# Application of Discrete-Event Simulation for Truck Fleet Estimation at an Open-Pit Copper Mine in Peru

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Development of the Calibration Model

#### 2.2. Yearly Plan Development

## 3. Case Study

#### 3.1. Calculations

#### 3.1.1. Development of the Calibration Model

Loading Equipment | Distribution | Expression | Sample Size | p-Value KS | Error |
---|---|---|---|---|---|

Shovel 1 | Normal | NORM(375, 18.9) | 267 samples | >0.15 | 0.002106 |

Shovel 2 | Normal | NORM(370, 16.1) | 240 samples | >0.15 | 0.006607 |

Shovel 3 | Normal | NORM(376, 15.7) | 256 samples | >0.15 | 0.003483 |

Front End Loader 3 | Beta | 321 + 96 × BETA(1.82, 2.96) | 96 samples | >0.15 | 0.007573 |

Front End Loader 1 | Normal | NORM(357, 13.9) | 75 samples | >0.15 | 0.007145 |

Type Time | Distribution | Expression | Sample Size | p-Value KS | Error |
---|---|---|---|---|---|

Truck arrival | Normal | NORM(4.18, 1.03) | 128 samples | >0.15 | 0.016269 |

Spotting at Shovel 1 | Beta | 0.73 + 0.84 × BETA(1.37, 1.46) | 267 samples | >0.15 | 0.003612 |

Waiting for load at Shovel 1 | Beta | 0.01 + 0.87 × BETA(8.67, 12.5) | 267 samples | >0.15 | 0.003061 |

Loading time at Shovel 1 | Beta | 1.76 + 1.24 × BETA(3.3, 3.31) | 267 samples | >0.15 | 0.002285 |

Spotting at Shovel 2 | Beta | 0.73 + 0.83 × BETA(1.21, 1.68) | 240 samples | >0.15 | 0.006755 |

Waiting for load at Shovel 2 | Beta | 0.01 + 0.87 × BETA(6.96, 7.49) | 240 samples | >0.15 | 0.00519 |

Loading time at Shovel 2 | Normal | NORM(2.32, 0.164) | 240 samples | >0.15 | 0.004032 |

Spotting at Shovel 3 | Normal | NORM(1.09, 0.136) | 256 samples | >0.15 | 0.017094 |

Waiting for load at Shovel 3 | Beta | 0.03 + 0.85 × BETA(6.54, 10.1) | 256 samples | >0.15 | 0.002007 |

Loading time at Shovel 3 | Beta | 1.78 + 1.35 × BETA(5.66, 9.83) | 256 samples | 0.0518 | 0.009006 |

Spotting at FEL 3 | Beta | 0.75 + 0.8 × BETA(4.75, 6.34) | 96 samples | >0.15 | 0.011225 |

Waiting for load at FEL 3 | Beta | 0.07 + 1.07 × BETA(0.917, 1.4) | 96 samples | >0.15 | 0.033927 |

Loading time at FEL 3 | Beta | 4.52 + 2.15 × BETA(7.7, 7.97) | 96 samples | >0.15 | 0.003864 |

Spotting at FEL 1 | Normal | NORM(1.08, 0.0938) | 75 samples | >0.15 | 0.000836 |

Waiting for load at FEL 1 | Beta | 0.15 + 0.69 × BETA(3.27, 3.12) | 75 samples | >0.15 | 0.008227 |

Loading time at FEL 1 | Normal | NORM(5.62, 0.248) | 75 samples | >0.15 | 0.005183 |

Spotting at Crusher | Normal | NORM(1.55, 0.0621) | 150 samples | >0.15 | 0.002465 |

Unloading time at Crusher | Normal | NORM(0.882, 0.0271) | 150 samples | >0.15 | 0.003761 |

Spotting at Stockpile | Beta | 0.88 + 0.17 × BETA(5.42, 5.89) | 160 samples | >0.15 | 0.002049 |

Unloading time at Stockpile | Normal | NORM(0.912, 0.021) | 160 samples | >0.15 | 0.005051 |

Spotting at Waste Dump | Normal | NORM(0.945, 0.0264) | 148 samples | >0.15 | 0.002304 |

Unloading time at Waste Dump | Normal | NORM(0.911, 0.0266) | 148 samples | >0.15 | 0.00675 |

#### 3.1.2. Yearly Plan Development

- -
- Number of hours worked by truck fleet: In Figure 10, the number of hours required between these two models is shown.
- -
- Truck productivity: By increasing the overall cycle time, the truck productivity was then reduced. In Figure 11, the results obtained from these models are compared.
- -
- Overall cycle time: The results obtained are shown in Figure 12.
- -
- Overall haul distance: In Figure 13, the overall haul distance traveled by trucks over twelve months can be seen.
- -
- Number of trucks: Clearly, in Figure 14, the results produced by the models estimated an increase in the number of trucks starting from 30 up to 42 by the end of 2023.

