Long-term Production Scheduling Research Articles

Development of an intelligent evolution algorithm for open pit mines’ long-term production scheduling using the concept of block aggregation

Development of an intelligent evolution algorithm for open pit mines’ long-term production scheduling using the concept of block aggregation

Simultaneous stochastic optimisation of mining complexes: Integrating progressive reclamation and waste management with contextual bandits

ABSTRACT Managing environmental performance of waste dump facilities in mining complexes is an integral part of long-term production planning. Sustainable long-term production scheduling solutions are desired to mitigate risk and return the environment to a productive post-mining state. A simultaneous stochastic optimisation framework for long-term production scheduling in mining complexes is developed that integrates waste management and progressive reclamation. The waste dump placement schedule is jointly optimised with the extraction sequence, destination policy, and stockpiling decisions in a single stochastic mathematical programming framework. This includes the timing of progressive reclamation activities in parallel with production to enhance waste dump rehabilitation. Uncertainty related to the production of acid rock drainage is quantified by simulating geochemical properties of waste and managing the blending of uncertain waste properties within the optimisation framework. With respect to the framework for simultaneous stochastic optimisation, contextual bandits are explored to improve the metaheuristic solution approach and solve the corresponding large-scale optimisation model. The framework is tested in a multi-mine copper-gold mining complex leading to improved environmental performance. Risk of acid rock drainage is decreased by 52.5% in the waste dump facilities. Reclamation planning activities for meeting environmental requirements are scheduled prior to closure. The solution approach more effectively improves the objective function with contextual bandits leading to a 24% improvement in the study presented.

Connecting planning horizons in mining complexes with reinforcement learning and stochastic programming

Connecting short- and long-term production schedules in mining complexes is essential to ensure that the long-term production schedule is achievable at shorter timescales. Previous research that addresses optimizing mining complexes under uncertainty focus on simultaneously optimizing different components in the mining complex to capitalize on advantageous synergies. Typically, short- and long-term production schedules are optimized separately in a number of stages. This poses risk of schedule misalignment, which can adversely affect the economic outcome of a mining complex and the ability to meet long-term production forecasts at shorter timescales. A framework is proposed to jointly optimize short- and long-term production schedules by connecting planning horizons with stochastic mathematical programming and reinforcement learning. The solution approach is tested in a large operating copper mining complex and demonstrates significant improvements in the resulting production and financial forecasts.

A Genetic algorithm scheme for large scale open-pit mine production scheduling

ABSTRACT Due to the large size of open-pit mines’ long-term production scheduling (OPMPS) problem in large-scale deposits, it is challenging to solve that problem as the mixed integer linear programming (MILP) model. This study used an approach of the genetic algorithm (GA) to tackle this challenge. So, in a small hypothetical deposit, based on the blocks in the ultimate pit limit and scenarios with 2–6 phases, net present values (NPV) and computational times obtained from the GA and MILP model were compared to evaluate the GA. Also, the GA was applied to a large-scale deposit to determine the efficiency of the GA in real deposits. The maximum NPV was obtained for the four-phase scenario in the hypothetical deposit and the six-phase scenario in the large-scale deposit. Although the GA’s NPV decreased slightly compared to the global optimum solution from the MILP model, the computational time was significantly reduced.

Optimising the mine production scheduling accounting for stockpiling and investment decisions under geological uncertainty

ABSTRACT This paper presents an approach to optimise the long-term production scheduling of an open pit mine with multiple processing streams, while accounting for investment decisions under mineral supply uncertainty. The solution approach consists of first solving the linear relaxation using an extension of the Bienstock-Zuckerberg algorithm to the stochastic optimisation. Then, a rounding heuristic based on the topological sorting is applied, followed by a parallel multi-neighbourhood Tabu search. The proposed method is applied to a multi-product open pit mine deposit, with the possibility of investing in new shovels, trucks or crushers to increase related capacities.

