Simultaneous optimisation of stope layouts and production schedules for long-term underground mine planning

Optimisation techniques for strategic underground mine planning are not commonplace, unlike the commercial optimisation packages routinely deployed by industry for open-cut mine planning. This lack of software limits a company’s capacity to develop underground mine plans which maximise the Net Present Value (NPV). The scope of this project relates to two of the three key components of a strategic mine plan – stope layouts and production schedules. Despite much work being focused on separately optimising stope layouts and production schedules, many operations continue to rely on manual techniques for mine planning with some computer aided input. This is because there is only one commercially available stope layout optimisation technique, which is unable to produce truly optimal results, and production scheduling techniques are either mine-site specific or the more general models are yet to be tested by industry. Additionally, while the general aim to optimise is largely unquestioned, work that has been completed has given no consideration to evaluating the best optimisation approach, which requires key areas to be considered simultaneously to ensure the mine plan is coherently formed based on the interaction and influence planning areas have on one another. The current practice of concentrating solely on optimising a single area can be counterproductive as there is a risk of either relocating costs or reducing revenue elsewhere in the mine plan. The objective of this study is to generate a mathematical optimisation model that will assist sublevel stoping (SLS) mining operations to create globally optimal strategic mine plans. This model will use integer programming (IP) techniques to maximise the NPV for SLS operations by simultaneously generating stope layouts and long-term production schedules, while adhering to specified operational constraints. Stope layouts are able to vary in size and location, and production schedules define the optimal timing for preparation, extraction and backfilling. In order to help the model produce a result without violating optimality, three integer variable reduction strategies are used. These are required because as the number of integer variables increases in an IP model, the likelihood of obtaining a solution, optimal or otherwise, decreases. The integer variable reduction strategies involve (1) aggregating data and then removing irrelevant information from consideration of the IP model, (2) simplifying constraint formulations through strategic data structuring, and (3) using one decision variable to represent many decisions. The first two strategies require the use of an external application developed for this project prior to running the optimisation model. The IP model is applied to a hypothetical SLS gold operation using a Datamine block model containing 64,443 blocks. Stopes are allowed to vary between two sizes and the operation is scheduled over 23 periods with each stope requiring five periods for production. Extraction, metal and backfilling quantity limits are defined as well as key geotechnical constraints. Variable and fixed costs for preparation, extraction and backfilling, and expected recovery and revenue factors are specified. Two optimisation approaches are tested – an integrated approach, where stope layouts and production schedules are optimised simultaneously, and an isolated approach, the common planning method, where stope layouts are first determined followed by the schedule. The model is written using a mathematical programming language (AMPL) code and solved using the package CPLEX 10.3 (ILOGTM) on a computer with a processor speed of 2.40GHz and 4GB of random access memory (RAM). Results demonstrate the model’s ability to produce optimal long-term mine plans for a SLS operation. Additionally, results show the benefits of using an integrated optimisation approach instead of the traditional step by step mine planning approach. The integrated approach provides a 36% higher NPV ($22.7M vs. $16.6M) and is able to satisfy all constraints. The isolated approach requires scheduling to be reduced to 21 periods to enable a feasible result to be obtained. The integrated approach also offers other, less quantifiable advantages, such as risk reduction and better realisation of opportunities in the mine plan. Despite a longer solution time required by the integrated approach compared to the isolated approach (31 hours vs. instantaneous), it also offers the potential to reduce overall time spent on mine planning due to the model’s ability to identify and address issues during the optimisation process. The contributions to the mining industry from this work are: (1) an IP model that can simultaneously optimise stope layout and production schedules for SLS operations, (2) strategies to efficiently formulate IP models which represent complex mine planning problems, and (3) a demonstration of the value of using an integrated optimisation approach for mine planning. This work also provides a foundation on which future advances can be developed. These include introducing a function for the addition of newly available information, incorporating development optimisation into the model, addressing geological and economic uncertainties, and applying the model to industry.