Linear Programming Approximations for Modeling Instant ‐ Mixing Stockpiles (original) (raw)
Related papers
2019
The open-pit mine production scheduling problem aims to optimize the net present value of a mining asset. Several solution methods have been proposed to find the most profitable mining sequence. Such methods entail determining which mining blocks from those used to represent the related mineral deposit should be extracted and when. However, little is reported in the technical literature that considers the material flow once mined and, more specifically, incorporating stockpiling as part of the mine scheduling strategy, thus adding technical intricacies due to the difficulty of correctly modeling the materials’ blending once sent into a stockpile. In this paper, a new model is provided to address the topic of open-pit mine production scheduling considering multiple destinations for the mined material, including stockpiles, and accounting for multielement uncertainty. Unlike conventional models, the proposed model allows for an accurate estimation of the resulting grade of the stockpi...
Open pit mine planning with stockpiling
2017
This dissertation consists of three papers; the first is published in European Journal of Operational Research, the second is nearing submission to Optimization and Engineering, and the third is nearing submission to International Journal of Mining, Reclamation and Environment. These papers apply operations research techniques to open pit mine production scheduling with stockpiling (OPMPS+S). The first paper, “Linear Models for Stockpiling in Open-pit Mine Production Scheduling Problems,” reviews existing models to solve OPMPS+S and shows that a nonlinear-integer model provides an exact solution but is intractable even for medium-size data sets. Then, we present an approximation to that nonlinear-integer model, solve the nonlinear-integer and proposed models for multiple data sets and show that the latter model provides solutions very close to those provided by the nonlinear-integer model. By pairing this novel formulation with recently developed linear programming algorithms and he...
A mathematical model for open pit mine production scheduling with Grade Engineering® and stockpiling
International Journal of Mining Science and Technology, 2021
This paper presents the development and implementation of an innovative mixed integer programming based mathematical model for an open pit mining operation with Grade Engineering framework. Grade Engineering comprises a range of coarse-separation based pre-processing techniques that separate the desirable (i.e. high-grade) and undesirable (i.e. low-grade or uneconomic) materials and ensure the delivery of only selected quantity of high quality (or high-grade) material to energy, water, and cost-intensive processing plant. The model maximizes the net present value under a range of operational and processing constraints. Given that the proposed model is computationally complex, the authors employ a data preprocessing procedure and then evaluate the performance of the model at several practical instances using computation time, optimality gap, and the net present value as valid measures. In addition, a comparison of the proposed and traditional (without Grade Engineering) models reflects that the proposed model outperforms the traditional formulation.
Linear Programming model for Long-term Mine Planning in the presence of Grade Uncertainty
2011
The optimality of an open pit production scheduling problem is affected dramatically by grade uncertainty. Recent research initiatives have attempted to consider the effect of grade uncertainty on production schedules. These methods either are aimed to minimize the risk using grade uncertainty or to maximize the net present value (NPV) without taking into account grade uncertainty explicitly. Another major problem in open pit production scheduling is the size of the optimization problem. The mathematical programming formulation of real size long-term open pit production schedules are beyond the capacity of current hardware and optimization software. In this paper a mathematical programming formulism is presented to find a sequence in which ore and waste blocks should be removed from a predefined open pit outline and their respective destinations, over the life of mine, so that the net present value of the operation is maximized and the deviations from the annual target ore productio...
Long-Term Mine Planning in Presence of Grade Uncertainty
2014
Behrang Koushavand, Hooman Askari‐Nasab and Clayton V. Deutsch Uncertainty is inevitable with sparse geological data. The optimality of the solution for an open pit production scheduling problem is affected dramatically by grade uncertainty. Recent research initiatives have attempted to consider the effect of grade uncertainty on production schedules. These methods either are aimed to minimize the risk or to maximize the net present value (NPV) without taking into account grade uncertainty explicitly. Another major problem in open pit production scheduling is the size of the optimization problem. The mathematical programming formulation of real size long‐term open pit production schedules are beyond the capacity of current hardware and optimization software. In this paper, a mathematical programming formulism is presented to find a sequence in which ore and waste blocks should be removed from a predefined open pit outline and their respective destinations, over the life of mine, so ...
