# The Application of Stochastic Mine Production Scheduling in the Presence of Geological Uncertainty

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## Abstract

**:**

## 1. Introduction

## 2. Description of Iron Ore Mine

## 3. Mathematical Model of Stochastic Mine Production Scheduling

## 4. Descriptive Statistics and Spatial Modelling

^{2}. The K–S goodness of fit test was carried out for the normality checking of the data at 5% level of significance. The result of the K–S test shows that the data are not normally distributed.

## 5. Results and Discussion

_{is}for all blocks i from simulation s are obtained from the resource model, which was generated the using sequential Gaussian simulation discussed in previous section. The geotechnical and economical parameters and the different constraint limits that are used in this case study are presented in Table 1.

#### Comparison of Model 1 and Model 2

## 6. Conclusions and Future Scope

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Experimental variogram of all three directions (North, East, up) (

**a**); experimental and fitted variogram model along azimuth 0° (

**b**); experimental and fitted variogram model along azimuth 90° (

**c**); experimental and fitted variogram model along downhole −90° (

**d**).

**Figure 6.**Three random realizations from a set of 20 simulated realizations of Fe grade maps (

**a**–

**c**); an ensemble map obtained by averaging 20 realizations, sometimes called an E-type map (

**d**).

Description | Values |
---|---|

Number of blocks in total | 49,603 |

Block Dimension (m × m × m) | 20 × 20 × 10 |

Rock’s specific gravity (ton/m^{3}) | 2.86 |

Recovery rate (%) | 0.74 |

Cutoff grade of iron (%) | 55.2632 |

Discount rate (%) | 0.10 |

Metal selling price (US $/ton) | 40 |

Ore selling cost (US $/ton) | 3.6 |

Ore processing cost (US $/ton) | 12 |

Rock mining cost (US $/ton) | 3 |

Block mass (ton) | 11,440 |

Maximum capacity of Mining constraints (Million ton) | 25 |

Maximum capacity of Mining constraints (Million ton) | 10 |

Maximum capacity of Processing constraints (Million ton) | 10 |

Minimum capacity of Processing constraints (Million ton) | 6 |

Maximum capacity of Metal production constraints (Million ton) | 4 |

Minimum capacity of Metal production constraints (Million ton) | 2 |

Model 1 | Model 2 | |
---|---|---|

Solution time (s) | 2814.96 | 1313.18 |

Total metal quantity (Mt) | 1.29 × 10^{8} | 1.29 × 10^{8} |

Discounted cash flow NPV (US M$) | 8.98 × 10^{8} | 9.40 × 10^{8} |

Life of mine (year) | 23 | 23 |

**Table 3.**Period-wise material production, expected (average) ore, metal, and NPV generated from the stochastic production scheduling using Model 1 and Model 2.

Year | Model 1 | Model 2 | ||||||
---|---|---|---|---|---|---|---|---|

Material (Mt) | Ore (Mt) | Metal (Mt) | NPV (M$) | Material (Mt) | Ore (Mt) | Metal (Mt) | NPV (M$) | |

1 | 24,996,400 | 23,382,216 | 11,709,413 | 1.59 × 10^{8} | 24,996,400 | 23,382,216 | 11,706,579 | 1.59 × 10^{8} |

2 | 24,996,400 | 21,985,392 | 10,907,384 | 1.35 × 10^{8} | 24,996,400 | 21,985,392 | 10,910,219 | 1.35 × 10^{8} |

3 | 24,996,400 | 19,767,176 | 9,729,532 | 1.09 × 10^{8} | 24,996,400 | 19,526,936 | 9,585,516 | 1.08 × 10^{8} |

4 | 24,996,400 | 16,728,712 | 8,148,157 | 8.31 × 10^{7} | 24,996,400 | 16,968,952 | 8,292,173 | 8.46 × 10^{7} |

5 | 24,996,400 | 15,219,776 | 7,405,514 | 2.65 × 10^{7} | 24,996,400 | 15,219,776 | 7,405,514 | 6.87 × 10^{7} |

6 | 24,996,400 | 14,342,328 | 6,968,436 | 5.87 × 10^{7} | 24,996,400 | 14,342,328 | 6,968,436 | 5.87 × 10^{7} |

7 | 24,996,400 | 13,290,992 | 6,445,284 | 4.94 × 10^{7} | 24,996,400 | 13,292,136 | 6,445,811 | 4.94 × 10^{7} |

