Application of mining-width‑constrained openpit mine production scheduling problem to the medium‑term planning of Radomiro Tomic Mine: A case study

Medium- and short-term mine planning holds immense significance in optimizing production and resource utilization. It serves as a vital link between the long-term strategic plans and the day-to-day operational activities of a mine. In this context, a mathematical formulation is proposed to incorporate mining width constraints into the production scheduling process, aiming to maximize the net present value (NPV) of the schedule while ensuring enough room for the operation of mining equipment. Background Radomiro Tomic Mine (RT), operated by Codelco Chile, stands as a significant copper mining operation renowned for its rich mineral deposits and strategic importance in the global copper industry. An algorithm aimed at resolving the linear programming relaxation related to the precedence-constrained production scheduling problem (PCPSP) was introduced by Bienstock and Zuckerberg [1]. Comprehensive studies on the algorithm applied to openpit mine production scheduling (OPMPS) can be found [2,3]. However, traditional OPMPS models often yield nonmineable solutions due to the scarce distribution of blocks mined at the same periods. Thus, the inclusion of minimum mining width conditions in OPMPS models may enhance the mineability of medium-term plans. We present a mathematical model that includes mining width constraints into the OPMPS problem (MW-OPMPS) and solve it in the context of medium-term mine planning. Methodology The mathematical model aims to maximize the NPV of an openpit mine’s production schedule while adhering to processing and geometrical constraints. For that, we utilize the Bienstock-Zuckerberg LP (BZ) algorithm to solve subproblems associated with the MW-OPMPS, given that use of the BZ algorithm is particularly relevant at RT, where materials can be processed in different processing plants. The model considers processing and mining upper limits per period, geotechnical wall slope constraints modeled as a set of block precedence, and multiple destinations for the mined blocks, such as heap leach, mills and waste dumps. To ensure its realism and applicability in medium-term planning, the model accounts for the mining width constraint per period — for simplicity — modeled as a series of rectangular templates [4,5], and a maximum vertical advance (also known as sinking rate) modeled as a set of intertemporal set of precedencies. Case study The key focus is not only on understanding the improvement in mining width satisfiability but also assessing the impact on the NPV and the change in sequence compared to the traditional OPMPS solution. For this reason, we conducted a set of four experiments to investigate the incorporation of mining width constraints in the OPMPS problem and its applications to real medium-term scheduling problems. Experiment 1 considers the capacities from the baseline case but introduces operational mining widths of a 4 × 4 blocks template, comparing a traditional OPMPS solution with the MW-OPMPS solution and expecting that the traditional OPMPS plan will appear less mineable: that is, scarce spatial distribution of blocks mined at the same periods. Experiments 2, 3 and 4 encompass different operational scenarios. Experiment 2 evaluates the impact on the mining sequence, production schedule and NPV of adjusting the total mining capacity to match it to real performance. Experiment 3 helps to estimate the impact and the best period for a major truck maintenance. Experiment 4 reevaluates the impact of the major maintenance decision studied in experiment 3 but considering an extra requirement of sulfide ore due to a delay of the Chuquicamata Underground Mine (Chuqui UG). From experiment 1, the optimality gap was 0.1 percent for the OPMPS and 2.57 percent for the MW-OPMPS. In terms of mining width satisfiability, the OPMPS achieved a rate of 2.47 percent, while the satisfiability of the MWOPMPS solution reached a rate of 57 percent. In general, all the instances of the four experiments obtained an increase in the mining width satisfiability from 2 percent with the OPMPS to 60 percent using MW-OPMPS, and an optimally gap consistently maintained of 4 percent for the MW-OPMPS model. Fig. 1 Isometric view of experiment 1 results: (a) solution of OPMPS and (b) solution of MW-OPMPS. Fig. 2 Plan view (level 2610) of experiment 1 results: (a) solution of OPMPS and (b) solution of MW-OPMPS. Discussion Particularly, the results of experiment 1 (Figs. 1 and 2) highlight the effectiveness of incorporating mining width constraints in ensuring a greater proportion of blocks satisfies the width requirements, leading to improved operational compliance and making the outputs more useful for engineering designs. Also, the research offers practical insights into real-world decision-making processes, even though solutions still need to be reworked to make them practical, enable engineers to conduct trade-off studies, such as optimizing the timing of major truck maintenance, and enable informed decisions considering the impact of external factors such as the delay of Chuqui UG. Conclusion By solving multiple instances based on an RT dataset, the study evaluates the performance of the developed algorithms in solving problems of varying complexities. The obtained solutions of the MW-OPMPS exhibit a notable improvement in mining width satisfiability, and the efficacy of the model is further demonstrated by the consistently lower optimal gap for all instances. Selected references Bienstock D, Zuckerberg M (2009) A new LP algorithm for precedence constrained production scheduling. Working Paper. Columbia University, New York Letelier OR, Espinoza D, Goycoolea M, Moreno E, Muñoz G (2020) Production scheduling for strategic open pit mine planning: a mixed-integer programming approach. Oper Res 68(5):1425–1444 Muñoz G, Espinoza D, Goycoolea M, Moreno E, Queyranne M, Letelier OR (2018) A study of the Bienstock-Zuckerberg algorithm: applications in mining and resource constrained project scheduling. Comput Optim Appl 69(2):501–534 Yarmuch JL, Brazil M, Rubinstein H, Thomas DA (2021) A model for open-pit pushback design with operational constraints. Optim Eng 24:623–639 Wharton C, Whittle J (1997) The effect of minimum mining width on NPV. Optimizing with Whittle, 173–178

Application of mining-width‑constrained openpit mine production scheduling problem to the medium‑term planning of Radomiro Tomic Mine: A case study

Authored by:
Gonzalo Sepulveda, Juan L. Yarmuch

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

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