Production scheduling under uncertainty of an open-pit mine using Lagrangian relaxation and branch-and-cut algorithm

ABSTRACT

The life-of-mine optimization of open pit mine production scheduling under geological uncertainty is a computationally intensive process. Production scheduling determines the optimal extraction sequence by maximizing net present value (NPV). In this paper, an algorithm is proposed to schedule an open pit mine under geological uncertainty, where instead of solving the whole problem at once, the production schedule is generated by sequentially solving sub-problems. The sub-gradient method is used to generate the upper bound solution of a Lagrangian relaxed sub-problem. If the upper bound relaxed solution is infeasible, a mixed integer programming is applied to the latter solution. The algorithm is validated by solving six problems and is compared to the linear relaxation of the original production scheduling problem. The results show that the proposed algorithm generates a solution that is very close to optimal, with less than a 3% optimality gap. An application at a copper mine, where geological uncertainty is quantified with geostatistical simulations of the related orebody, shows that all constraints are satisfied and an 11% higher NPV is generated when compared to the corresponding deterministic equivalent of the proposed approach, while a 26% higher NPV is generated compared to a common conventional industry approach.     

Conditional simulation algorithms for modelling orebody uncertainty in open pit optimisation

Abstract

Conditional simulation is a class of Monte Carlo techniques that can be used to generate equally probable representations of in-situ orebody variability. Contrary to the traditional smooth orebody models, conditionally simulated orebodies provide the tools to quantify uncertainty in grade variability and the resulting effects on various aspects of open pit design and planning. This paper outlines a general framework for modelling uncertainty and assessing geological risk, presents currently used geostatistical simulation algorithms, and presents examples.     

A Variational Approach to Video Registration with Subspace Constraints

This paper addresses the problem of non-rigid video registration, or the computation of optical flow from a reference frame to each of the subsequent images in a sequence, when the camera views deformable objects. We exploit the high correlation between 2D trajectories of different points on the same non-rigid surface by assuming that the displacement of any point throughout the sequence can be expressed in a compact way as a linear combination of a low-rank motion basis. This subspace constraint effectively acts as a trajectory regularization term leading to temporally consistent optical flow. We formulate it as a robust soft constraint within a variational framework by penalizing flow fields that lie outside the low-rank manifold. The resulting energy functional can be decoupled into the optimization of the brightness constancy and spatial regularization terms, leading to an efficient optimization scheme. Additionally, we propose a novel optimization scheme for the case of vector valued images, based on the dualization of the data term. This allows us to extend our approach to deal with colour images which results in significant improvements on the registration results. Finally, we provide a new benchmark dataset, based on motion capture data of a flag waving in the wind, with dense ground truth optical flow for evaluation of multi-frame optical flow algorithms for non-rigid surfaces. Our experiments show that our proposed approach outperforms state of the art optical flow and dense non-rigid registration algorithms.     

Recoverable Reserves and Support Effects when Optimizing Open Pit Mine Designs

Orebody modelling, support effects and the estimation of recoverable reserves are key parts of open pit optimization studies. A case study is presented on the estimation of recoverable reserves using an implementation of indicator kriging where metal quantity is used to select cutoffs, and support corrections founded on a conditional simulation approach. Mining selectivity is explored in the subsequent optimization study to compare results from indicator kriging of grade estimates on a regular size blocks and indicator kriging estimates on small size blocks. The use of indictor kriging models adjusted for a given selectivity and the use of grade proportions in each block for the optimization study, provide a presentation of the expected ore recovery for a predefined level of selectivity. The case study shows that indicator kriging estimation with full accounting of block grade distributions generates substantially better results in the pit optimization study. In addition, the adverse effects of small blocks and over-smoothing on optimization results are illustrated.     

Pressure support ventilation in adult respiratory distress syndrome: short-term effects of a servocontrolled mode

