PRIMJENA STOHASTIČKOGA MODELA NA ODLAGALIŠTU JALOVINE KAO POTPORA DUGOROČNOJ PROIZVODNJI U OTVORENOME KOPU S CILJEM POVEĆANJA POSTOTKA RUDE U OBRADBI

This paper presents a chance-constrained integer programming approach based on the linear method to solve the longterm open pit mine production scheduling problem. Specifically, a single stockpile has been addressed for storing excess low-grade material based on the availability of processing capacity and for possible future processing. The proposed scheduling model maximizes the project NPV while respecting a series of physical and economic constraints. Differently from common practice, where deterministic models are used to calculate the average grade for material in the stockpiles, in this work a stochastic approach was performed, starting from the time of planning before the stockpile realization. By performing a probability analysis on two case studies (on iron and gold deposits), it was proven that the stockpile attributes can be treated as normally distributed random variables. Afterwards, the stochastic programming model was formulated in an open pit gold mine in order to determine the optimum amount of ore dispatched from different bench levels in the open pit and at the same time a low-grade stockpile to the mill. The chance-constrained programming was finally applied to obtain the equivalent deterministic solution of the primary model. The obtained results have shown a better feed grade for the processing plant with a higher NPV and probability of grade blending constraint satisfaction, with respect to using the traditional stockpile deterministic model.Rad prikazuje uporabu vjerojatnosnoga cjelobrojnog programiranja, temeljenoga na linearnome algoritmu, za dugoročno rješavanje proizvodnje u rudniku otvorenoga kopa. Obrađeno je jedno odlagalište jalovine sa „siromašnom” koncentracijom rude u cilju aktiviranja toga materijala u budućoj preradbi korisne sirovine. Takav projekt maksimizira trenutačnu vrijednost rudarenja uzimajući u obzir niz fizičkih i ekonomskih varijabli. Posebnost u odnosu na determinističke modele koji se danas uglavnom koriste za izračun granične prosječne vrijednosti koncentracije rude prije odlaganja kao jalovine izražena je stohastikom. Ona je uključila vjerojatnosnu analizu dvaju slučajeva, tj. za ležište željeza i zlata. U obama je dokazano kako se varijable određene na odlagalištu mogu opisati normalnom razdiobom. Stohastički model programiran je za rudnik zlata te je uzeta u obzir optimalna vrijednost rude razvrstane na različitim rudničkim razinama, a prije slanja na obradbu (mljevenje). Optimizirani model zatim je primijenjen za dobivanje usporednoga determinističkog modela. Rezultati su upozorili na to da je konačno rješenje pokazalo znatno bolji odabir granične koncentracije rude koja se mogla poslati na daljnju obradbu. Time je uvećana i ukupna vrijednost rudnika/ležišta

The application of a stockpile stochastic model into long-term open pit mine production scheduling to improve the feed grade for the processing plant

This paper presents a chance-constrained integer programming approach based on the linear method to solve the long-term open pit mine production scheduling problem. Specifically, a single stockpile has been addressed for storing excess low-grade material based on the availability of processing capacity and for possible future processing. The proposed scheduling model maximizes the project NPV while respecting a series of physical and economic constraints. Differently from common practice, where deterministic models are used to calculate the average grade for material in the stockpiles, in this work a stochastic approach was performed, starting from the time of planning before the stockpile realization. By performing a probability analysis on two case studies (on iron and gold deposits), it was proven that the stockpile attributes can be treated as normally distributed random variables. Afterwards, the stochastic programming model was formulated in an open pit gold mine in order to determine the optimum amount of ore dispatched from different bench levels in the open pit and at the same time a low-grade stockpile to the mill. The chance-constrained programming was finally applied to obtain the equivalent deterministic solution of the primary model. The obtained results have shown a better feed grade for the processing plant with a higher NPV and probability of grade blending constraint satisfaction, with respect to using the traditional stockpile deterministic model.

Integrated Parametric Graph Closure and Branch-and-Cut Algorithm for Open Pit Mine Scheduling under Uncertainty

Open pit mine production scheduling is a computationally expensive large-scale mixed-integer linear programming problem. This research develops a computationally efficient algorithm to solve open pit production scheduling problems under uncertain geological parameters. The proposed solution approach for production scheduling is a two-stage process. The stochastic production scheduling problem is iteratively solved in the first stage after relaxing resource constraints using a parametric graph closure algorithm. Finally, the branch-and-cut algorithm is applied to respect the resource constraints, which might be violated during the first stage of the algorithm. Six small-scale production scheduling problems from iron and copper mines were used to validate the proposed stochastic production scheduling model. The results demonstrated that the proposed method could significantly improve the computational time with a reasonable optimality gap (the maximum gap is 4%). In addition, the proposed stochastic method is tested using industrial-scale copper data and compared with its deterministic model. The results show that the net present value for the stochastic model improved by 6% compared to the deterministic model

