Mine planning optimization aims at maximizing the profit obtained from extracting valuable ore. Beyond its theoretical complexity—the open-pit mining problem with capacity constraints reduces to a knapsack problem with precedence constraints, which is NP-hard—practical instances of the problem usually involve a large to very large number of decision variables, typically of the order of millions for large mines. Additionally, any comprehensive approach to mine planning ought to consider the underlying geostatistical uncertainty as only limited information obtained from drill hole samples of the mineral is initially available. In this regard, as blocks are extracted sequentially, information about the ore grades of blocks yet to be extracted changes based on the blocks that have already been mined. Thus, the problem lies in the class of multi-period large scale stochastic optimization problems with decision-dependent information uncertainty. Such problems are exceedingly hard to solve, so approximations are required. This paper presents an adaptive optimization scheme for multi-period production scheduling in open-pit mining under geological uncertainty that allows us to solve practical instances of the problem. Our approach is based on a rolling-horizon adaptive optimization framework that learns from new information that becomes available as blocks are mined. By considering the evolution of geostatistical uncertainty, the proposed optimization framework produces an operational policy that reduces the risk of the production schedule. Our numerical tests with mines of moderate sizes show that our rolling horizon adaptive policy gives consistently better results than a non-adaptive stochastic optimization formulation, for a range of realistic problem instances.

矿山规划优化旨在最大程度地提取有价值的矿石而获得的利润。除了其理论上的复杂性之外，具有容量约束的露天采矿问题简化为具有优先级约束的背包问题，这是NP难题。该问题的实际情况通常涉及大量到非常大的决策变量，通常是阶数数以百万计的大型矿山。此外，任何采矿计划的综合方法都应考虑潜在的地统计学不确定性，因为最初只能从矿物的钻孔样品中获得有限的信息。就这一点而言，当块被顺序地提取时，关于尚未被提取的块的矿石等级的信息基于已经被开采的块而改变。从而，问题在于具有决策相关信息不确定性的多周期大规模随机优化问题。这些问题极难解决，因此需要近似值。本文提出了在地质不确定性下露天矿多周期生产调度的自适应优化方案，使我们能够解决实际问题。我们的方法基于滚动式水平自适应优化框架，该框架从开采区块时可获得的新信息中学习。通过考虑地统计不确定性的演变，所提出的优化框架产生了可降低生产进度风险的操作策略。