Incorporating operational modes into long-term open-pit mine planning under geological uncertainty

Sophisticated models have progressively been developed to address the challenges related to long-term, openpit mine planning under conditions of geological uncertainty. Prior research has acknowledged that strategies for mine planning and the design of mineral concentrators are interdependent; thus, it is highly desirable to optimize them together. However, achieving detailed holistic optimization of the mineral value chain remains unresolved because of the inherent limitations associated with mathematical formulations and computational processing capacity. This paper details a method that contributes to bridging these limitations by employing a novel parallelized variable neighborhood descent approach combined with an embedded mass–balance component using linear programming techniques refined through Dantzig–Wolfe decomposition. This approach is exemplified through a case study of a gold deposit, which illustrates the enhanced performance capabilities of the new algorithm. The findings demonstrate significant improvements in the optimization process for mine planning, providing a stronger link between the mine’s output and processing plant’s capabilities. Fig. 1 The Shift-Before method is an iterative search technique that moves block i and its successors, mined in the same period t (gray area), to the subsequent period t + 1 (white area). Background Long-term openpit mine planning focuses on designing mine layouts and extraction schedules. However, integrating downstream processes such as metallurgical plants into this planning remains a significant challenge. Metallurgical plants are critical for economic viability as their operations are constrained by energy-intensive processes like comminution. Optimizing mine planning and metallurgical plants within a unified framework requires robust models, efficient algorithms and effective implementation strategies. Navarra et al. [1] proposed a model based on hierarchical data structures rather than traditional algebraic equations, offering flexibility and eliminating the need for parameter adjustments commonly required in other formulations. The model incorporates operational modes in plants, enhancing their adaptability to variations in ore feed. However, the dynamics of tactical changes in operational modes over the mine’s life remain underexplored. Exact methods are computationally intensive for complex problems, making metaheuristics a viable alternative even though they do not guarantee an optimal solution. Among them, Lamghari’s variable neighborhood descent (VND) [2] stands out for its specific adaptation to mine planning and its minimal dependence on parameter tuning. This last characteristic is particularly important, as parameter adjustments can affect the performance of metaheuristics and introduce potential sources of errors. Reducing the number of parameters is, therefore, highly desirable. Unfortunately, despite these advantages, VND still heavily depends on the quality of the initial solution and lacks mechanisms for improving implementation efficiency. Proposal and implementation Based on Navarra et al. [1], this study introduces a two-stage optimization framework to address long-term openpit mine planning under geological uncertainty while integrating metallurgical plant operations. The first stage focuses on block selection and mining scheduling, maximizing the net present value (NPV) across multiple geological scenarios while adhering to slope stability and mining capacity constraints: The second stage centers on optimizing block processing within the metallurgical plant, considering multiple operational modes that cater to varying ore characteristics and blending requirements: The first-stage optimization was implemented using a customized VND metaheuristic. To address its limitations, this version of the VND mitigates reliance on initial solutions by starting from an empty plan and employs a new parallelization strategy to enhance computational efficiency through multithreading. Blocks are allocated across time through iterative searches (Fig. 1), with further computational improvements achieved by minimizing thread overhead and incorporating the ultimate pit limit to preselect blocks for analysis. The second stage employs Dantzig–Wolfe decomposition (DW) to optimize the processing of blocks selected by the VND under specific scenarios. This approach decomposes the problem into a master problem and subproblems, efficiently allocating ore across operational modes to maximize the discounted recoverable value. The use of the delayed column generation technique, a component of DW, significantly reduces computational time compared to other implementations using CPLEX.Both implementations were carried out in C++ and ran on a server equipped with an Intel Xeon Gold 5118 processor, utilizing 24 threads for parallelization. Case study and results The proposed optimization was applied to a conceptual gold-copper (Au-Cu) porphyry deposit in the Maricunga belt, Chile. The project spans a six-year operational horizon, analyzing 20 geological scenarios: 10 for plan generation and 10 for risk assessment. The metallurgical plant operates under two modes tailored to ore type and blending requirements, with parameters such as recovery rates and processing costs defined for each mode (Table 1). Fig. 2 P10, P50 and P90 curves of the cumulative NPVfor the case study (risk profiles). Fig. 3 Tons of rock mined over the periods, divided by rock type. The risk profile for the project’s NPV indicates a P50 value of $1,280 million, with a range of ±$140 million between the P10 and P90 values (Fig. 2). The analysis revealed that extraction consistently operated at its maximum capacity of 6.5 million tons per period, except during periods 4 and 5, when processing limitations, such as plant availability, became the primary constraint (Fig. 3). The results indicate that the algorithm utilized the plant’s full capacity, except during the first year, when mining capacity was constrained due to the ramp-up phase. An analysis of the P50 scenario highlights the dynamics of changes, showing how modes A and B alternated over time to process the ore. In the first three years, mode B processed more ore than mode A, while this pattern reversed during the subsequent three years (Fig. 4). Fig. 4 Tons of ore processed in (a) operational mode A and (b) operational mode Bper period, divided by rock type. This analysis suggests that, had only one mode been implemented, the plant would have faced a dilemma: either compromising optimal operation by violating the blending strategy to achieve higher grades or maintaining adherence to the blending strategy at the expense of a lower NPV. The algorithm completed its computations in 40.6 minutes without requiring any repetitions resulting from adjustments to formulation parameters, metaheuristic tuning parameters, or reliance on initial solutions. Conclusion This study contributes to the field by developing an algorithm that integrates strategic mine planning with metallurgical plant operations. The two-stage framework, which combines a parallelized VND metaheuristic with DW decomposition, effectively addresses geological uncertainties and variations in ore characteristics. A case study on a gold deposit demonstrates the approach’s practicality and suitability for real-world scenarios. While further experiments are needed to fully evaluate the impact of operational modes, the results show promise in optimizing mine-to-plant operations. Future research can build on this foundation by incorporating approximation algorithms for faster mine planning, leveraging clustered environments to reduce runtimes and introducing features such as stockpiling, multiple processing streams and market uncertainty. These advancements will promote a more integrated and multidisciplinary approach to mine planning, bridging the gap between mining and plant operations. Selected references Navarra A, Montiel L, Dimitrakopoulos R (2018) Stochastic strategic planning of open-pit mines with ore selectivity recourse. Int J Min Reclam Environ 32:1–17 Lamghari A, Dimitrakopoulos R, Ferland J (2014) A variable neighborhood descent algorithm for an open-pit mine production scheduling problem with metal uncertainty. J Oper Res Soc. 65(9):1305–1314