Stochastic-optimization of equipment productivity in multi-seam formations

Short and long range planning and execution for multi-seam coal formations (MSFs) are challenging with complex extraction mechanisms. Stripping equipment selection and scheduling are functions of the physical dynamics of the mine and the operational mechanisms of its components, thus its productivity is dependent on these parameters. Previous research studies did not incorporate quantitative relationships between equipment productivities and extraction dynamics in MSFs. The intrinsic variability of excavation and spoiling dynamics must also form part of existing models. This research formulates quantitative relationships of equipment productivities using Branch-and-Bound algorithms and Lagrange Parameterization approaches. The stochastic processes are resolved via Monte Carlo/Latin Hypercube simulation techniques within @RISK framework. The model was presented with a bituminous coal mining case in the Appalachian field. The simulated results showed a 3.51% improvement in mining cost and 0.19% increment in net present value. A 76.95yd³ drop in productivity per unit change in cycle time was recorded for sub-optimal equipment schedules. The geologic variability and equipment operational parameters restricted any possible change in the cost function. A 50.3% chance of the mining cost increasing above its current value was driven by the volume of material re-handled with 0.52 regression coefficient. The study advances the optimization process in mine planning and scheduling algorithms, to efficiently capture future uncertainties surrounding multivariate random functions. The main novelty includes the application of stochastic-optimization procedures to improve equipment productivity in MSFs --Abstract, page iii

Optimum waste dump planning using Mixed Integer Programming (MIP)

This research project aims to optimise the long term mine rock dump planning by generating the optimum rock dumping schedules using mixed integer programming (MIP) models. Through the modelling of the problem, three new MIP models were developed and implemented in a greenfield mining project. The life of mine dumping schedules were successfully generated by the models, which focuses on minimising the haulage cost, maximising the equipment utilisation, and seeking the balance between the two

Production Scheduling of an Open-pit Mining Complex with Waste Dump Constraints

The research work aims to solve the production scheduling problem for open pit mining complexes. It establishes a Mixed-Integer Programming (MIP) model that maximises the net present value of future cash flows and satisfies reserve, production capacity, mining block precedence, waste disposal, stockpiling, and pit sequence constraints. The model is validated and implemented with real-world case

Incorporating cut-off grade optimization and stockpiling into oil sands production scheduling and waste management.

In achieving maximum benefit in oil sands mining, the long-term production schedule should have the time and sequence of removing ore, dyke material and waste from the final pit limit. An optimum cut-off grade profile and stockpiling will ensure the segregation between these materials meet economic and regulatory requirements. In-pit waste management strategy for oil sands mining requires dyke construction to occur simultaneously with the advancement of mining operations. This research seeks to determine: 1) the optimum life of mine cut-off grade profile and its corresponding tonnages; 2) the time and sequence for removal of ore, dyke material and waste to maximize NPV; 3) the dyke material schedule for dyke construction to minimize construction costs; and 4) the associated impacts of stockpiling and stockpile reclamation with limited time duration. Cut-off grade optimization was used to generate an optimum grade schedule which specifies the cut-off grade, duration of mining of the grade and tonnage mined during the mine life. A heuristic framework, referred to as the Integrated Cut-Off Grade Optimization (ICOGO) model was developed in this research. It generates an optimum cut-off grade policy and a schedule for mining ore and waste, as well as overburden, interburden and tailings coarse sand dyke material for long-term production planning. Subsequently, a mathematical programming framework based on Mixed Integer Linear Goal Programming (MILGP) model was developed to generate a detailed production schedule for removal of ore, waste and dyke materials from the final pit limit. Stockpiling scenarios investigated during the study include: i) no stockpiling; ii) stockpiling and reclaiming at the end of mine life; and iii) stockpiling for one year or two years prior to reclamation. The developed models were applied to two oil sands case studies to maximize the Net Present Value (NPV) of the operations. In both case studies, the NPV generated by the ICOGO model for one year stockpiling scenario was higher than other stockpiling scenarios. For the MILGP the NPV generated for the two year stockpiling scenario was higher than the one year stockpiling scenario. In comparison, whereas the ICOGO model solved the optimization problem faster, the MILGP model results provide detailed mining-cut extraction sequencing for mining.Master of Science (MSc) in Natural Resources Engineerin

Modelling the tactical decisions for open-pit mines

Open-pit deposits are often characterized by a stack of layers of different geological nature. Some layers are worthless while the ore of the others is of a varying economic value depending on grade. To reach a layer, it is necessary to have first removed the upper layers above the extraction zone. This action results in uncovering the layer in this particular place and in facilitating access to the layers below. This process involves a series of 2 to 7 operations; each one is performed by a machine, some of which are able to perform up to 3 different operations. Ensuring the consistency of mining extraction scheduling over a few months, in order to meet known or forecast demand, is a challenging task. A mining extraction model based on mathematical programming has been proposed but it is hardly usable due to its size. A Discrete Events Simulator modelling is currently being tested to measure the impact of dynamic rules used to allocate the machines and select the target mining area

