | min | min | max | min | min | max |

A_{1} | 0.1;0.1;0.5 | 0.5;0.75;1 | 0.5;0.5;0.75 | 0.1;0.1;0.5 | 0.1;0.1;0.5 | 0.5:0.75;1 | 0.1;0.1;0.5 | 0.75;1;1 | 0.1;0.1;0.5 |

A_{2} | 0.5;0.75;1 | 0.75;1;1 | 0.1;0.1;0.5 | 0.75;1;1 | 0.75;1;1 | 0.5;0.75;1 | 0.75;1;1 | 0.1;0.1;0.5 | 0.1;0.1;0.5 |

A_{3} | 0.75;1;1 | 0.75;1;1 | 0.5;0.5;0.75 | 0.1;0.1;0.5 | 0.5;0.75;1 | 0.5;0.75;1 | 0.1;0.1;0.5 | 0.75;1;1 | 0.1;0.1;0.5 |

A_{4} | 0.75;1;1 | 0.75;1;1 | 0.75;1;1 | 0.1;0.1;0.5 | 0.5;0.75;1 | 0.5;0.75;1 | 0.1;0.1;0.5 | 0.75;1;1 | 0.1;0.1;0.5 |

Π | 1.18;1.60;1.80 | 1.39;1.89;2.00 | 1.04;1.23;1.54 | 0.77;1.01;1.32 | 1.04;1.46;1.80; | 1.00;1.50;2.00 | 0.77;1.01;1.32 | 1.30;1.73;1.80 | 0.20;0.20;1.00 |

x_{1} | x_{2} | x_{3} | x_{4} | x_{5} | x_{6} | x_{7} | x_{8} | x_{9} | |
---|---|---|---|---|---|---|---|---|---|

Weight | 0.12 | 0.08 | 0.17 | 0.12 | 0.10 | 0.12 | 0.18 | 0.03 | 0.08 |

Opt | min | max | max | min | min | max | min | min | max |

A_{1} | 0.06;0.06;0.42 | 0.25;0.40;0.72 | 0.32;0.41;0.72 | 0.08;0.10;0.65 | 0.06;0.07;0.48 | 0.25;0.50;1.00 | 0.08;0.10;0.65 | 0.42;0.58;0.77 | 0.10;0.50;2.50 |

A_{2} | 0.28;0.47;0.85 | 0.38;0.53;0.72 | 0.06;0.08;0.48 | 0.57;0.99;1.30 | 0.42;0.68;0.97 | 0.25;0.50;1.00 | 0.57;0.99;1.30 | 0.06;0.06;0.38 | 0.10;0.50;2.50 |

A_{3} | 0.42;0.62;0.85 | 0.38;0.53;0.72 | 0.32;0.41;0.72 | 0.08;0.10;0.65 | 0.28;0.51;0.97 | 0.25;0.50;1.00 | 0.08;0.10;0.65 | 0.42;0.58;0.77 | 0.10;0.50;2.50 |

A_{4} | 0.42;0.62;0.85 | 0.38;0.53;0.72 | 0.49;0.81;0.97 | 0.08;0.10;0.65 | 0.28;0.51;0.97 | 0.25;0.50;1.00 | 0.08;0.10;0.65 | 0.42;0.58;0.77 | 0.10;0.50;2.50 |

Π = A/B | α | γ | β | K_{i} |
---|---|---|---|---|

A_{1} | 0.09 | 4160.26 | 177821.22 | 60660.53 |

A_{2} | 0.02 | 7.40 | 421.50 | 142.97 |

A_{3} | 0.04 | 73.96 | 4741.90 | 1605.30 |

A_{4} | 0.04 | 73.96 | 6322.53 | 2132.18 |

**Table 9.**Weighted and normalized decision-making matrix and results of the task solution using the Min–Max method.

x_{1} | x_{2} | x_{3} | x_{4} | x_{5} | x_{6} | x_{7} | x_{8} | x_{9} | |
---|---|---|---|---|---|---|---|---|---|

Opt | min | max | max | min | min | max | min | min | max |

A_{1} | 0.01;0.01;0.05 | 0.02;0.03;0.06 | 0.06;0.07;0.12 | 0.01;0.01;0.08 | 0.01;0.01;0.05 | 0.03;0.06;0.12 | 0.01;0.02;0.12 | 0.01;0.02;0.02 | 0.01;0.04;0.20 |

