Classical and stochastic mine planning techniques, state of the art and trends

Abstract Determination of the best possible ultimate pit for an open pit mine is a fundamental subject that has undergone a highly evolutionary process, reviewed in this study, since the correct choice carries substantial economic impact for the industry. The correct choice can be very beneficial for project analysis, whereas an incorrect choice has the potential to mask huge financial and economic future losses that could render a project unfeasible. The advent of computers in the 1960s allowed sophisticated analysis for the selection of the best ultimate pit determination, under specific modifying factors such as economic, social, environmental, and political, but only in deterministic situations, i.e., when the problem and variables for the ultimate pit determinations were considered deterministically and almost always based on average values. Techniques such as the Lerchs-Grossman algorithm and mixed-integer programming are among many standard tools now used by the mineral industry. Geological uncertainty and the associated risks as well as the need to consider the appropriate time to mine a block during a mine operation have a significant impact on the net present value of the resulting ultimate pits. Stochastic aspects embed a probabilistic component that varies in time and are now under intense investigation by researchers, who are creating algorithms that can be experimented with and tested in real mine situations. One can expect that once these algorithms demonstrate their efficiency and superior results, they will readily dominate the industry.

摘要 露天矿最优最终开采境界（ultimate pit）的确定是一项历经高度演进发展的基础课题，本研究对此进行了综述。正确的最终开采境界选择对矿业行业具有显著的经济影响：其不仅可为项目分析带来可观收益，而不当的境界选择则可能掩盖潜在的巨额财务与经济损失，甚至导致项目丧失可行性。20世纪60年代计算机技术的出现，使得针对最优最终开采境界选择的复杂分析成为可能，当时的分析可结合经济、社会、环境与政治等特定修正因素，但仅适用于确定性场景——即最终境界确定的问题与变量均按确定性方式考量，且几乎始终基于平均值开展计算。勒尔奇-格罗斯曼算法（Lerchs-Grossman algorithm）、混合整数规划等技术，现已成为矿业行业广泛使用的诸多标准工具之一。地质不确定性及其相关风险，以及矿山开采过程中需考量矿块回采时序的需求，均会对最终开采境界对应的净现值（net present value, NPV）产生显著影响。随机特性引入了随时间变化的概率性要素，当前正受到研究者的深入研究，相关人员正开发可在实际矿山场景中开展试验与验证的算法。可以预见，一旦这些算法展现出高效性与优异性能，便将迅速主导矿业行业的相关应用。