A simulated annealing based stochastic long-term production scheduling of open-pit mines with stockpiling under grade uncertainty

ABSTRACT This research presents a new Simulated Annealing based stochastic optimisation algorithm to integrate geological uncertainty into the optimization process through multiple equiprobable simulated realisations of an orebody while considering stockpiling options and other relevant constraints. The stockpiling option is included, increasing the chances of processing high-grade and most certain ore blocks in early periods. The efficiency of the proposed algorithm in creating a single good enough production schedule that minimises the risk of deviation from production targets while maximising the net present value of the operation is demonstrated through three case studies, i.e. case A with 2448 blocks, B with 6,578 and C with 10,810 blocks. The comparison of results with the two-stage stochastic model reveals that the proposed methodology reduces the risk of production deviation to a minimal and provides a near-optimal solution with an optimality gap of 3.53, −0.87, and 8.19% for cases A, B, and C within a reasonable amount of time.

A hybrid approach for improving the flexibility of production scheduling in flat steel industry

Nowadays the steel market is becoming ever more competitive for European steelworks, especially as far as flat steel products are concerned. As such competition determines the price products, profit can be increased only by lowering production and commercial costs. Production yield can be significantly increased through an appropriate scheduling of the semi-manufactured products among the available sub-processes, to ensure that customers’ orders are timely completed, resources are optimally exploited, and delays are minimized. Therefore, an ever-increasing attention is paid toward production optimization through efficient scheduling strategies in the scientific and industrial communities. This paper proposes a hybrid approach to improve the flexibility of production scheduling in steelworks producing flat steel products. Such approach combines three methods holding different scopes and modelling different aspects: an auction-based multi-agent system is applied to face production uncertainties, multi-objective mixed-integer linear programming is used for global optimal scheduling of resources under steady conditions, while a continuous flow model copes with long-term production scheduling. According to the obtained simulation results, the integration and combination of these three approaches allow scheduling production in a flexible way by providing the capability to adapt to different production conditions.

Integrated stochastic optimization of stope design and long-term underground mine production scheduling

In the commonly used underground mine planning framework, mine design is first established and is the main input for the subsequent long-term mine production scheduling optimization. This sequential optimization approach cannot, therefore, capture the synergies between the involved planning steps, generating solutions that depart substantially from a global optimum. In addition, traditional underground mine planning methods for stope design and life-of-mine production scheduling are deterministic and are based on a single estimated orebody model. As a result, the uncertainty and variability in grades and material types are not incorporated into the optimization process, resulting in designs that misrepresent all high-, medium- and low-grade stoping volumes and production schedules with misleading forecasts. A two-stage stochastic integer program (SIP) for integrated optimization of stope and development network designs and an underground mine production scheduling are proposed for the sublevel open stoping mining method under grade uncertainty and variability, quantified by a set of geostatistical simulations of the mineral deposit considered. Assuming a mine is accessed through a shaft, the model defines a schedule of levels and stopes, which aims to maximize the discounted revenues, minimize development costs, and manage the risk of not meeting production targets, while satisfying geotechnical constraints. The practical aspects of the proposed method are presented through an application at an underground gold mine. A comparison with the stepwise framework, where the stope design is input to a subsequent optimization of the production schedule, shows that the proposed approach provides a physically different design and production schedule with an 11% higher net present value (NPV) and a life-of-mine that is two years shorter, affirming the advantages of the integrated optimization process.

CPS-enabled and knowledge-aided demand response strategy for sustainable manufacturing

The utilization of advanced industrial informatics, such as industrial internet of things and cyber-physical system (CPS), provides enhanced situation awareness and resource controllability, which are essential for flexible real-time production scheduling and control (SC). Regardless of the belief that applying these advanced technologies under electricity demand response can help alleviate electricity demand–supply mismatches and eventually improve manufacturing sustainability, significant barriers have to be overcome first. Particularly, most existing real-time SC strategies remain limited to short-term scheduling and are unsuitable for finding the optimal schedule under demand response scheme, where a long-term production scheduling is often required to determine the energy consumption shift from peak to off-peak hours. Moreover, SC strategies ensuring the desired production throughput under dynamic electricity pricing and uncertainties in manufacturing environment are largely lacking. In this research, a knowledge-aided real-time demand response strategy for CPS-enabled manufacturing systems is proposed to address the above challenges. A knowledge-aided analytical model is first applied to generate a long-term production schedule to aid the real-time control under demand response. In addition, a real-time optimization model is developed to reduce electricity costs for CPS-enabled manufacturing systems under uncertainties. The effectiveness of the proposed strategy is validated through the case study on a steel powder manufacturing system. The results indicate the exceptional performance of the proposed strategy as compared to other real-time SC strategies, leading to a reduction of electricity cost up to 35.6% without sacrificing the production throughput.