A_{2} | 0.03;0.06;0.10 | 0.03;0.04;0.06 | 0.01;0.01;0.08 | 0.07;0.12;0.16 | 0.04;0.07;0.10 | 0.03;0.06;0.12 | 0.10;0.18;0.23 | 0.00;0.00;0.01 | 0.01;0.04;0.20 |

A_{3} | 0.05;0.07;0.10 | 0.03;0.04;0.06 | 0.06;0.07;0.12 | 0.01;0.01;0.08 | 0.03;0.05;0.10 | 0.03;0.06;0.12 | 0.01;0.02;0.12 | 0.01;0.02;0.02 | 0.01;0.04;0.20 |

A_{4} | 0.05;0.07;0.10 | 0.03;0.04;0.06 | 0.08;0.14;0.16 | 0.01;0.01;0.08 | 0.03;0.05;0.10 | 0.03;0.06;0.12 | 0.01;0.02;0.12 | 0.01;0.02;0.02 | 0.01;0.04;0.20 |

**Table 10.**The distance from the point of reference and the result of the decision of the task using the reference point (RP).

x_{1} | x_{2} | x_{3} | x_{4} | x_{5} | x_{6} | x_{7} | x_{8} | x_{9} | K_{i} | |
---|---|---|---|---|---|---|---|---|---|---|

Opt | min | max | max | min | min | max | min | min | max | |

A_{1} | 0.00;0.00;0.04 | 0.04;0.03;0.00 | 0.11;0.09;0.04 | 0.00;0.00;0.07 | −0.09;−0.05;−0.07 | 0.09;0.06;0.00 | 0.00;0.00;0.10 | 0.01;0.02;0.02 | 0.19;0.16;0.00 | 0.28 |

A_{2} | 0.03;0.05;0.10 | 0.03;0.02;0.00 | 0.15;0.15;0.08 | 0.06;0.11;0.15 | −0.07; −0.09;−0.03 | 0.09;0.06;0.00 | 0.09;0.16;0.22 | 0.00;0.00;0.01 | 0.19;0.16;0.00 | 0.61 |

A_{3} | 0.04;0.07;0.10 | 0.03;0.02;0.00 | 0.11;0.09;0.04 | 0.00;0.00;0.07 | −0.05; −0.05;−0.05 | 0.09;0.06;0.00 | 0.00;0.00;0.10 | 0.01;0.02;0.02 | 0.19;0.16;0.00 | 0.37 |

A_{4} | 0.04;0.07;0.10 | 0.03;0.02;0.00 | 0.08;0.03;0.00 | 0.00;0.00;0.07 | 0.00;0.00;0.00 | 0.09;0.06;0.00 | 0.00;0.00;0.10 | 0.01;0.02;0.02 | 0.19;0.16;0.00 | 0.32 |

RP | 0.10;0.10;0.10 | 0.06;0.06;0.06 | 0.16;0.16;0.16 | 0.01;0.01;0.01 | 0.10;0.10;0.10 | 0.12;0.12;0.12 | 0.01;0.01;0.01 | 0.00;0.00;0.00 | 0.20;0.20;0.20 |

**Table 11.**The MULTIMOORA method of ranking alternatives: full part of the product form, part of the relationship system, part of the base point, and justification of dominance by theoretical methods of obtaining grades.

MULTIMOORA Rankings | |||||
---|---|---|---|---|---|

Opt | Π = A/B | Σ = A − B | Reference point | Average | Final rank |

A_{1} | 1 | 3 | 4 | 2.7 | 4 |

A_{2} | 4 | 4 | 1 | 3.0 | 1 |

A_{3} | 3 | 2 | 2 | 2.3 | 2 |

A_{4} | 2 | 1 | 3 | 2.0 | 3 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Turskis, Z.; Antuchevičienė, J.; Keršulienė, V.; Gaidukas, G.
Hybrid Group MCDM Model to Select the Most Effective Alternative of the Second Runway of the Airport. *Symmetry* **2019**, *11*, 792.
https://doi.org/10.3390/sym11060792

**AMA Style**

Turskis Z, Antuchevičienė J, Keršulienė V, Gaidukas G.
Hybrid Group MCDM Model to Select the Most Effective Alternative of the Second Runway of the Airport. *Symmetry*. 2019; 11(6):792.
https://doi.org/10.3390/sym11060792

**Chicago/Turabian Style**

Turskis, Zenonas, Jurgita Antuchevičienė, Violeta Keršulienė, and Gintaras Gaidukas.
2019. "Hybrid Group MCDM Model to Select the Most Effective Alternative of the Second Runway of the Airport" *Symmetry* 11, no. 6: 792.
https://doi.org/10.3390/sym11060792