# Multi-Criteria Analysis for the Selection of the Optimal Mining Design Solution—A Case Study on Quarry “Tambura”

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology (Methods of Multi-Criteria Decision Making)

#### 2.1. Analytical Hierarchy Process (AHP)

- Define the problem (the desired optimal solution);
- Create a hierarchy of criteria according to their level of importance, the most important at the top and the least important at the lowest level as they usually represent alternatives;
- Determine/create a square matrix of comparisons where you compare criteria (or alternatives) at the same level with other elements of the same level;
- Select the optimal alternative (solution) based on weighting coefficients.

_{ij}. In accordance with that, if the criterion i is more important than the criterion j, the importance is shown with the element a

_{ij}> 1, if the criterion j is more important than the criterion I, the importance is shown with the element a

_{ij}< 1, and for the criteria of same importance, the following is valid: a

_{ij}= 1 [46].

#### 2.2. PROMETHEE II Method

- Preference modelling,
- Aggregation,
- Exploitation.

_{i}—weight of criteria,

_{i}—preference function.

^{−}(a) shows the inclination towards other alternatives in comparison to alternative a, meaning how much weaker alternative a is when compared to other alternatives. The leaving flow ϕ

^{+}(a) displays the inclination towards alternative a when compared to other alternatives, i.e., how much better alternative a is [51]. Entering and leaving flows are defined according to the following formula:

## 3. Selection of the Optimal Final Contour for the Quarry “TAMBURA”—Case Study

#### 3.1. Site Location

#### 3.2. Criteria Selection for Optimization—Application of the AHP Method

- Compliance with the relevant Croatian legislation,
- Maximally adapt to the present situation of the previously done mining work,
- Ensure the maximum possible level of safety for people and environment,
- Consider other neighbouring objects and works,
- Enable carrying out of biological reclamation after the exploitation is finished, and
- Enable the settlement of all property legal relations on all cadastral parcels covered by the exploitation field.

#### 3.3. Application of the PROMETHEE II Method

- Selection of design solution alternatives (models) for further exploitation,
- Evaluation of models according to the set criteria and their sub-criteria,
- Comparison and ranking of alternative solutions, and
- Selection of the optimal model.

- Criteria evaluated based on the quantitative data,
- Criteria evaluated on the subjective assessment of the designer.

^{3}of rock mass with the profit of 16,457,578 kn and total expense fees of 825,983 kn. The environmental impact is weak. The settlement of property legal relations is not possible for all cadastral parcels inside the exploitation field.

^{3}of technical building stone with the profit of 16,546,579 kn and expense fees of 830,433 kn. The environmental impact is weak. The settlement of property legal relations is not possible for all cadastral parcels inside the exploitation field.

^{3}of technical building stone with the profit of 12,442,405 kn and expense fees of 625,152 kn. The environmental impact is weak or there is none. The settlement of property legal relations is possible on all cadastral parcels inside the intervention area.

## 4. Discussion

^{−}(a)) (Equation (11)) and leaving flow (ϕ

^{+}(a)) (Equation (12)) were obtained. The values are shown in Table 10.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

## References

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**Figure 3.**Site location of quarry “Tambura”: (

**a**) site location, (

**b**) top view of quarry “Tambura”, (

**c**) and quarry working face.

Degree/Intensity of Importance | Definition | Description |
---|---|---|

1 | Equally favourable | 2 elements (i and j) have equal value |

3 | Slightly more favourable | Element (i) is slightly more favourable than element (j) |

5 | Highly favourable | Element (i) is highly favourable than element (j) |

7 | Very highly favourable | Element (i) is very highly favourable than element (j) |

9 | Extremely favourable | Element (i) is extremely favourable than element (j) |

2, 4, 6, 8 | Median values between two definitions |

n | RI |
---|---|

1 | 0.00 |

2 | 0.00 |

3 | 0.58 |

4 | 0.90 |

5 | 1.12 |

6 | 1.24 |

7 | 1.32 |

8 | 1.41 |

9 | 1.45 |

10 | 1.49 |

Criteria Group | Degree/Intensity of Importance | Definition |
---|---|---|

Project parameters | 1 | Equally preferred |

Mineral deposit reserves | 1 | Equally preferred |

Economic indicators | 4 | Moderately to strongly preferred |

Environmental impact | 5 | Strongly preferred |

Property legal relations | 9 | Extremely preferred |

Criteria Group | Project Parameters | Mineral Deposit Reserves | Economic Indicators | Environmental Impact | Property Legal Relations |
---|---|---|---|---|---|

Project parameters | 1.00 | 1.00 | 0.25 | 0.20 | 0.11 |

Mineral deposit reserves | 1.00 | 1.00 | 0.20 | 0.25 | 0.11 |

Economic indicators | 4.00 | 4.00 | 1.00 | 0.20 | 0.33 |

Environmental impact | 5.00 | 5.00 | 5.00 | 1.00 | 0.33 |

Property legal relations | 9.00 | 9.00 | 3.00 | 3.00 | 1.00 |

Criteria Group | Weighting Coefficient | Weighting Coefficient (%) |
---|---|---|

