Long-term Production Scheduling Research Articles

A Set of Classified Integer Programming (IP) Models for Optimum Transition from Open Pit to Underground Mining Methods

During the last few decades, open pit mines have been deepened to the remote depths of the ground such that removing great volumes of waste rocks may jeopardize their profitability. In such circumstances, an early transition from open pit to underground mining may prove more profitable. This is the case in many large-scale open pit mines, where considerable amount of mineral reserve remains beneath the pit bottom. This paper develops a set of classified integer programming models for determining an optimum transition depth (OTD) between open pit and various underground mining methods. The models lie within the scope of long-term production scheduling because the OTD is revealed through scheduling of all mineral reserve. To provide a quantitative analysis, two optimization models with distinct solution strategies are executed on a three-dimensional sector of a real orebody. The results indicate that the integrated models increase the total NPV of the mining operations by up to 8.62%. However, the scenario-based models enhance the primitive solution (the base scenario) by up to 3.42%. It is also shown that the integrated models present solutions that are practically more realistic.

Simultaneous stochastic optimisation of an open-pit gold mining complex with waste management

ABSTRACTSimultaneous stochastic optimisation manages risk and capitalises on the unique interactions that occur in a mining complex, where materials are transferred between mines, processors, stockpiles, and waste facilities to achieve a marketable product. Typically, when optimising the production schedule, the primary focus is to deliver valuable products to the market. However, this tends to ignore the environmental and economic impact of simplifying waste management requirements, including the storage and disposal of waste material. Stricter regulations and engineering requirements are transforming past mining practices to develop more sustainable operations. These transformations increase the financial cost of waste management and identify the requirement to integrate waste management into the production schedule. Additionally, misrepresenting the material uncertainty and variability associated with the amount of waste produced can impact, both, the stakeholders and the profitability of a mining complex. In this case study, a simultaneous stochastic optimisation approach is applied in a gold mining complex that integrates waste management into the long-term production schedule. The resulting schedule leads to a 6% increase in the net present value when compared to a conventional approach, while minimising the likelihood of deviating from production targets and ensuring permit constraints are satisfied.

Open pit mine production schedule optimization using a hybrid of maximum-flow and genetic algorithms

Production scheduling is a critical activity for the long-term production planning of open pit mining operations. It deals with the effective management of resources and maximizes cash flows to generate higher profits over the life of a mine. Production scheduling problems determine that blocks be mined and processed over a number of periods subjected to mining and processing constraints, which makes the problem more complex. The complexity is further increased due to the uncertainty in the input parameters. In this study, the maximum flow algorithm with a genetic algorithm is used to generate the long-term production schedule. The graph structure for maximum flow is created for multiple periods under uncertainty, and the flow in the arcs is controlled by a genetic algorithm to develop a production schedule. Numerical results for realistic instances are provided to indicate the efficiency of the solutions.

A two-step approach to incorporate cut-off grade and stockpiling in oil sands mine planning optimization framework

In achieving maximum benefit in oil sands mining, the time and sequence of removing ore, dyke material and waste from the final pit limit is essential to the long-term production schedule. In-pit waste management strategy requires the simultaneous construction of dykes with the advancement of mining operations. This paper seeks to determine: (1) the time and sequence for removal of ore, dyke material and waste to maximize Net Present Value (NPV); (2) the quantity of dyke material required for dyke construction to minimize construction costs; and (3) the impacts of stockpiling and stockpile reclamation with limited time duration. An Integrated Cut-Off Grade Optimization (ICOGO) model was used to generate an optimum cut-off grade policy and a schedule for mining ore and waste, as well as overburden, interburden and tailings coarse sand dyke materials in long-term production planning. Subsequently, a 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. The cut-off grade profile and schedule generated by the ICOGO model are used as guides to define the grade constraints and production goals required by the MILGP model. The developed models feature stockpiling with limited duration for long-term production scheduling. The models were applied to an oil sands case study to maximize the NPV of the operation. In comparison, whereas the ICOGO model solved the optimization problem faster, the MILGP model results provided detailed mining-cut extraction sequencing for practical mining.

