**Description**

The following case study is realized on a block model of a massive polimetalic deposit with copper as the main mineral. The aim is to compare the traditional scheduling methodology of nested pits and the direct block scheduling using the computational software DOPPLER (Delphos Open Pit Planner), developed at the Mine Planning Lab DELPHOS.

**Model Definition**

Name: definitivo2_bme

Number of blocks: 74.849

Dimensions: 20 x 20 x 15

Coordinates range: x = 26.799.98 to 29.519,98

y = 80.810,17 to 82.950,17

z = 3.992,50 to 4.667,50

Model variables: Cobre, Molibdeno, Oro, Plata, Recuperación Metalurgica, Recuperación Metalúrigica del Molibdeno, Densidad

Additionally, it was added columns from the previous ones, according to model parameters and requirements.

**Block Model Visualization **

As it can be seen from the image below, the greatest grades concentrate at the bottom of the deposit.

* Isometric View*

Frontal View Plan view

The shape of the model is explained by a preexisting pit.

**Grade-Tonnage Graph**

From the image below one can see that the sensibility of the ore tonnage by the grade is high.

**Grade Distribution**

The vast majority of the blocks are associated with low grades.

**Economic parameters**

It was executed 3 cases of valuation, which vary by the copper price.

Valuation |
Copper price [USD/lb] |

A | 2.0 |

B | 2.5 |

C | 1.5 |

## Scheduling by Nested-Pits

Based on the pseudo-flow algorithm, the Final Pit and its Nested-Pits were determined, upon which it was done the traditional scheduling by phase-bench, considering specific parameters for the Project. From a parametric price multiplication, the “Revenue Factor”, different envelopes were generated (nested pits), on which pushbacks or “phase-candidates” that can be used as a guide to the scheduling were chosen.

**Problem Description**

It was executed three valuations for the main economic element, Copper. For each one of them, Final Pit and Nested Pits are determined. The conditions on which the analysis were done are as it follows:

Two destinations: Processing Plant and Waste Dump

Capacity restrictions: Mining and Processing

No blending restrictions are considered.

**Final Pit**

**Nested Pits**

**Best and Worst Case**

To speed up development work, case B was chosen for further analysis, so from now on the focus will be case B.

**Best Case - Valuation B**

Scheduling by "Pit and Bench" – Case B.

Total Tonnage: 70 [Mton]

* Isometric View*

**Worst Case - Valuation B**

Scheduling by "Bench" - Case B.

Total Tonnage: 70 [Mton]

* Isometric View*

## Direct Block Scheduling (DBS)

The Direct Block Scheduling is an alternative way which emphasis the temporality of the problem and the opportunity cost, searching to solve since the beggining the problem of when is more convenient to extract a block and what destination should it take (processing plant or waste dump). Traditionally, this methodology is based on big linear programming models.

The software Doppler provides the Direct Block Scheduling – BOS2M. Next it is possible to see the input parameters:

Mine Capacity: 70 [Mt]

Plant Capacity: 50 [Mt]

Horizon: 10 periods

* Isometric View*

## Phase-Bench-Destination Scheduling by UDESS

It’s done a scheduling by phase-bench-destination on the software UDESS.

The original block model has a default tonnage column, which was used to do the scheduling.

For each block in the block model it is predefined a destination – plant or waste dump – according to which of them provide the greatest profit.

For the block value calculation the following tecnical-economical parameters are applied: Copper Price: 2.5 [USD/t], Mine Cost: 2.5 [USD/t], Plant Cost: 10 [USD/t], Refining Cost: 0.5 [USD/lb].

Afterwards, it is obtained the total tonnage, profit and copper fines for each phase, bench and destination.

The objective function is to maximize NPV with a discount rate of 10%.

The constraints are the mine capacity of 70 [Mt/year] and a processing capacity of 20 [Mt/año]. The maximum and minimum difference between consecutive phases are 4 and 1 benches, respectively.

The NPV (10%) obtained is de 3 886 [MUSD]. The average grade of recovered copper fine is 0.87 %. Total recovered fine is 2468 [kt]. Waste tonnage and ore tonnage is 347 and 285 [Mt]. Mine life of 10 years.

The following parameters are applied:

Minimum difference between benches: 1

Maximum difference between benches: 4

Mine Capacity: 70 Mt/year

Plant Capacity: 50 Mt/year

Discount Rate: 10%

Valuation B

## Comparision

Considering a discount rate of 10%, the differences are significant.

NPV Toposort: 6 472 929 122 USD

NPV Full MIP: 6 487 514 853 USD

NPV UDESS: 3 886 000 000 USD

## Conclusions

For this exemple, two of the optmization methods available in Doppler were used, Toposort and Full MIP. It is worth mentioning that the execution time for each one varies depending on the constraints applied.

As it can be seen in the previous item, NPV provided by Full MIP is greater than the one provided by Toposort.

NPV (10%) obtained algorithms for the direct scheduling block (Toposort and Full MIP) is similar.

Otherwise, the NPV obtained by direct scheduling algorithms block is considerably higher than obtained by prior definition phase. This happens because the direct block scheduling can select any blocks within a bench, while the phase-based scheduling, you must remove all waste and then start extraction of ore.

Also, the extraction is more restrictive in the case based in phase scheduling, since it does not support the deepening of many benchs as possible if direct block scheduling.

Thus, the scheduling based in phase is more feasible to carry out that direct the scheduling block. However, the definition phase to carry out this scheduling is performed using criteria scheduler turn.

Efforts should be made to the definition of phases that do not depend on the judgment of shift planner.