Solving mixed integer nonlinear programming problems for mine production planning with stockpiling
2012
Abstract. The open-pit mine production scheduling problem has received a great deal of attention in recent years, both in the academic literature, and in the mining industry. Optimization approaches to strategic planning for mine exploitation have become the industry standard, as the recent review of Newman et al.[19] highlights. However most of these approaches focus on extraction sequencing, and don't consider the material flow after mining.
Mixed integer linear programming formulations for open pit production scheduling
Journal of Mining Science, 2011
One of the main obstacles in using mixed integer linear programming (MILP) formulations for large-scale open pit production scheduling is the size of the problem. The objective of this work is to develop, implement, and verify deterministic MILP formulations for long-term large-scale open pit production scheduling problems. The objective of the model is to maximize the net present value, while meeting grade blending, mining and processing capacities, and the precedence of block extraction constraints. We present four MILP formulations; the first two models are modifications of available models; we also propose, test and validate two new MILP formulations. To reduce the number of binary integer variables in the formulation, we aggregate blocks into larger units referred to as mining-cuts. We compare the performances of the proposed models based on net present value generated, practical mining production constraints, size of the mathematical programming formulations, the number of integer variables required in formulation, and the computational time required for convergence. An iron ore mine case study is represented to illustrate the practicality of the models as well.
Journal of The South African Institute of Mining and Metallurgy, 2012
Long-term production scheduling involves the determination of sequences of ore and waste blocks to give the maximum net present value (NPV). This problem is subject to many aspects being satisfied, such as grade constraints, tonnage requirement for the plants, wall slope restriction, equipment capacities, etc. Long-term production scheduling determines the distribution of cash flow over life of mines. The NPV of each project depends on the grade and tonnage of the deposit, economic issues (operating and capital costs, and commodity price), and technical mining specifications (slope constraints, excavation capacities, etc.) In reality, some of the abovementioned issues can vary within certain limits, and the planner should make his decision on the production plan before knowing the exact values of the data. Among these uncertainties, those that are related to the orebody model lead to considerable deviation from production targets during the extraction process. Orebody model uncertai...
Journal of the Southern African Institute of Mining and Metallurgy, 2020
SYNOPSIS Long-term production scheduling is a major step in open pit mine planning and design. It aims to maximize the net present value (NPV) of the cash flows from a mining project while satisfying all the operational constraints, such as grade blending, ore production, mining capacity, and pit slope during each scheduling period. Long-term plans not only determine the cash flow generated over the mine life, but are also the basis for medium- and short-term production scheduling. Mathematical programming methods, such as linear programming, mixed integer linear programming, dynamic programming, and graph theory, have shown to be well suited for optimization of mine production scheduling. However, the long-term plans generated by the mathematical formulations mostly create a scattered block extraction order on several benches that cannot be implemented in practice. The reason is the excessive movement of mining equipment between benches in a single scheduling period. In this paper,...
Optimizing Long-Term Production Plans in Underground and Open-Pit Copper Mines
Operations Research, 2012
We present a methodology for long-term mine planning based on a general capacitated multicommodity network flow formulation. It considers underground and open-pit ore deposits sharing multiple downstream processing plants over a long horizon. The purpose of the model is to optimize several mines in an integrated fashion, but real size instances are hard to solve due to the combinatorial nature of the problem. We tackle this by solving the relaxation of a tight linear formulation, and we round the resulting near-integer solution with a customized procedure. The model has been implemented at Codelco, the largest copper producer in the world. Since 2001, the system has been used on a regular basis and has increased the net present value of the production plan for a single mine by 5%. Moreover, integrating multiple mines provided an additional increase of 3%. The system has allowed planners to evaluate more scenarios. In particular, the model was used to study the option of delaying by four years the conversion of Chiquicamata, Codelco's largest open-pit mine, to underground operations.