8 | 24,996,400 | 11,777,480 | 5,696,374 | 3.97 × 10^{7} | 24,996,400 | 11,775,192 | 5,694,723 | 3.97 × 10^{7} |

9 | 24,996,400 | 10,554,544 | 5,092,161 | 3.22 × 10^{7} | 24,996,400 | 10,548,824 | 5,089,480 | 3.22 × 10^{7} |

10 | 24,996,400 | 9,421,984 | 4,528,680 | 2.61 × 10^{7} | 24,996,400 | 9,440,288 | 4,537,681 | 2.61 × 10^{7} |

11 | 24,996,400 | 9,630,192 | 4,654,957 | 2.44 × 10^{7} | 24,996,400 | 9,618,752 | 4,649,761 | 2.43 × 10^{7} |

12 | 24,996,400 | 9,499,776 | 4,599,436 | 2.19 × 10^{7} | 24,996,400 | 9,499,776 | 4,599,436 | 2.19 × 10^{7} |

13 | 24,996,400 | 9,333,896 | 4,525,560 | 1.96 × 10^{7} | 24,996,400 | 9,333,896 | 4,525,560 | 1.96 × 10^{7} |

14 | 24,996,400 | 9,566,128 | 4,641,459 | 1.82 × 10^{7} | 24,996,400 | 9,566,128 | 4,641,459 | 1.82 × 10^{7} |

15 | 24,996,400 | 11,252,384 | 5,480,425 | 1.96 × 10^{7} | 24,996,400 | 11,252,384 | 5,480,425 | 1.96 × 10^{7} |

16 | 24,996,400 | 12,728,144 | 6,257,446 | 2.03 × 10^{7} | 24,996,400 | 12,729,288 | 6,258,193 | 2.03 × 10^{7} |

17 | 24,996,400 | 10,516,792 | 5,158,022 | 1.52 × 10^{7} | 24,996,400 | 10,515,648 | 5,157,275 | 1.52 × 10^{7} |

18 | 24,996,400 | 9,480,328 | 4,642,326 | 1.25 × 10^{7} | 24,996,400 | 9,480,328 | 4,642,326 | 1.25 × 10^{7} |

19 | 24,996,400 | 8,807,656 | 4,305,478 | 1.05 × 10^{7} | 24,996,400 | 8,799,648 | 4,301,247 | 1.05 × 10^{7} |

20 | 24,996,400 | 7,752,888 | 3,786,262 | 8.40 × 10^{6} | 24,996,400 | 7,760,896 | 3,790,493 | 8.41 × 10^{6} |

21 | 24,996,400 | 5,940,792 | 2,906,814 | 5.86 × 10^{6} | 24,996,400 | 5,940,792 | 2,906,814 | 5.86 × 10^{6} |

22 | 24,996,400 | 3,123,120 | 1,526,226 | 2.80 × 10^{6} | 24,996,400 | 3,123,120 | 1,526,226 | 2.80 × 10^{6} |

23 | 17,537,520 | 426,712 | 207,353.2 | 3.43 × 10^{5} | 17,537,520 | 426,712 | 207,353.2 | 3.43 × 10^{5} |

Sum | 5.68 × 10^{8} | 2.65 × 10^{8} | 1.29 × 10^{8} | 8.98 × 10^{8} | 5.68 × 10^{8} | 2.65 × 10^{8} | 1.29 × 10^{8} | 9.40 × 10^{8} |

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**MDPI and ACS Style**

Joshi, D.; Gholami, H.; Mohapatra, H.; Ali, A.; Streimikiene, D.; Satpathy, S.K.; Yadav, A.
The Application of Stochastic Mine Production Scheduling in the Presence of Geological Uncertainty. *Sustainability* **2022**, *14*, 9819.
https://doi.org/10.3390/su14169819

**AMA Style**

Joshi D, Gholami H, Mohapatra H, Ali A, Streimikiene D, Satpathy SK, Yadav A.
The Application of Stochastic Mine Production Scheduling in the Presence of Geological Uncertainty. *Sustainability*. 2022; 14(16):9819.
https://doi.org/10.3390/su14169819

**Chicago/Turabian Style**

Joshi, Devendra, Hamed Gholami, Hitesh Mohapatra, Anis Ali, Dalia Streimikiene, Susanta Kumar Satpathy, and Arvind Yadav.
2022. "The Application of Stochastic Mine Production Scheduling in the Presence of Geological Uncertainty" *Sustainability* 14, no. 16: 9819.
https://doi.org/10.3390/su14169819