An Integer Mathematical Programming Model for Production Scheduling Problem in Open-Pit Mines under Grade Uncertainty and Solving Using the Firefly Algorithm

Long-term production scheduling in open-pit mines is a crucial issue in mining planning and determines the distribution of cash flow throughout the life of the mine. The purpose of the planning is to maximize the net present value by taking into account all operational constraints such as slope, mixing of different grades, mineral production, and extraction capacity. The uncertainties associated with model data play an important role in optimizing long-term production plans. Among the uncertainties, grade uncertainty plays a major role. In this paper, hybrid models are presented by the Lagrangian relaxation (LR) method, augmented Lagrangian relaxation (ALR) method, and firefly algorithm (FA) to solve the long-term production scheduling problem of open-pit mines with the assumption of deterministic and also considering the grade uncertainty. The firefly algorithm is used to update the Lagrange multipliers. The newly proposed approaches are based on optimizing Lagrangian multipliers and comparing them with the results of combined Lagrangian relaxation method and augmented Lagrangian relaxation with the Genetic Algorithm (GA), and the traditional sub-gradient (SG) method. For solving and validating the obtained model, Chadarmelo iron ore mine is considered as a suitable case study. The results of the case study show that the combined strategy (ALR-FA) can provide a near-optimal solution over other methods such that, over a given period, the net present value using the proposed hybrid approach is 20.11% higher than the traditional method is available. Also, the CPU speed of the proposed model is 4.7% more than the other methods.

A Framework for Open-Pit Mine Production Scheduling under Semi-Mobile In-Pit Crushing and Conveying Systems with the High-Angle Conveyor

In-pit crushing and conveying (IPCC) systems have drawn attention to the modern mining industry due to the numerous benefits than conventional truck-and-shovel systems. However, the implementation of the IPCC system can reduce mining flexibility and introduce additional mining sequence requirements. This paper investigates the long-term production scheduling and the crusher relocation plan of open-pit mines using a semi-mobile IPCC system and high-angle conveyor. A series of candidate high-angle conveyor locations is generated around the pit limit, with a crusher located along each conveyor line. Each conveyor location is solved independently by an integer linear programming model for making production scheduling and crushing station decisions, aiming to maximize the net present value (NPV) considering the material handling and crushing station relocation costs. The production schedule with the highest NPV and the associated conveyor and crusher location is considered the optimum or near-optimum solution.

Optimisation of long-term quarry production scheduling under geological uncertainty to supply raw materials to a cement plant

ABSTRACT The success of a cement production project depends on the supply of raw materials. Long-term quarry production scheduling (LTQPS) based on resource models is essential to maintain a consistent supply to cement plants. Geological uncertainty is inherent due to sparse exploration data in resource models and significant risk factors for not achieving production targets. This research proposes a stochastic framework for LTQPS that considers the impact of geological uncertainty on raw material supply. A clustering algorithm uses multiple simulated deposit models to aggregate blocks into mining cuts. A new stochastic mixed-integer programming model is formulated with two objectives: to minimise the cost for developing the raw mix and the risk of not meeting production targets. The proposed framework is implemented successfully in a limestone deposit in Southern Vietnam, resulting in an increase of 5 million tons (Mt) and a 30% reduction in unit cost over the deterministic mixed-integer programming model.

