High production rates and low operating costs highlight block caving as one of the favorable underground mining methods. However, the uncertainties involved in the material flow make it complicated to optimize the production schedule for such operations. In this paper, a stochastic mixed-integer linear optimization model is proposed in order to capture horizontal mixing that occurs among the draw columns within the production scheduling optimization. The goal is to not only consider the material above each drawpoint for extraction from the same drawpoint, as traditional production scheduling does, but also to capture the horizontal movements among the adjacent draw columns. In this approach, different scenarios are generated to simulate the horizontal mixing among adjacent slices within a neighborhood radius. The best height of draw for draw columns is also calculated as part of the optimization. The model is tested for a block-cave mine with 640 drawpoints to feed a processing plant for 15 years. The resulting NPV is 473M$ while the deviations from the targets in all scenarios during the life of the mine are minimized. Using the proposed model will result in more reliable mine plans as it takes the horizontal mixing into account in addition to achieving the production goals. Using different penalties for grade deviations shows that the model is a flexible tool in which the mine planners can achieve their goals based on their priorities.

中文翻译：

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块状洞穴开采的水平混合模拟生产调度

高生产率和低运营成本凸显了区块崩落作为有利的地下采矿方法之一。然而，物料流中涉及的不确定性使得优化此类操作的生产计划变得复杂。在本文中，提出了一种随机混合整数线性优化模型，以捕捉生产调度优化过程中拉丝塔之间发生的水平混合。目标不仅是像传统的生产调度一样考虑每个拉丝点上方的材料从同一拉丝点提取，而且还要捕捉相邻拉丝柱之间的水平运动。在这种方法中，生成不同的场景来模拟邻域半径内相邻切片之间的水平混合。绘制柱的最佳绘制高度也作为优化的一部分进行计算。该模型已在一个有 640 个抽油点的块状洞穴矿中进行了测试，可为加工厂提供 15 年的数据。由此产生的 NPV 为 4.73 亿美元，同时在矿山生命周期内所有场景中与目标的偏差都被最小化。使用提议的模型将产生更可靠的采矿计划，因为除了实现生产目标外，它还考虑了水平混合。对品位偏差使用不同的惩罚表明该模型是一种灵活的工具，矿山规划人员可以在其中根据优先级实现目标。由此产生的 NPV 为 4.73 亿美元，同时在矿山生命周期内所有场景中与目标的偏差都被最小化。使用提议的模型将产生更可靠的采矿计划，因为除了实现生产目标外，它还考虑了水平混合。对品位偏差使用不同的惩罚表明该模型是一种灵活的工具，矿山规划人员可以在其中根据优先级实现目标。由此产生的 NPV 为 4.73 亿美元，同时在矿山生命周期内所有场景中与目标的偏差都被最小化。使用提议的模型将产生更可靠的采矿计划，因为除了实现生产目标外，它还考虑了水平混合。对品位偏差使用不同的惩罚表明该模型是一种灵活的工具，矿山规划人员可以在其中根据优先级实现目标。