Mine planning optimization under circular reference loop characteristics: A workflow combining grid search and mixed integer programming

Mine planning traditionally involves three critical subproblems that are typically solved sequentially: capacity planning (selecting maximum possible production rates), cut-off grade selection (deciding material destinations), and block sequencing (determining extraction order). However, these decisions are fundamentally interdependent, creating circular reference loops where each decision influences the others. This interdependency means that combining individually optimal solutions cannot guarantee overall optimization, yet current approaches fail to address these relationships adequately. This study presents a comprehensive workflow that simultaneously optimizes these three interdependent subproblems using mixed integer programming (MIP) combined with grid search methodology. The approach leverages cost-capacity relationships derived from the historical data of similar mining projects to develop empirical models representing economies of scale (EoS) effects on mining costs, processing costs, capital recovery and metal recovery parameters. Background and methods The historic data of selected mining projects were extracted from their NI 43-101 reports, which provide standardized technical documentation. The selection of six NI 43-101 projects as reference cases was based on multiple operational characteristics to ensure comparability and reliability of the derived cost functions. The selection criteria included geographical region (specifically, Canadian operations), commodity type (gold), mining method (openpit operations), deposit characteristics, regulatory environment and operational scale. These criteria were designed to minimize variations in external factors that could confound the cost-capacity relationships, such as different regulatory frameworks, labor market conditions and infrastructure availability. Based on the cost and metal recovery functions derived from the historical data, a mine planning model was then developed to optimize block sequencing and material destination decisions for given operational capacities. While the original intention was to develop a model that could concurrently optimize all three subproblems — block sequencing, capacity planning and cut-off grade selection — the inherent interdependencies among these variables create complex nonlinear relationships, resulting in a nonlinear programming problem that would be computationally intensive to solve. To address this complexity, a two-stage approach was adopted. In the first stage, the model assumes predetermined mining and processing capacities, allowing for the simultaneous optimization of block sequencing and cut-off grade decisions within these capacity constraints. A systematic grid search method efficiently explores the solution space to determine optimal capacity configurations, while MIP optimizes block sequencing and material destinations for each capacity scenario. The grid search method evaluates various capacity configurations to identify the option that yields the highest net present value (NPV). Each capacity configuration is evaluated through the optimization model, allowing for a comprehensive comparison of potential operational scenarios. The systematic nature of the grid search ensures that a wide range of capacity combinations is considered, while the simultaneous optimization of block sequencing and destination selection for each configuration ensures that the evaluation accurately reflects the operational potential of each scenario. This methodological framework mitigates computational complexity while ensuring the identification of optimal operational parameters through a structured evaluation process, effectively balancing computational efficiency with optimization accuracy. The grid search represents a systematic approach to optimization by dividing a search area into equally sized grids and evaluating each grid point to find the optimal solution. This methodology consists of three main steps: (1) defining an appropriate search area within the grid space, (2) calculating objective values for each selected grid point and (3) identifying the optimal grid point based on the computed objective values. Using the operational data collected from the NI 43-101 reports of the six mining projects, published between 2018 and 2023, regression analyses were performed to establish cost and recovery functions, as illustrated in Figs. 1a-d. These empirically derived functions formed the foundation for the subsequent optimization process. The functions capture the relationships between operational scale and various cost components, as well as the impact of capacity on metal recovery rates. The block sequencing model was then solved through the application of a grid search method, requiring 33 distinct iterations to identify the optimal combination of capacity configuration, block sequencing and material destination decisions. Each iteration represented a unique combination of mining and processing capacities, systematically exploring the solution space to find the configuration that maximizes project value. The optimization process was executed using AMPL submitted to the IBM ILOG CPLEX solver. The grid search optimization process began with a systematic division of the capacity configuration search area into equal grids. The initial phase of optimization involved the selection of four distinct values for both mining and processing capacities, with these values chosen based on the reserve characteristics. Discussion For mining operations, the selected capacities ranged from 4.5 to 60 Mtpa, with specific values of 4.5, 23, 41.5 and 60 Mtpa. Similarly, the mineral processing capacities were selected to range from 2.5 to 30 Mtpa, with specific values of approximately 2.5, 11.7, 20.9 and 30 Mtpa. These capacity ranges were chosen to explore a wide spectrum of operational scales while maintaining practical feasibility. The case study successfully identified an optimal configuration of 20.79 Mtpa mining capacity and 15 Mtpa processing capacity. The results reveal that processing capacity has a more significant impact on project value than mining capacity, highlighting the critical importance of balanced capacity planning for both mining and mineral processing operations. This integrated optimization approach provides mining operators with a more robust decision-making framework that properly accounts for the complex interdependencies of operational parameters, leading to improved project economics compared to traditional sequential optimization methods. Fig. 1 (a) Processing capacity: processing cost data set and fitted function.(b) Mining capacity: mining cost data set and fitted function. (c) Mining capacity:capital recovery data set and fitted function. (d) Processing capacity:metal recovery data set and fitted function.Mining, Metallurgy & Exploration, https://doi.org/10.1007/s42461-025-01346-6 Conclusion Mine planning shows circular reference loop characteristics that require solving subproblems concurrently. This research takes a step toward a concurrent solution despite computational limitations. The results highlight the critical importance of balanced capacity planning between mining and mineral processing operations. Rather than maximizing individual capacities in isolation, the optimal solution emerges from a careful balance between mining and mineral processing capacities. The analysis shows that changing mineral processing capacity has a greater impact on the project value, though any adjustments of mineral processing capacity must be accompanied by corresponding changes in mining capacity to maintain operational efficiency. Future research can present several promising directions to extend the framework of this study. First, future research should incorporate stochastic optimization techniques that explicitly account for uncertainties in commodity prices, discount rates and geological parameters, as the interaction effects between these uncertainties may lead to significantly different optimal capacity configurations than those identified through deterministic approaches. References A list of all references is available in the full paper.

Mine planning optimization under circular reference loop characteristics: A workflow combining grid search and mixed integer programming

Authored by: Mehmet Balci, Sena Senses and Mustafa Kumral

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

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

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