Delineation of the cut-off grade in terms of the boundary between ore and waste is important when strategizing open-pit mining projects. Cut-off grade refers to the minimum ore grade which can be economically extracted. Lane’s algorithm, on the other hand, forms the main dynamic optimization algorithm used in determining this grade (Goycoolea et al., 2021). Unlike break-even models which do not consider the time value of money, the Lane theory maximizes Net Present Value (NPV) by extracting higher ore grades earlier in the process.
The conventional Lane theory has to be understood when applying the algorithm. The theory considers a mining project as a system consisting of three major constraints: mining, milling/concentrating, and refining (Githiria, 2016). Through a careful analysis of the relationship between grade-tonnage curve and economic considerations, such as metal prices, cost of mining and processing, among others, cut-off grades are determined through a limiting and balancing exercise. The best cut-off grade at any point is chosen depending on the stage in order to avoid bottlenecks.
However, modern mining complexes do not generally use just one processing path. As a result, the optimization process becomes more complicated. If there are several processing paths in place, such as direct flotation, heap leaching, and stockpiling, the standard single-path Lane method cannot be used anymore. In this case, each destination has unique metallurgical recoveries, processing costs, and capacities (Cutler & Dimitrakopoulos, 2025). The key question in this case is to route the extracted material to the destination, which will generate the maximum marginal value taking into account the capacity of each processing path.
The application of Lane’s algorithm in environments where there are more than one routes of processing requires the objective function to be altered in order to make an estimation of the opportunity cost of each individual route that may be chosen. The algorithm needs to produce more than one cut-off grade rather than just one cut-off grade which differentiates ore from the waste (Ahmadi & Shahabi, 2018). Each extracted block needs to have its own profitability calculated for all destinations in order to send the material to the destination where it produces the most profit as long as the capacity of the destination has not been reached; otherwise, the algorithm will consider the feasibility of sending the low-quality blocks to the secondary heap leach pad or stockpile.
The application of complex mathematical modeling is common in advanced multi-destination routing solutions due to the increased complexity. Even though the original algorithm by Lane is rather efficient, current modifications are based on stochastic programming and mixed integer-linear programming in order to simultaneously optimize cut-off grades and production schedules (Cutler & Dimitrakopoulos, 2025). This allows incorporating both geological and market uncertainty in the algorithm, which ensures the robustness of the modified variable cut-off strategy. The process involves iterative adjustment of cut-off grades based on the residual capacity of all possible processing routes.
To sum up, the adaptation of Lane’s algorithm to support multi-destination routing transforms an optimization problem into a dynamic, value-based routing problem. It involves establishing unique cut-off grades for each of the available processing streams while taking into consideration their capacities and expenses. In this way, the profitability of mining activities can be significantly improved. With ore bodies becoming more complex, it becomes necessary to use such modified multi-stream cut-off grade approach in order to maximize NPV of mining assets through optimal processing of each ton of mined ore.
References
Ahmadi, M. R., & Shahabi, R. S. (2018). Cutoff grade optimization in open pit mines using genetic algorithm. Resources Policy, 55, 184–191. https://doi.org/10.1016/j.resourpol.2017.11.016
Cutler, J., & Dimitrakopoulos, R. (2025). Optimising multi-element cut-off grades for a strategic production plan under geological uncertainty. International Journal of Mining, Reclamation and Environment, 1–15. https://doi.org/10.1080/17480930.2025.2455567
Githiria, J. (2016). Development of a computer-aided application using Lane’s algorithm to optimize cut-off grade. Journal of the Southern African Institute of Mining and Metallurgy, 116, 1027–1035. https://doi.org/10.17159/2411-9717/2016/v116n11a4
Goycoolea, M., Lamas, P., Pagnoncelli, B. K., & Piazza, A. (2021). Lane’s Algorithm Revisited. Management Science, 67, 3087–3103. https://doi.org/10.1287/mnsc.2020.3685