Incorporating operational modes into long-term open-pit mine planning under geological uncertainty

To view this article you must be a member of SME/UCA.

Caterpillar Announces Leadership Transition in Resource Industries

Copper squeeze breathes new life into old mines

Cartier-owner Richemont weighs joining De Beers acquisition race, source says

Caterpillar Announces Leadership Transition in Resource Industries

Copper squeeze breathes new life into old mines

Cartier-owner Richemont weighs joining De Beers acquisition race, source says

To view this article you must be a member of SME/UCA.

Geofingerprinting of coltan using handheld spectroscopic devices

Evaluation and comparison of rock bolting versus steel arch support systems in thick coal seam underground galleries: A case study

Related Articles

Rare earth elements in the global economy: Usage, recovery and the quest for supply security — A review

A systematic evaluation of localization signals in the advancing openpit mine Aitik

From foundation to future: Revisiting AI integration in mining engineering education through current perspectives of students, educators and industry

Iron ore tailings reprocessing by electrostatic separation plus two-stage froth flotation

Caterpillar Announces Leadership Transition in Resource Industries

Copper squeeze breathes new life into old mines

Cartier-owner Richemont weighs joining De Beers acquisition race, source says

Caterpillar Announces Leadership Transition in Resource Industries

Copper squeeze breathes new life into old mines

Cartier-owner Richemont weighs joining De Beers acquisition race, source says

Use Single Sign On