Optimisation de la planification stratégique d’une mine à ciel ouvert en tenant compte de l’incertitude géologique

RÉSUMÉ: Pour l’industrie minière, la planification est une étape critique impliquant plusieurs niveaux de décisions. Ces décisions se prennent à chaque maillon de la chaine d’approvisionnement d’un complexe minier à savoir l’extraction, le transport, le stockage, le concassage, le traitement, etc. La complexité des problèmes de planification est modulable selon le degré de détails qu’on veut considérer et le nombre de composantes de la chaine qu’on veut intégrer. Cette thèse s’intéresse aux problèmes de planification stratégique des mines à ciel ouvert dans un contexte d’incertitude géologique. L’objectif principal porte sur le développement d’un outil mathématique efficace et robuste pour soutenir les compagnies minières dans leurs processus de prise de décision. Pour ce faire, différentes variantes du problème ont été à l’étude, considérant, entre autres, plusieurs destinations et plusieurs éléments géologiques d’intérêt et incluant aussi des options d’investissement. Dans le premier article, un modèle de base est présenté. À partir d’une représentation du gisement discrédité en blocs, on cherche à déterminer quand, le cas échéant, extraire chaque bloc et où l’envoyer : vers le stérile ou les usines de traitement. Cet ordonnancement doit être choisi de sorte que les profits générés par l’exploitation du gisement soient maximisés tout en minimisant les déviations des objectifs de production et en respectant les liens de préséance existants entre les blocs ainsi que les contraintes de ressources. Pour cet article, l’emphase est surtout mise sur la méthode de résolution qui servira de gabarit pour les autres variantes. Il s’agit d’une méthode de décomposition (basée sur l’approche de Bienstock et Zuckerberg) combinée avec une heuristique d’arrondissement et une recherche Tabou (RT). Les résultats obtenus, tant au niveau de la qualité de la solution que le temps de résolution, ont motivé l’extension du modèle en deux variantes dans les articles 2 et 3 tout en conservant plus ou moins la même stratégie de résolution. Le deuxième article intègre les piles de minerai au modèle précédent. Le défi était de correctement modéliser le flux de matière au niveau des piles en considérant les limitations des méthodes d’optimisation existantes. Pour ce faire, un nouveau modèle linéaire a été développé. Ce dernier rompt avec les modèles classiques qui assument une homogénéisation parfaite des matériaux une fois arrivés dans la pile et propose une toute nouvelle approche permettant une estimation exacte du contenu des piles. Les limitations de cette formulation sont discutées et des recommandations pour y remédier sont aussi suggérées. Comme troisième objectif, une certaine forme de flexibilité est rajoutée au modèle en intégrant des options d’investissement sur de nouveaux équipements. On montre que cette flexibilité permet d’augmenter la production et générer ainsi plus de profits. Pour résoudre cette variante, des adaptations ont dû être apportées à la méthode de résolution initiale. Une parallélisation au niveau de la RT a notamment été implémentée afin d’améliorer les temps de calcul de cette étape.----------ABSTRACT: In the mining industry, planning is a critical step involving multiple decision levels. These decisions are made at each stage of the mineral value chain in a mining complex, namely extraction, transportation, storage, crushing, processing, etc. The complexity of scheduling problems can be varied according to the degree of details we want to consider and the number of components of the chain we want to integrate. This thesis addresses the open pit mine strategic planning problem under geological uncertainty. The main objective is to develop an effective and robust mathematical tool to support mining companies in their decision-making processes. In order to achieve this, different variants of the problem have been studied, considering, among others, several destinations and multiple geological elements of interest and including investment options. In the first paper, a basic model is presented. Given a three-dimensional representation of the deposit discretized into blocks, the model seeks to determine when, if ever, to extract each block and where to send it: towards waste dump or processing facilities. This scheduling must be chosen in a way that the profits generated by the deposit exploitation are maximized while minimizing the deviations from the production targets and respecting the slope constraints as well as the resource constraints. For this paper, the emphasis is mainly on the solution approach that will be used as a template for the next variants. It is based on a decomposition method (originally presented by Bienstock and Zuckerberg) combined with a rounding heuristic and a Tabu search. The results obtained, both in terms of solution quality and running time, motivated the extension of the model to two variants in papers 2 and 3 while retaining the same resolution strategy’s structure. The second paper integrates stockpiling as part of the optimization process. The challenge was how to correctly model the material flow inside the stockpiles considering the limitations of existing optimization methods. To tackle that, a new linear model has been developed. The latter breaks with the classic models that assume homogeneous mixing of the material once arrived in the stockpile and proposes a new approach for an accurate estimation of the stockpile content. The limitations of this formulation are discussed and recommendations to bypass them are also suggested. As third objective, some form of flexibility is added to the model by including capital expenditure options. This flexibility allowed to increase production tonnage and thus generate more profits. To solve this variant, some adaptations had to be made to the initial solution approach. In particular, a parallelization at the level of the Tabu search heuristic was implemented in order to speed-up this step