A Clustering Algorithm for Block-Cave Production Scheduling

Production scheduling is one of the most important steps in the block-caving design process. Optimum production scheduling could add significant value to a mining project. The goal of long-term mine production scheduling is to determine the mining sequence, which optimizes the company’s strategic objectives while honouring the operational limitations over the mine life. Mathematical programming with exact solution methods is considered a practical tool to model block-caving production scheduling problems; this tool makes it possible to search for the optimum values while considering all of the constraints involved in the operation. This kind of model seeks to account for real-world conditions and must respond to all practical problems which extraction procedures face. Consequently, the number of subjected constraints is considerable and has tighter boundaries, solving the model is not possible or requires a lot of time. It is thus crucial to reduce the size of the problem meaningfully by using techniques which ensure that the absolute solution has less deviation from the original model. This paper presents a clustering algorithm to reduce the size of the large-scale models in order to solve the problem in a reasonable time. The results show a significant reduction in the size of the model and CPU time. Application and comparison of the production schedule based on the draw control system with the clustering technique is presented using 2,487 drawpoints to be extracted over 32 years.

In-situ coal quality variability analysis by combining Gaussian co-simulation and a JavaScript

ABSTRACTThis study covers an in-situ analysis of simulated coal quality attribute variations of a power plant in Tufanbeyli/Adana, Turkey. Three main coal quality variables including calorific value, sulfur and ash content were simulated by Sequential Gaussian co-simulation method. The results were validated by a number of tests. A this-study-specific JavaScript is written to reveal the variations of coal qualities in a specific extraction route and capacity for both short and long-term production planning and scheduling. Results declared that the JavaScript successfully reflected the simulated variations in the candidate route and very adaptable to similar studies easily.

Long-Term Service Agreement in Electricity Supply Chain with Renewable Energy Penetration

Problem Definition: We study a long-term service agreement (LTSA) between an OEM of conventional power generators and a power plant operator (utility firm) in the electricity supply chain. The OEM offers maintenance based on the LTSA which specifies the service fee and the maintenance interval. The utility firm dynamically chooses among different resources (conventional, renewable, or emergency) to meet energy demand. Academic/Practical Relevance: Although being widely used in power systems, LTSA has not been studied in the OM literature. Different from traditional supply chain contracts, LTSA contracts on a generator’s long-term production schedule (i.e., usage time and number of starts). A good understanding of LTSA provides guidance on how to design such a complex contract. Methodology: We use game theory to model the LTSA between the OEM and the utility firm and use dynamic programming to study the utility firm’s power generation decision. Results: We first characterize that the conventional generator’s optimal operating mode (i.e., on or off) follows a two-threshold policy which shows a hysteresis phenomenon. Then the optimal output from different resources can be obtained by minimizing the utility firm’s cost of the current period. We show that the OEM’s optimal LTSA design on the maintenance interval and service fee can be solved sequentially, and capture the OEM’s tradeoff between the service margin and the usage of conventional generator. Managerial Implications: We find that the OEM does not have incentives to significantly reduce the maintenance cost of a generator start, while both OEM and utility firm prefer greater generator flexibility. While overall availability of renewable output is important, renewable source characteristics such as autocorrelation and variation do not have a significant impact on the equilibrium outcomes. By incorporating the number of starts into the contract, LTSA is effective in preventing the utility firm from frequently cycling the equipment.

The Rise of 3D Seismic in Hardrock Mineral Exploration

3D seismic has been a cornerstone of the coal and petroleum industries for decades. And yet, its adoption by the hardrock minerals industry has been much slower. This delay has many causes, with the most obvious being the sheer complexity of acquiring and processing seismic data in a hardrock setting. Fortunately, this topic is the subject of much ongoing research.A less obvious cause is the limitations of the available software for visualising and interpreting the processed data. Hardrock miners have long enjoyed the flexibility of general mining packages (GMPs) for displaying, analysing, and modelling everything from first-pass geochemical sampling to optimised long-term production scheduling. But these applications are optimised towards massive numbers of drillholes, block (voxel) models, and triangulations, and they perform poorly when asked to display 3D seismic. The result is a massive file, with a long loading time and slow graphics interaction. On the other hand, petroleum software is optimised towards seismic data, but can’t handle massive numbers of drillholes.These limitations can be overcome by incorporating modern gaming graphics technology and efficient file storage platforms within an application, and this presentation concludes by illustrating the results of applied research and development carried out at MICROMINE towards producing a fluid real-time seismic visualisation environment.

