Stochastic Open Pit Mine Production Scheduling under Geological Uncertainties

Abstract

The mine production scheduling defines the sequence of extraction of mine mining blocks over the life of mine, which establishes the ore supply and total material movement. This process should be optimized to maximize the overall discounted cash flow value of a mining project. The optimization strategies for limestone mine is significantly different from the metal mine production optimization. Moreover, the deterministic scheduling method cannot incorporate level uncertainty into scheduling problem, may lead to serious deviations from the forecast production target. Stochastic mine production scheduling is considered to get a more robust mine production scheduling plan. However, the computational time is key problems associated with large scale stochastic mine production scheduling of an open pit mine. This thesis has attempted to solve two aspects of mine production scheduling: (a) new deterministic optimization formulation for limestone mine production scheduling; and (b) developing a new solution algorithm for solving large scale stochastic production scheduling under geological uncertainty.
For limestone production scheduling, a limestone quarry from India is selected. A new formulation of long term production planning of limestone quarry is presented according to the existing problem of the study mine to supply consistent quantity and quality of limestone to the cement plant. A case study quarry is served as a captive quarry for the cement plant. The objectives of this study are: (a) to investigate how long the limestone quarry can alone supply the desire quality and quantity materials to the cement plant; and (b) to investigated the possibility of extending the quarry life by utilizing some quantity of the limestone from the different source and blending that limestone with the limestone from the quarry to achieve the target quality and quantity of the cement plant. These objectives are achieved by generating the production sequencing of the mining blocks using a sequential branch and cut algorithm. The results revealed that up to 15 years, the existing quarry alone can served the cement plant. This production scheduling problem was solved using two different objectives: maximizing the utilization of low grade limestone and maximizing the profit over mine life. In both the cases, if certain quantity of limestone can be brought from the other sources, the life of the study quarry can be significantly increased. The life of the quarry increased from 15 years to 85 years. The study also helps to calculate the desire quality of the limestone that will be brought from other sources throughout the life of the quarry. The results also revealed that the maximizing the profit over mine life approach generates more profit (10% more) when compared with existing production planning formulation that mine is presently adopting (maximizing the utilization of low grade limestone).
To developing the new solution strategy for stochastic production scheduling under geological uncertainty, the standard metal mine open pit production scheduling formulation was considered. The goal of the open pit stochastic production scheduling is to assign mining blocks in different production periods to maximize the profit over the life-of-the-mine and minimizing the deviation from the targets. Since, stochastic mine production schedule requires multiple simulated orebody models, the number of decision variables and constraints are increased significantly which leads to huge computational time. The stochastic production scheduling of industrial size mining problem is generally impossible to solve optimally. The objective of this research is to develop an algorithm which helps to solve real size problem within reasonable amount of computational time with minimum gap from true optimum solution. Only geological uncertainty was considered in this production scheduling in this thesis; however, any other types of uncertainty can also be incorporated with little effort. The proposed solution approach for production scheduling is a two-step process. In first step, the stochastic production scheduling problem will be iteratively solved using parametric minimum-cut algorithm, after relaxing resource constraints. Finally, branch and cut algorithm will be applied to respect the resources constrains which might be violated during first stage of the algorithm. The validation of the proposed method was performed by calculating the percentage of gap from the upper bound of true optimality. The proposed model was validated by solving six small scale production scheduling problems from iron and copper mines. The results demonstrated that the proposed method can significantly improve the computational time with reasonable optimality gap. The proposed method was tested with industrial scale copper data set, and compare with its deterministic model. The results show that the stochastic model can improved the net present value by 6% with reasonable computational time.
Finally, a case study was performed in Indian iron mine to show the efficiency of proposed algorithm. A comparative study with one existing stochastic production scheduling method (Branch and cut with longest path algorithm) was performed, and results demonstrated that both the algorithm can generate similar net present value from the study mine; however, the computational time of the proposed method is 46.64% less than the existing method.