Abstract

This article addresses an underground mine design and scheduling problem, in which ore extraction methods are determined and resulting mining activities are scheduled. The mining method influences necessary infrastructure, the activities selected, and their timing. We divide the ore body into partitions (i.e., panels), each of which is extracted using a specific method, if at all. We consider two extraction methods, namely open-stope mining and bottom-up stoping with backfill, as well as an option of doing nothing. The myriad decisions present a challenging integer-programming problem for which we propose an optimization-based heuristic to generate an initial feasible solution. We further expedite solutions to the monolith by (i) eliminating unnecessary variables and (ii) strengthening the formulation.

Our empirical study, conducted using 36 instances – four of which are directly obtained from our industry partner, demonstrate that the proposed model and corresponding solution methodology provide good-quality solutions with gaps averaging less than 8% and superior to those obtained via several general-purpose-solver heuristics; CPU times of two hours or fewer are considered to be reasonable for long-term planning purposes. Our results also show that instances with irregular disposition and lower development rates are more tractable. We provide managerial insights gained from our solutions which reveal that the mining method selected depends heavily on the extraction rate. Finally, we note that solving an industry-partner-provided instance results in a design with 44% additional value compared to that obtained via industry practice.

摘要

本文解决了地下矿山的设计和调度问题，其中确定了矿石提取方法并计划了由此产生的采矿活动。挖掘方法会影响必要的基础结构，选定的活动及其时间安排。我们将矿体划分为多个分区（即面板），每个分区都使用一种特定的方法提取（如果有的话）。我们考虑两种提取方法，即露天开采和回填自下而上的开采以及不做任何选择的选择。无数的决策提出了一个具有挑战性的整数编程问题，为此，我们提出了一种基于优化的启发式方法来生成初始可行的解决方案。我们通过（i）消除不必要的变量和（ii）加强配方来进一步加快整体解决方案。

我们使用36个实例进行了实证研究，其中四个实例是直接从我们的行业合作伙伴处获得的，表明所提出的模型和相应的解决方案方法可提供高质量的解决方案，其平均差距小于8％，并且优于通过几种通用方法获得的差距。目的解决者启发法；对于长期计划而言，两个小时或更短的CPU时间被认为是合理的。我们的结果还表明，具有不规则配置和较低开发速度的实例更容易处理。我们提供从我们的解决方案中获得的管理洞察力，这些洞察力表明所选的采矿方法在很大程度上取决于提取率。最后，我们注意到，与通过行业实践获得的设计相比，解决由行业合作伙伴提供的实例所产生的设计具有44％的附加值。