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