PURPOSE: To assess the short-term effects of pressure support ventilation in adult respiratory distress syndrome (ARDS), we studied 17 patients with moderate to severe ARDS using mandatory rate ventilation (MRV), a servocontrolled mode of PSV having respiratory rate as the targeted parameter. MATERIALS AND METHODS: Based on the duration of ARDS, the patients were divided into two groups: Group 1, early ARDS (duration up to 1 week), 10 patients; Group 2, intermediate ARDS (duration between 1 and 2 weeks). The patients were initially ventilated with assisted mechanical ventilation then with MRV, and finally with controlled mechanical ventilation. After a 20-minute period allowed for stabilization in each mode, ventilatory variables, gas exchange, hemodynamics, and patient's inspiratory effort were evaluated. RESULTS: During MRV blood gases, airway pressures and hemodynamic variables remained within acceptable limits in all patients. Compared with assisted mechanical ventilation, during MRV, patients of group 1 decreased their VT and V (from 0.64 +/- 0.04 to 0.42 +/- 0.03 L/sec) and increased their TI/TT (from 0.39 +/- 0.03 to 0.52 +/- 0.03). f did not change. PAO2 - PaO2 and QS/QT decreased (from 306 +/- 16 to 269 +/- 15 mm Hg, and from 20.2 +/- 1.4 to 17.5 +/- 1.1, respectively), while PaCO2 increased (from 44 +/- 3 to 50 +/- 3 mm Hg). On the contrary, patients of group 2 increased their VT (from 0.69 +/- 0.02 to 0.92 +/- 0.09 L), decreased their f (from 22.3 +/- 0.5 to 19.3 +/- 0.3 b/min), although they did not change their V and TI/TT. PAO2 - PaO2 and QS/QT remained stable. PaCO2 diminished (from 39 +/- 3 to 34 +/- 3 mm Hg). Pressure support level was higher in group 2 than in group 1 (29.4 +/- 3.0 v 19.8 +/- 2.9 cm H2O). CONCLUSIONS: We conclude that (1) PSV delivered by MRV may adequately ventilate patients with moderate to severe ARDS, preserving gas exchange and hemodynamics, at least for the short period tested; (2) early and intermediate ARDS respond in a different manner to MRV in terms of breathing pattern, gas exchange, and level of pressure assistance; and (3) patients with early ARDS are those who have an improvement in intrapulmonary oxygenation probably due, at least in part, to alveolar recruitment augmented by active diaphragmatic contraction.     

Reliability life-testing and failure-analysis of GaAs monolithicKu-band driver amplifiers

`Gallium-arsenide monolithic microwave integrated-circuit (MMIC) Ku-band driver amplifiers were life tested under accelerated high temperature, DC and RF conditions until failure. These MMIC are used in various applications such as radar and satellite communication systems. The failure mechanisms controlling their reliability must be understood in order to improve the lifetime for these and other applications. This paper discusses the experimental procedures, statistical evaluation of the data and failure analysis of the devices. To the authors' knowledge, this is the first report of RF life testing of dual-gate driver amplifiers. The majority of the devices failed catastrophically due to high drain current, while others failed parametrically due to low output power. Failure analysis indicates that degradation of the Si₃N₄ dielectric layer to be the main failure mechanism in these MMIC. Statistical analysis revealed an activation energy of 0.87 eV and a median lifetime of 5.8·10⁴ hours at 140°C channel temperature, which is consistent with surface-phenomena failure mechanisms     

GaAs MMIC reliability studies

Three types of GaAs monolithic microwave integrated circuits (MMICs) were RF high temperature accelerated life tested to determine the median time before failure (MTBF). Life testing was performed under the d.c. bias conditions and RF input power levels the MMICs would be expected to use under actual operating conditions. the accelleration condition was to raise the base-plate temperature high enough to result in degradation in approximately 1000 hours at the highest test temperature. Because the MMICs were designed for power applications, the input signal level was large enough to cause approximately 1 dB compression. Device failure was defined as a 20 per cent decrease in output power as measured at 125°C, or room temperature when the temperature control system was turned off. Under these conditions the MTBF extrapolated to a channel temperature of 125°C varied between 8 × 10³ hours and 2 × 10⁵ hours depending on the MMIC type. The primary failure mode appeared to be surface leakage currents under the passivation layer.     

A matheuristic approach for optimizing mineral value chains under uncertainty

Optimization and Engineering - Mineral value chains, also known as mining complexes, involve mining, processing, stockpiling, waste management and transportation activities. Their optimization is...     

Incorporating geological and equipment performance uncertainty while optimising short-term mine production schedules

ABSTRACT

Short-term production scheduling in open pit mining consists of defining the extraction sequence and process allocation of mineralised material over time-scales of either months, weeks, or days. An effective short-term production schedule ensures compliance with the production targets and restrictions imposed by the long-term plan. The method proposed herein outlines a new approach to simultaneously optimise the short-term production sequence with the mobile equipment allocation plan while incorporating both material grade and equipment performance uncertainty. A new simulation methodology is introduced to generate more realistic equipment performance scenarios, as well as a new concept of including ramp positions in the formulation to efficiently facilitate minable extraction patterns. This short-term model is bench-marked against a conventional design at one of the largest copper mines in the world, and the results show improved production target compliance by delivering more consistent ore quantity and quality to each processing destination, and a physical extraction sequence that has a greater likelihood of being realised in the face of equipment performance and truck cycle time uncertainty.