The life-of-mine optimization of open pit mine production scheduling under geological uncertainty is a computationally intensive process. Production scheduling determines the optimal extraction sequence by maximizing net present value (NPV). In this paper, an algorithm is proposed to schedule an open pit mine under geological uncertainty, where instead of solving the whole problem at once, the production schedule is generated by sequentially solving sub-problems. The sub-gradient method is used to generate the upper bound solution of a Lagrangian relaxed sub-problem. If the upper bound relaxed solution is infeasible, a mixed integer programming is applied to the latter solution. The algorithm is validated by solving six problems and is compared to the linear relaxation of the original production scheduling problem. The results show that the proposed algorithm generates a solution that is very close to optimal, with less than a 3% optimality gap. An application at a copper mine, where geological uncertainty is quantified with geostatistical simulations of the related orebody, shows that all constraints are satisfied and an 11% higher NPV is generated when compared to the corresponding deterministic equivalent of the proposed approach, while a 26% higher NPV is generated compared to a common conventional industry approach.

地质不确定性下露天矿生产调度的矿井寿命优化是一个计算密集型过程。生产计划通过最大化净现值（NPV）来确定最佳提取顺序。本文提出了一种在地质条件不确定的情况下调度露天矿的算法，该算法通过依次解决子问题来产生生产调度，而不是立即解决整个问题。子梯度法用于生成拉格朗日松弛子问题的上限解。如果上限松弛解决方案不可行，则将混合整数编程应用于后一种解决方案。通过解决六个问题对算法进行了验证，并将其与原始生产计划问题的线性松弛进行了比较。结果表明，所提出的算法产生的解决方案非常接近最优，最优间隙小于3％。在铜矿中的一个应用（通过相关矿体的地统计学模拟对地质不确定性进行了量化）表明，与拟议方法的相应确定性等价物相比，满足了所有约束条件，并且产生了11％的净现值与常规的常规行业方法相比，可以产生更高的净现值。