Project parameters | 0.05 | 5.00 |

Mineral deposit reserves | 0.05 | 5.00 |

Economic indicators | 0.16 | 16.00 |

Environmental impact | 0.27 | 27.00 |

Property legal relations | 0.48 | 48.00 |

Project Parameters | Models | ||
---|---|---|---|

Model 1 | Model 2 | Model 3 | |

Maximum bench height (h_{e}), m | 20.0 | 17.0 | 24.0 |

Minimum width of bench level (B), m | 3.0 | 5.0 | 5.0 |

Angle of inclination of bench slope (α_{e}), ° | ≤70 | ≤70 | ≤70 |

Angle of inclination of final slope (α_{z}), ° | ≤60 | ≤61 | ≤61 |

Area of exploitation field, ha | 3.88 | 3.88 | 3.79 |

Selection Criteria | ||||||
---|---|---|---|---|---|---|

Criteria Group | % | Criteria Name | % | Category Mark | ||

Project parameters | 5 | Maximum bench height (h_{e}), m | 8 | C1 | ||

Minimum width of bench level (B), m | 6 | C2 | ||||

Angle of inclination of bench slope (α_{e}), ° | 23 | C3 | ||||

Angle of inclination of final slope (α_{z}), ° | 43 | C4 | ||||

Area of exploitation field, ha | 19 | C5 | ||||

Mineral deposit reserves | 5 | Balance reserves, m^{3} | 28 | C6 | ||

Out of balance reserves, m^{3} | 10 | C7 | ||||

Exploitation reserves, m^{3} | 62 | C8 | ||||

Economic indicators | 16 | Profit, kn | 19 | C9 | ||

Fee expenses, kn | Fixed fee, kn | 17 | C10 | |||

Variable fee, kn | Government budget, kn | 14 | C11 | |||

Local regional unit, kn | 24 | C12 | ||||

Local government unit, kn | 27 | C13 | ||||

Environmental impact | 27 | Biodiversity | 7 | C14 | ||

Geological and hydrological characteristics | 9 | C15 | ||||

Seismological, pedological, and climatological characteristics | 7 | C16 | ||||

Infrastructural and economic characteristics | 16 | C17 | ||||

Cultural and landscape characteristics | 6 | C18 | ||||

Noise | 18 | C19 | ||||

Blasting | 21 | C20 | ||||

Population | 17 | C21 | ||||

Property legal relations | 48 | Possibility of enabling access to all cadastral parcels | 100 | C22 |

Environmental Impact | ||||||
---|---|---|---|---|---|---|

None | / | Weak | / | Moderate | / | High |

7 | 6 | 5 | 4 | 3 | 2 | 1 |

Selection Criteria | Models | |||||
---|---|---|---|---|---|---|

Criteria Group | % | Criteria Mark | Model 1 | Model 2 | Model 3 | |

Project parameters | 5 | C1 | m max | 20 | 17 | 24 |

C2 | m min | 3 | 5 | 5 | ||

C3 | ° max | 70 | 70 | 70 | ||

C4 | ° max | 60 | 61 | 61 | ||

C5 | ha max | 3.88 | 3.88 | 3.79 | ||

Mineral deposit reserves | 5 | C6 | m^{3}max | 839,672 | 844,213 | 634,817 |

C7 | m^{3}max | 507,177 | 500,038 | 553,694 | ||

C8 | m^{3}max | 822,879 | 827,329 | 622,120 | ||

Economic indicators | 16 | C9 | kn min | 16,457,578 | 16,546,579 | 12,442,405 |

C10 | kn max | 3104 | 3104 | 3032 | ||

C11 | kn min | 411,439 | 413,664 | 311,060 | ||

C12 | kn min | 164,576 | 165,466 | 124,424 | ||

C13 | kn min | 246,864 | 248,199 | 186,636 | ||

Environmental impact | 27 | C14 | max | 4 | 3 | 6 |

C15 | max | 5 | 6 | 7 | ||

C16 | max | 4 | 4 | 5 | ||

C17 | max | 6 | 6 | 7 | ||

C18 | max | 6 | 6 | 6 | ||

C19 | max | 4 | 3 | 6 | ||

C20 | max | 3 | 3 | 5 | ||

C21 | max | 5 | 5 | 6 | ||

Property legal relations | 48 | C22 | yes/no | no | no | yes |

Flow | Model 1 | Model 2 | Model 3 |
---|---|---|---|

ϕ^{−} entering flow | 0.2509 | 0.2940 | 0.4043 |

ϕ^{+} leaving flow | 0.2789 | 0.1924 | 0.4779 |

Model | ϕ(a) | Final Ranking |
---|---|---|

Model 1 | 0.0280 | 2 |

Model 2 | −0.1017 | 3 |

Model 3 | 0.0737 | 1 |

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**MDPI and ACS Style**

Farkaš, B.; Hrastov, A.
Multi-Criteria Analysis for the Selection of the Optimal Mining Design Solution—A Case Study on Quarry “Tambura”. *Energies* **2021**, *14*, 3200.
https://doi.org/10.3390/en14113200

**AMA Style**

Farkaš B, Hrastov A.
Multi-Criteria Analysis for the Selection of the Optimal Mining Design Solution—A Case Study on Quarry “Tambura”. *Energies*. 2021; 14(11):3200.
https://doi.org/10.3390/en14113200

**Chicago/Turabian Style**

Farkaš, Branimir, and Ana Hrastov.
2021. "Multi-Criteria Analysis for the Selection of the Optimal Mining Design Solution—A Case Study on Quarry “Tambura”" *Energies* 14, no. 11: 3200.
https://doi.org/10.3390/en14113200