Optimizing a mineral value chain with market uncertainty using benders decomposition

A Benders decomposition-based method is developed to simultaneously optimize upstream and downstream operations of a mineral value chain. In each iteration of the proposed method, the mineral value chain optimization model is decomposed to a master problem that only includes the variables that determine the upstream mine production schedule, and a subproblem that includes all other variables that define the downstream material flow and processing plan. In order to reduce the master problem in each iteration, mining blocks representing mineral deposits are dynamically aggregated based on the dual solution of the subproblem. The production schedule obtained based on the aggregated scheduling units is then improved through a moving-window amelioration method. By observing the results of a series of numerical tests, we show that the proposed method efficiently optimizes a mineral value chain by synchronizing the upstream mine production scheduling as well as the downstream material flow and process planning. The numerical tests also show that ignoring market uncertainty results in profits being underestimated because of the underestimated value of low-grade material. To adapt to market uncertainty, the stochastic optimizer suggests greater investment to increase capacity in the processing plant and a different long-term mine production schedule.

Comparison between the application of the conventional mine planning and of the direct block scheduling on an open pit mine Project

Abstract Historically, since the 60's, traditional mine planning consists of several distinct stages: 1) Definition of the ultimate pit - the portion of the blocks that results in the greatest total value; 2) Pushback selection - based on the generation of nested pits, obtained with the change in the value of the ore price; 3) Long-term production scheduling. Although considered quite satisfactory, this methodology presents some flaws: The stages, even if considered individually optimal, may not be when put together. The opportunity cost is not considered and the cut-off is fixed. Due to the recent computational advances, a new technique has been growing and is more reliable: the direct block sequencing. In this methodology, the steps are consolidated into only one process, improving the economic results, reducing the total execution time and obtaining, in fact, an optimal planning. The aim of this work is to compare the results of the two planning methods applied in a database of a Brazilian iron ore mine and to show the real advantages and disadvantages of each one. To solve the direct block sequencing technique, Doppler was used, a tool developed by Delphos Mine Planning Laboratory, located at the University of Chile. The traditional methodology was executed through Whittle software. Lastly, a medium-term scheduling was performed using Deswik software.

Long-term production scheduling of open pit mines using particle swarm and bat algorithms under grade uncertainty

Long-term production scheduling of open pit mines using particle swarm and bat algorithms under grade uncertainty

Risk management and long-term production schedule optimization at the LabMag iron ore deposit in Labrador, Canada

Risk management and long-term production schedule optimization at the LabMag iron ore deposit in Labrador, Canada

Modelling geological variability in the LabMag iron ore deposit and effects on the long-term production schedule

In this study, a set of geological simulations of the LabMag iron ore deposit in Labrador, Canada, is generated in order to quantify the geological risk in a pre-existing life of mine production schedule. The approach employs, firstly, min/max autocorrelation factors with missing data that allows for the joint geostatistical simulation of spatially correlated variables of interest for large-scale deposits such as LabMag. The seven structural layers of the deposit are simulated with the layer thicknesses acting as the set of correlated variables of interest. Secondly, four correlated geochemical properties within each domain (layer) are simulated. The simulated scenarios of LabMag represent the uncertainty of the deposit’s attributes of interest and are subsequently utilised to quantify and assess the risk of an existing mine plan, in terms of meeting production targets and generating the cash flows expected. The LabMag mine plan assessed by quantifying risk in its production forecasts is based on a single conventional (deterministic) deposit model.

Long term planning and hedging for a lignocellulosic biorefinery in a carbon constrained world

While bioethanol has become a promising candidate for replacing fossil based transportation fuels, its economic feasibility still eludes industry investors. In particular, uncertainties exist in both production processes and associated markets. Hence, it is critical to develop process technology and strategize the operation and hedging decisions that improve financial viability. This paper considers long-term production scheduling under the impact of carbon tax constraints and ethanol spot price uncertainty, as well as risk management via ethanol swap contracts. More specifically, a framework consisting of a two-stage stochastic program and a two-factor time series model is presented to determine the weekly production rate and swap portfolios to maximize the process profit under spot price uncertainty.

APPLICATION OF OPERATIONS RESEARCH IN OPEN PIT MINE PLANNING AND A CASE STUDY IN SINQUYEN COPPER DEPOSIT, VIETNAM

Operations research has been applied to open pit mine planning since 1960s. This approach has proved its ability in optimising mine planning problems, including long-term and shortterm production scheduling, ultimate pit limit, mine design and mining equipment dispatching. In this paper, we review the history and methodology of applying operations research in long-term production scheduling and a case study in Sin Quyen copper deposit, Vietnam.