## 4. Results and Discussion

#### 4.1. Number of Hours Worked by Truck Fleet

#### 4.2. Truck Productivity

#### 4.3. Overall Cycle Time

#### 4.4. Overall Haul Distance

#### 4.5. Number of Trucks

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Function | Square Error |
---|---|

Normal | 0.00211 |

Weibull | 0.00301 |

Beta | 0.00355 |

Triangular | 0.00414 |

Erlang | 0.00924 |

Gamma | 0.00946 |

Lognormal | 0.0192 |

Uniform | 0.0311 |

Exponential | 0.0582 |

Grade (%) | Velocity When Loaded (km/h) | Velocity When Empty (km/h) | Grade (%) | Velocity When Loaded (km/h) | Velocity When Empty (km/h) |
---|---|---|---|---|---|

−12 | 14.3 | 30.8 | 12 | 10.5 | 12.7 |

−11 | 14.3 | 30.8 | 11 | 10.5 | 12.7 |

−10 | 14.3 | 30.8 | 10 | 10.5 | 12.7 |

−9 | 16.9 | 32.3 | 9 | 12.0 | 15.2 |

−8 | 19.6 | 33.8 | 8 | 13.4 | 17.6 |

−7 | 22.2 | 35.3 | 7 | 14.9 | 20.0 |

−6 | 24.9 | 36.8 | 6 | 16.3 | 22.4 |

−5 | 27.5 | 38.3 | 5 | 17.8 | 24.8 |

−4 | 29.0 | 39.8 | 4 | 21.2 | 29.0 |

−3 | 30.4 | 41.4 | 3 | 24.6 | 33.3 |

−2 | 31.9 | 42.9 | 2 | 28.0 | 37.5 |

−1 | 33.3 | 44.4 | 1 | 31.4 | 41.7 |

0 | 34.8 | 45 |

Equipment/Destination | Crusher | Stock 1 | Stock 2 | Stock 3 | Waste Dump 2 |
---|---|---|---|---|---|

Shovel 1 | 58,762 | 39,558 | 10,400 | ||

Shovel 2 | 42,276 | 36,962 | 13,500 | 766 | |

Shovel 3 | 13,443 | 38,987 | 43,776 | ||

FEL 3 | 17,257 | ||||

FEL 1 | 17,066 | ||||

Total Tonnage | 101,038 | 50,405 | 39,558 | 62,887 | 78,865 |

Parameters | Real | Simulation | Error | |
---|---|---|---|---|

Mean | Half-Width | |||

Total Production | 332,752.3 | 334,780.1 | 107.1 | 0.61% |

Moved Tons Shovel 1 | 108,720.0 | 109,236.0 | 56.8 | 0.47% |

Moved Tons Shovel 2 | 93,503.3 | 94,376.5 | 52.3 | 0.93% |

Moved Tons Shovel 3 | 96,206.0 | 96,474.6 | 86.5 | 0.28% |

Moved Tons FEL 3 | 17,257.0 | 17,457.7 | 23.3 | 1.15% |

Moved Tons FEL 1 | 17,066.0 | 17,235.3 | 24.0 | 0.98% |

Equipment | Number of Trucks |
---|---|

Shovel 1 | 6 |

Shovel 2 | 7 |

Shovel 3 | 7 |

FEL 3 | 2 |

FEL 1 | 2 |

Month | Number of Days | Month | Number of Days |
---|---|---|---|

January | 25 | July | 30 |

February | 31 | August | 31 |

March | 29 | September | 31 |

April | 31 | October | 30 |

May | 30 | November | 31 |

June | 31 | December | 36 |

Month | Mechanical Availability (%) | Month | Mechanical Availability (%) |
---|---|---|---|

January | 80.55 | July | 81.82 |

February | 80.35 | August | 82.06 |

March | 82.08 | September | 81.94 |

April | 81.92 | October | 81.84 |

May | 81.9 | November | 81.82 |

June | 81.96 | December | 82.99 |

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## Share and Cite

**MDPI and ACS Style**

Huayanca, D.; Bujaico, G.; Delgado, A.
Application of Discrete-Event Simulation for Truck Fleet Estimation at an Open-Pit Copper Mine in Peru. *Appl. Sci.* **2023**, *13*, 4093.
https://doi.org/10.3390/app13074093

**AMA Style**

Huayanca D, Bujaico G, Delgado A.
Application of Discrete-Event Simulation for Truck Fleet Estimation at an Open-Pit Copper Mine in Peru. *Applied Sciences*. 2023; 13(7):4093.
https://doi.org/10.3390/app13074093

**Chicago/Turabian Style**

Huayanca, Diego, Gabriel Bujaico, and Alexi Delgado.
2023. "Application of Discrete-Event Simulation for Truck Fleet Estimation at an Open-Pit Copper Mine in Peru" *Applied Sciences* 13, no. 7: 4093.
https://doi.org/10.3390/app13074093