A mathematical model for the scheduling and definition of mining cuts in short-term mine planning

Short-term open pit planners have to deal with the task of designing a feasible production schedule. This schedule must fulfill processing, mining and operational constraints and, at the same time, maximize the profit or total metal produced. It also must comply with the long-term production schedule and must incorporate new blasthole sampling data. This task is performed with little support of optimization tools, and therefore, there is a risk of generating suboptimal results. Several approaches have been proposed in the literature to deal with these issues, either generating operational mining cuts or obtaining a mining schedule to fulfill the short-term constraints. However, an integrated approach has remained an open challenge. In this paper, we propose an optimization model to tackle the operational and scheduling issues simultaneously. The model defines the mining cut configuration and the production schedule in the short-term. It is based on representative Selective Mining Units (SMUs) as the potential locations of the mining cuts and then each SMU is assigned to one of these locations. We tested the model with a real case study, and it was able to generate mining cuts and an extraction sequence fulfilling mining, processing and operational constraints, as well as access restrictions given by the ramp location in each bench. The mining cut design captured most of the profit, and thus it can be used as a guide for the short-term mine planner. The location of the representative SMUs and the precedence definition both impact the mining cut configuration, and future research could address how to incorporate different operational considerations and strategies on the location of these representatives.

Improving performance of open-pit mine production scheduling problem under grade uncertainty by hybrid algorithms

One of the surface mining methods is open-pit mining, by which a pit is dug to extract ore or waste downwards from the earth’s surface. In the mining industry, one of the most significant difficulties is long-term production scheduling (LTPS) of the open-pit mines. Deterministic and uncertainty-based approaches are identified as the main strategies, which have been widely used to cope with this problem. Within the last few years, many researchers have highly considered a new computational type, which is less costly, i.e., meta-heuristic methods, so as to solve the mine design and production scheduling problem. Although the optimality of the final solution cannot be guaranteed, they are able to produce sufficiently good solutions with relatively less computational costs. In the present paper, two hybrid models between augmented Lagrangian relaxation (ALR) and a particle swarm optimization (PSO) and ALR and bat algorithm (BA) are suggested so that the LTPS problem is solved under the condition of grade uncertainty. It is suggested to carry out the ALR method on the LTPS problem to improve its performance and accelerate the convergence. Moreover, the Lagrangian coefficients are updated by using PSO and BA. The presented models have been compared with the outcomes of the ALR-genetic algorithm, the ALR-traditional sub-gradient method, and the conventional method without using the Lagrangian approach. The results indicated that the ALR is considered a more efficient approach which can solve a large-scale problem and make a valid solution. Hence, it is more effectual than the conventional method. Furthermore, the time and cost of computation are diminished by the proposed hybrid strategies. The CPU time using the ALR-BA method is about 7.4% higher than the ALR-PSO approach.

Barrick’s Turquoise Ridge Gold Mine Optimizes Underground Production Scheduling Operations

Mining operations determine a long-term production schedule, often to maximize net present value. For a time horizon of between years and decades, optimization models seek the extraction times—with monthly or yearly fidelity—of three-dimensional, notional blocks of ore and waste within a deposit to satisfy spatial precedence constraints, as well as resource constraints on the amount of material extracted and sent to the mill. With algorithmic advances, as well as those in mine planning software and in hardware, we are able to solve instances with a decade-long horizon at daily fidelity. The resulting objective, repeatable, and defensible schedules inform production and maintenance supervisory decisions based on resource availability, that is, loaders, shovels, haul trucks, and mineral processors. We implement our solutions at the Turquoise Ridge underground gold mine in Nevada, United States. These solutions indicate more than a 2% increase in total ounces extracted over a decade while decreasing development footage by as much as 11% over the same time horizon. Furthermore, we are able to incorporate rules governing a shared resource and to evaluate binding versus nonbinding capacity constraints.

A New Mathematical Model for Production Scheduling in Sub-level Caving Mining Method

Production scheduling in underground mines is still a manual process, and achieving a truly optimal result through manual scheduling is impossible due to the complexity of the scheduling problems. Among the underground mining methods, sub-level caving is a common mining method with a high production rate for hard rock mining. There are limited studies about long-term production scheduling in the sub-level caving method. In this work, for sub-level caving production scheduling optimization, a new mathematical model with the objective of net present value (NPV) maximization is developed. The general technical and operational constraints of the sub-level caving method such as opening and developments, production capacity, sub-level mining geometry, and ore access are considered in this model. Prior to the application of the scheduling model, the block model is processed to remove the unnecessary blocks. For this purpose, the floating stope algorithm is applied in order to determine the ultimate mine boundary and reduce the number of blocks that consequently reduces the running time of the model. The model is applied to a bauxite mine block model and the maximum NPV is determined, and then the mine development network is designed based on the optimal schedule.

