A dynamic long-term and medium-term integrated open-pit mine production scheduling system based on the genetic algorithm

Abstract

Open-pit mine production scheduling (OPMPS) is systematically divided into long-term (LT), medium-term (MT) and short-term (ST) scheduling. There is a clear interdependence between these scheduling horizons. An integrated optimisation approach to these scheduling horizons is essential since the horizons can be linked together to ensure spatial and temporal scheduling alignment. The linkages include feedback loops to enable dynamic updates of the scheduling system to incorporate changes whenever they occur. Traditionally, optimisation techniques have often focussed on solving LT, MT and ST scheduling horizons independently from each other, despite there being some shortcomings associated with the independent optimisation of LT, MT and ST production schedules. Current studies have not adequately presented an integrated scheduling system in which all horizons are incorporated and correlated to mitigate scheduling misalignment. Generating independent mine production schedules is known to be detrimental to a project’s net present value (NPV) due to scheduling misalignment and inconsistency. This raises the question of whether a solution approach can be developed to dynamically integrate scheduling horizons to overcome challenges associated with spatial and temporal misalignment and inconsistency in scheduling. This thesis developed a new approach to dynamically integrate LT and MT production scheduling to improve temporal and spatial alignment while attempting to maximise NPV as opposed to when these scheduling horizons are optimised independently. The reason for integrating LT and MT production schedules is to provide a framework to support ST scheduling which introduces more complexity and variability to account for operational planning. Firstly, the thesis expressed the scheduling problem as a mixed integer programming (MIP) problem to integrate LT and MT production scheduling horizons. The MIP model was employed in this thesis because it can formulate practical extraction sequences and incorporates continuous variables, compared to linear programming (LP) and integer programming (IP) models. Then, the thesis developed an integrated solution approach based on the genetic algorithm (GA), which is a metaheuristic algorithm, to solve the integrated LT and MT MIP scheduling problem. GA was selected because it can provide solutions to problems that are unattainable with exact or deterministic techniques. GA can also incorporate geological, economic and operational uncertainties, although in this thesis the focus was on operational uncertainty. Since GA is a stochastic technique, the combined MIP model and GA approach generated stochastic solutions that accounted for constraints and uncertainties associated with mining rate, processing rate and ore grade target. The combined MIP model and GA approach was coded in Python programming language and validated by applying it to a block model downloaded from Geovia Surpac® software. Results show that when the integrated LT and MT production scheduling system was solved using the combined MIP model and GA approach, NPV improved by 2.60% compared to when the scheduling horizons were independently optimised. In addition, spatial and temporal alignment between the LT and MT production schedules was achieved. Therefore, the thesis demonstrated that a combined MIP model and GA approach can dynamically integrate LT and MT production scheduling horizons to improve NPV as opposed to when these scheduling horizons are independently optimised. The combined MIP model and GA approach was also applied to the Newman and Zuck Small block models downloaded from MineLib, to validate the solution approach. The results were compared to some of the MineLib existing solutions obtained by applying the TopoSort heuristic algorithm to solve a LP relaxation model of the scheduling optimisation problem. The integrated LT and MT scheduling system solved using the combined MIP model and GA approach had a 10.86% higher and a 4.86% lower NPV compared to the TopoSort algorithm when applied to the Zuck Small and Newman block models, respectively. Although the aim was to improve NPV, a lower NPV was generated during the validation using the Newman block model. This is because GA can generate a different outcome each time it is run on the block model, due to its stochastic solution process. Another run of the combined MIP model and GA approach on the same block model with the same inputs may generate a higher NPV. However, in both instances, the combined MIP model and GA approach delivered an integrated production schedule that ensured that spatial and temporal alignment was achieved between LT and MT production schedules. Future research may focus on developing solution approaches that can fully integrate LT, MT and ST production scheduling horizons, and incorporate factors like stockpiling and blending to further improve scheduling effectiveness. Further research could also investigate the fine-tuning of GA parameters to ensure that the application of the combined MIP model and GA approach can consistently generate higher NPVs.