Probabilistic practical optimization of production schedulling for multi-element deposits

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Optimization of production schedules in open pit mines is important for managing cash flows. The risk of not meeting planned production targets is a critical aspect of optimization, however, it is not accounted for by traditional schedulling methods. This paper describes a new, probabilistic, mixed integer programming (MIP) formulation. The formulation has been developed so as to minimize the risk of not achieving planned production targets, both ore feed for the mill and metal production, while aiming to maximize the total discounted economic value. In addition, the new MIP formulation minimizes the movement of excavators and accommodates equipment access.
In the proposed formulation, a probability is assigned to each ore block under consideration. This represents the desirability of the particular block being mined in a given period and expresses the chance that a block will contain the desired quality and quantity of ore, ore grades above given cutoffs, quantity of metal, and deleterious elements being within required ranges. The probability is calculated from jointly simulated geostatistical models representing the pertinent attributes of the mineral deposit under consideration. The probability is multiplied by the economic value, which is referred to as probabilistic value in the objective function of the schedulling formulation.
The orebody risk discounting concept is also implemented to manage the risk distribution over production periods. Due to the orebody risk discounting effect, the low-grade and high-risk areas of the deposit will be scheduled for later periods of production. In addition, the proposed model considers the smoothness of the schedules internally during the optimization process. A smooth schedulling pattern is defined as the pattern generated by assigning the same periods to several blocks that are adjacent to each other so as to minimize the movement of equipment during mining operations.
A case study is carried out using a multi-element nickel laterite orebody characterized by seven attributes: Ni, Co, Mg, and Al grades, volume of per cent rock, and the thicknesses of two layers (LS and RS). The seven attributes are simulated using a joint conditional simulation method on a dense grid of nodes. For the purpose of schedulling, the deposit is represented by 2,030 blocks, 40 by 40 m2, along east-west and north-south directions. The figure summarizes the comparison of the proposed probabilistic schedule (PS) with the traditional schedule (TS). It shows average deviations per mining period from expected optimal ore production targets (bars), and the probability of deviations in ore production per mining period (lines), each with respect to the 35 jointly simulated orebody models. In the first year, the TS model has a 91% chance of deviating by around 383,000 t on average.  However, the PS model has only a 57% chance of deviating by only about 85,000 t on average. Furthermore, in the second period, the PS has only a 34% chance of deviating by around 91,000 t, while the TS has a 74% chance of deviating by almost 270,000 t. Note that the PS model does not consider minimizing the risk of not meeting production targets for the last period. The risk in the earlier periods is considered more costly for the objective function than the risks in the later periods.
The results indicate that the proposed probabilistic method is superior to traditional optimization methods in terms of minimizing the risks of not meeting production targets and maximizing the achievable net present value (NPV) of the operation.
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This paper discusses the classification of gold ores and gold minerals, mineralogical factors affecting gold extractive metallurgy, and study procedures and techniques commonly employed in gold process mineralogy.A case study of a refractory gold ore is provided to show the need and importance of process mineralogy in gold extractive metallurgy.
From the perspective of metallurgical processing, gold ores can be classified into free-milling and refractory...
Publication: CIM Bulletin
Author(s): J. Zhou, B. Jago, C. Martin
Issue: 2
Volume: 1
Year: 2006
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The coarse particle recovery (CPR) process captures coarse particles that are not recoverable by regular flotation. Several porphyry copper operations in the world operate analogous circuits that recover non-floated copper from tailings; however, the case presented here for Minera Escondida Ltda. is unique in that extensive underlying test work has allowed the authors to elucidate some fundamental principles behind recovery enhancement.
The concept is to...
Publication: CIM Bulletin
Author(s): B.J. Huls, G.S. Hill
Issue: 2
Volume: 1
Year: 2006
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In underground mines, material handling systems rely on a network of vertical or steeply inclined ore and waste passes. The design and operation of ore pass systems is often based on past experience, which can be anecdotal and, at times, contradictory in nature. This paper provides quantifiable information on ore pass practice and performance in Quebec underground metalliferous mines. The presented field data were derived during a series of site visits in...
Publication: CIM Bulletin
Author(s): J.-F. Lessard, J. Hadjigeorgiou
Issue: 2
Volume: 1
Year: 2006
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Stereolithography is a well known rapid prototyping technique in the manufacturing sector. Essentially, it is a three-dimensional printing process that produces plastic prototype parts from standard CAD files. At present, Canadian mining companies are not fully aware of the potential of rapid prototyping techniques (RPTs) for their production and mine design systems. Mining engineers and geologists attempt to visualize and understand the characteristics and...
Publication: CIM Bulletin
Author(s): C.P. O’Connor, N. Vayenas, A. Akerman
Issue: 2
Volume: 1
Year: 2006
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Mining has several characteristics, uncommon in other business sectors, which pose additional challenges to the implementation or design of IT and management systems that use the information. Understanding these characteristics would improve the chances of successfully importing new information technology and management techniques to mineral producers. The most important characteristics that should be understood are workplace issues, the industry’s...
Publication: CIM Bulletin
Author(s): S.D. Dessureault, A.P. Schissler
Issue: 2
Volume: 1
Year: 2006
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Electric cable shovels are the most extensively used highvolume excavators in open pit mining. The design of dippers for cable shovels has essentially remained unchanged for the last 100 years. Previous work to improve the production capability of these units focused on updating mechanical and electrical components, and optimizing utilization and operational approaches. Little work has been done to improve dippers and their ground interactions. With the...
Publication: CIM Bulletin
Author(s): N. Shi, T.G. Joseph
Issue: 2
Volume: 1
Year: 2006
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