Mustafa Kumral

Optimizing ore–waste discrimination and block sequencing through simulated annealing

Abstract This paper attempts to solve ore–waste discrimination and block sequencing problems for given capacities through a combination of goal programming (GP) and simulated annealing (SA). The problem is firstly formulated in a goal programming form, which is expressed as the minimization of the violations between the production rates and the installed capacities under access, metal quantity and the required net present value (NPV) constraints. In the model, block sequencing is first solved by CPLEX. The violations from the capacities are allowed under a cost because actual grade and tonnage values of blocks cannot be known. The violations can be accepted to some extent because mines are planned and designed on the basis of simulated/estimated grades. This solution is then submitted to the SA module such that ore–waste discrimination is incorporated into the modeling. A case study was carried out to demonstrate the approach. The findings show that the approach gives rise to the profitability and can be used to generate mining schedules.

Optimizing Ore–Waste Dig-Limits as Part of Operational Mine Planning Through Genetic Algorithms

Dig-limit optimization is an operational decision making problem that significantly affects the value of open-pit mining operations. Traditionally, dig-limits have been drawn by hand and can be defined as classifying practical ore and waste boundaries suiting equipment sizes in a bench. In this paper, an optimization approach based on a genetic algorithm (GA) was developed to approximate optimal dig-limits on a bench, given grade control data, equipment constraints, processing, and mining costs. A case study was conducted on a sample disseminated nickel bench, in a two destination and single ore-type deposit. The results from using the GA are compared to hand-drawn results. The study shows that GA-based approach can be effectively used for dig-limit optimization.

Grade control in multi-variable ore deposits as a quality management problem under uncertainty

Purpose – The purpose of this paper is to provide a decision-making tool on where to send mining parcels extracted in such a way as to minimize losses arising from mis-classification. The problem is complicated because actual values of mining parcels cannot be known and the decision is made on the basis of the estimation/simulations of the parcels generated from sparse data. Design/methodology/approach – The loss minimization associated with mis-classification is formulated as a non-linear optimization problem and solved by successive mixed integer programming. By assigning reasonable values to some variables making problem non-linear, the problem is converted to a mixed integer programming (MIP) and is solved by a standard MIP optimization engine. Findings – A case study was conducted to see the performance of the proposed approach on a deposit with gold and silver variables. The proposed approach was also compared with conventional grade control approaches. The results showed that the approach proposed ...

Genetic algorithms for the optimisation of the Schwartz–Smith two-factor model: a case study on a copper deposit

Abstract Mining companies typically seek ways to hedge risks affecting their production. One useful instrument to mitigate the financial risk is the futures contracts on commodity prices. Information from the transactions in futures markets is publicly available and can be analysed with the Schwartz–Smith two-factor model (SSTF). However, finding the parameters governing this model can be very challenging. This step is done using a deterministic optimisation approach called the Expectation–Maximisation algorithm (EM). The starting values of the model will have a significant effect on the convergence of the EM. To ensure the solution does not get stuck in a local maximum, the EM algorithm is performed multiple times with different starting values. This paper assesses the value of genetic algorithms (GA) to optimise the parameters of the SWTF model. Although they are slower than EM algorithms because they use random number generators to search for the optimal solution, GA optimise a population of solutions instead of working on only one solution at the time. Moreover, a constraint on the range parameter can be applied to ensure the parameter has a sound economic meaning. Once the SWTF parameters have been calibrated on the observation of futures contracts, the model can be used for the simulation of spot and futures prices. To demonstrate the performance of the proposed approach, a case study was conducted on a copper deposit. The simulations based on the SWTF model whose parameters are determined by GA are used. An active management strategy of the stockpile, dependent on discrepancies in commodity futures prices is tested. Results show that the active management strategy produces positive returns over the passive investment approach.

Simulation-based mine extraction sequencing with chance constrained risk tolerance:

Technical and financial uncertainties present significant risks to the profitability and efficiency of mining operations. Unexpected realizations (e.g., price or grade) may result in catastrophic consequences. This phenomenon forces mining industries to use probabilistic decision-making tools to assess, mitigate, and manage the risks associated with these uncertainties. In this context, mining operations need robust schedules, which are insensitive to market changes and/or unexpected grade realizations. The mine production scheduling problem consists of three sub-problems: extraction sequencing (timing), ore-waste discrimination (classification) and production rates (utilization). The solutions to these problems are generated under significant parameter uncertainties. This paper proposes an extraction sequencing approach in which the net present value of a mining project is, for a given risk tolerance, maximized and the actual risk tolerance is then verified through Monte-Carlo simulations. The risk tolerance is a measure of uncertainty and that secures the project net present value with a given probability. Risk tolerance is derived through the use of standard deviations of block economic values in the medium of multiple grade and economic images of orebody. The proposed approach is demonstrated on a case study using gold mine data. The results of the case study show that the proposed approach, combining chance-constrained programming and Monte-Carlo simulation, can be used to solve the mine extraction sequencing problem in an uncertain financial and technical environment.