A Comprehensive Study of Several Meta-Heuristic Algorithms for Open-Pit Mine Production Scheduling Problem Considering Grade Uncertainty

It is significant to discover a global optimization in the problems dealing with large dimensional scales to increase the quality of decision-making in the mining operation. It has been broadly confirmed that the long-term production scheduling (LTPS) problem performs a main role in mining projects to develop the performance regarding the obtainability of constraints, while maximizing the whole profits of the project in a specific period. There is a requirement for improving the scheduling methodologies to get a good solution since the production scheduling problems are non-deterministic polynomial-time hard. The current paper introduces the hybrid models so as to solve the LTPS problem under the condition of grade uncertainty with the contribution of Lagrangian relaxation (LR), particle swarm optimization (PSO), firefly algorithm (FA), and bat algorithm (BA). In fact, the LTPS problem is solved under the condition of grade uncertainty. It is proposed to use the LR technique on the LTPS problem and develop its performance, speeding up the convergence. Furthermore, PSO, FA, and BA are projected to bring up-to-date the Lagrangian multipliers. The consequences of the case study specifies that the LR method is more influential than the traditional linearization method to clarify the large-scale problem and make an acceptable solution. The results obtained point out that a better presentation is gained by LR–FA in comparison with LR-PSO, LR-BA, LR-Genetic Algorithm (GA), and traditional methods in terms of the summation net present value. Moreover, the CPU time by the LR-FA method is approximately 16.2% upper than the other methods.

An optimisation approach for uncertainty-based long-term production scheduling in open-pit mines using meta-heuristic algorithms

ABSTRACT In mines planning, the long-term production scheduling problem (LTPSP) in open-pit mines is considered as a significant issue. It also specifies the distribution of cash flow during the course of the mine-life. Actually, LTPSP is a large-scale optimisation problem including large data-sets, multiple constraints, and uncertainty in the input factors that, has to be solved in a reasonable time. LTPSP, despite the valuable efforts of researchers, has not yet been well resolved. In this paper, hybrid models have been offered by the Lagrangian relaxation (LR) method with meta-heuristic methods, bat algorithm and particle swarm optimisation for solving the LTPSP due to the deterministic assumption and concerning the grade uncertainty. To bring update the Lagrange multipliers, the meta-heuristic algorithms have been applied. In terms of cumulative net present value, average ore grade, and computational time in a 12-year production period, the consequences achieved from the case studies point out that a solution close to optimisation can be presented by the LR-bat algorithm hybrid strategy in comparison with other methods. The results analysis has shown that the proposed method produces a near-optimal solution with a rational time that can be a good suggestion for utilising in the mining industry.

Application of an improved Lagrangian relaxation approach in the constrained long-term production scheduling problem under grade uncertainty

In open-pit mines, the long-term production scheduling (LTPS) problem is a mixed-integer programming problem and is considered as a class of NP-hard problems that has to be solved in a reasonably small time owing to the operational requirements. The LTPS problem cannot be considered a well-solved problem. The current article presents hybrid models to elucidate the LTPS problem regarding grade uncertainty with the involvement of Lagrangian relaxation and augmented Lagrangian relaxation (ALR) with metaheuristic methods, firefly algorithm (FA) and bat algorithm. The results demonstrate that the ALR-FA has the best results in terms of net present value, average ore grade and computational time, and it is significantly better than the conventional method. Finally, analysis of the results shows that the proposed method generates a near-optimal solution within a reasonable time; thus, it could be a good proposition for use in the industry.

A practical, long-term production scheduling model in open pit mines using integer linear programming

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, an alternative integer linear programming (ILP) formulation is presented for long-term production scheduling that reduced the number of active benches in any scheduling period. Numerical results of the proposed model on a small-scale open pit gold mine show a 34% reduction in the average number of working benches in a given scheduling period. Keywords: long-term production scheduling, mathematical programming, practical plans, equipment movements.