A hybrid augmented Lagrangian multiplier method for the open pit mines long-term production scheduling problem optimization

To improve the quality of decision making in the mining operation, it is essential to find global optimum in problems with large dimensional scales. It is widely accepted that Long-term production scheduling (LTPS) problem is playing key role in mining projects to improve their performance by considering availability constraints while maximizing the project total profits during the period. Since production scheduling problems are NP-hard, there is need of improving scheduling methodologies to get good solution. This paper presents a hybrid model between augmented Lagrangian relaxation (ALR) and Genetic algorithm (GA) to solve the LTPS problem. We propose to apply the ALR method on the LTPS problem which to improve its performance speeding up the convergence and also, GA is used to update the Lagrangian multipliers. The results from case study show that the ALR method is effective in solving large-scale problem and generation a feasible solution then the traditional linearization method. Furthermore, the proposed hybrid strategy based on GA showed better performance in comparison to the available methods.

Stochastic optimization of mine production scheduling with uncertain ore/metal/waste supply

Optimization of long-term mine production scheduling in open pit mines deals with the management of cash flows, typically in the order of hundreds of millions of dollars. Conventional mine scheduling utilizes optimization methods that are not capable of accounting for inherent technical uncertainties such as uncertainty in the expected ore/metal supply from the underground, acknowledged to be the most critical factor. To integrate ore/metal uncertainty into the optimization of mine production scheduling a stochastic integer programming (SIP) formulation is tested at a copper deposit. The stochastic solution maximizes the economic value of a project and minimizes deviations from production targets in the presence of ore/metal uncertainty. Unlike the conventional approach, the SIP model accounts and manages risk in ore supply, leading to a mine production schedule with a 29% higher net present value than the schedule obtained from the conventional, industry-standard optimization approach, thus contributing to improving the management and sustainable utilization of mineral resources.

A multi-step approach for block-cave production scheduling optimization

Production schedules that provide optimal operating strategies while meeting practical, technical, and environmental constraints are an inseparable part of mining operations. Relying only on manual planning methods or computer software based on heuristic algorithms will lead to mine schedules that are not the optimal global solution. Mathematical mine planning models have been proved to be very effective in supporting decisions on sequencing the extraction of material in mines. The objective of this paper is to develop a practical optimization framework for caving operations’ production scheduling. To overcome the size problem of mathematical programming models and to generate a robust practical near-optimal schedule, a multi-step method for long-term production scheduling of block caving is presented. A mixed-integer linear programming (MILP) formulation is used for each step. The formulations are developed, implemented, and verified in the TOMLAB/CPLEX environment. The production scheduler aims to maximize the net present value of the mining operation while the mine planner has control over defined constraints. Application and comparison of the models for production scheduling using 298 drawpoints over 15 periods are presented.

Stochastic long-term production scheduling of iron ore deposits: Integrating joint multi-element geological uncertainty

Meeting production targets in terms of ore quantity and quality is critical for a successful mining operation. In-situ grade variability and uncertainty about the spatial distribution of ore and quality parameter cause both deviations from production targets and general financial deficits. A stochastic integer programming formulation (SIP) is developed herein to integrate geological uncertainty described by sets of equally possible scenarios of the unknown orebody. The SIP formulation accounts not only for discounted cashflows and deviations from production targets, discounts geological risk, while accounting for practical mining. Application at an iron ore deposit in Western Australia shows the ability of the approach to control a risk of deviating from production targets over time. Comparison shows that the stochastically generated mine plan exhibits less risk in deviating from quality targets than the traditional mine planning approach based on a single interpolated orebody model.

A lexicographic approach to bi-objective scheduling of single-period orders in make-to-order manufacturing

This paper presents a lexicographic approach and integer programming formulations for a dual-objective, long-term production scheduling in make-to-order manufacturing environment. The problem objective is to assign single-period customer orders for various product types to planning periods to complete all the orders with minimum number of tardy orders as a primary criterion and to level the aggregate production or the total capacity utilization over a planning horizon as a secondary criterion. Each order must be completed during one planning period. The basic integer programming formulation has been strengthened by the addition of some cutting constraints derived by relating the demand on required capacity to available capacity for each subset of orders with the same due date. The approach has been applied to optimize production schedules in a flexible flowshop made up of several processing stages in series, with identical, parallel machines, and an output buffer of limited capacity for holding completed products before delivery to the customers. Numerical examples modeled after a real-world make-to-order flexible assembly line in the electronics industry are provided and some computational results are reported.