Planning additional drilling campaign using two-space genetic algorithm: A game theoretical approach

Grade and tonnage are the most important technical uncertainties in mining ventures because of the use of estimations/simulations, which are mostly generated from drill data. Open pit mines are planned and designed on the basis of the blocks representing the entire orebody. Each block has different estimation/simulation variance reflecting uncertainty to some extent. The estimation/simulation realizations are submitted to mine production scheduling process. However, the use of a block model with varying estimation/simulation variances will lead to serious risk in the scheduling. In the medium of multiple simulations, the dispersion variances of blocks can be thought to regard technical uncertainties. However, the dispersion variance cannot handle uncertainty associated with varying estimation/simulation variances of blocks. This paper proposes an approach that generates the configuration of the best additional drilling campaign to generate more homogenous estimation/simulation variances of blocks. In other words, the objective is to find the best drilling configuration in such a way as to minimize grade uncertainty under budget constraint. Uncertainty measure of the optimization process in this paper is interpolation variance, which considers data locations and grades. The problem is expressed as a minmax problem, which focuses on finding the best worst-case performance i.e., minimizing interpolation variance of the block generating maximum interpolation variance. Since the optimization model requires computing the interpolation variances of blocks being simulated/estimated in each iteration, the problem cannot be solved by standard optimization tools. This motivates to use two-space genetic algorithm (GA) approach to solve the problem. The technique has two spaces: feasible drill hole configuration with minimization of interpolation variance and drill hole simulations with maximization of interpolation variance. Two-space interacts to find a minmax solution iteratively. A case study was conducted to demonstrate the performance of approach. The findings showed that the approach could be used to plan a new drilling campaign.

Dig-limits optimization through mixed-integer linear programming in open-pit mines

As a type of general layout problems, dig-limits optimization focuses on generating the ore–waste boundaries of a bench sector in an open-pit mining operation. Typically, blast holes are dense; therefore, selective mining units (SMUs) are small, which is not compatible with loading equipment. Loader cannot select ore-waste boundaries of SMUs because the arm of the excavator is generally longer than SMU sizes. Therefore, clusters of SMUs being compatible with loader movements need to be formed. In this paper, the dig-limits optimization problem is shown to be NP-hard and formulated to maximize profit to be obtained from a mining sector such that ore and waste clusters corresponding to mine excavator movements are considered and solved by mixed-integer linear programming. To see the efficiency of the proposed approach, a case study is conducted on seven sectors of a bench in a gold mine. The results showed that the approach is practical and has potential to increase the value of operation. The resulting average economic value of seven sectors is

Underground mine planning: stope layout optimisation under grade uncertainty using genetic algorithms

129,060. Additionally, optimal design of one bench solved by the model is compared to a manual design of a mining engineer and a deviation of 6.4% has been observed.

Cost analysis of material handling systems in open pit mining: Case study on an iron ore prefeasibility study

Abstract Stope layout optimisation finds a technically producible orebody portion that maximises the profit of the mining operation based on the stoping method used. A three-stage stochastic optimisation model combining genetic algorithms (GA) is proposed to account for grade uncertainty. The first stage computes the stope layout uncertainty, the second stage creates average design and their feasibility evaluation breeds the initial population, and the third stage uses GAs to improve this initial population over generations. The approach generates higher profit, less planned dilution, and a robust stope layout that is insensitive to orebody grade fluctuations.

Heuristic stope layout optimisation accounting for variable stope dimensions and dilution management

ABSTRACT Selection of the optimal material handling system is one of the most significant decisions to be made in mineral industries. Rapid economic changes and technological improvements make cost analysis a complicated process. On the other hand, current low commodity prices have put a greater emphasis on cost reduction and process optimization to ensure viability of mining projects. In this article, two material handling systems, a semimobile in-pit crusher and conveyor systems (IPCC) and traditional truck and shovel systems (TS), are compared through the cost analysis of an iron ore prefeasibility study. Furthermore, robustness of the design parameters is evaluated through a sensitivity analysis to determine the relative importance of project parameters. Finally, risks associated with uncertain design parameters affecting cost analysis are assessed through Monte Carlo simulation. The results indicated that IPCC is more cost effective than TS.