Optimizing open-pit block scheduling with exposed ore reserve

Abstract

Open pit mines are characterized by high production levels and low operational costs compared to other exploitation methods. Unfortunately, when using this technique, material with poor economic value (waste) usually has to be removed to give access to more economically profitable material. Each block is characterized by its metal content, density, lithology, and other relevant attributes that are derived by using estimation techniques specifically designed to deal with the spatial nature of the mineralization. The value of a mine plan is thus determined by the value contained in the blocks that are extracted at certain periods and has a clear dependency on the block schedule, the order in which the material is extracted and processed.Generally speaking, different problems are usually considered by mining planners for the economic valuation, design, and planning of open-pit mines, as pointed out by Hustrulid and Kuchta (2006); for example, the 'final pit problem', also called the 'ultimate pit limit problem', which aims to find the region of maximal undiscounted economic value for exploitation under certain geotechnical stability constraints. Another example is known as the open pit production scheduling problem, which aims to find an optimal sequence of extraction in a certain finite time horizon with bounded capacities (for example, extraction and processing) at each period and where the usual optimality criterion is the total discounted profit. A common practice for the formulation of these problems consists of describing an ore reserve via the construction of a three-dimensional block model from the orebody with each block corresponding to the basic volume of extraction, characterized by several geological and economic properties that are estimated from sample data. For this reason, the open pit production scheduling problem is also known as the block scheduling problem. Block models can be represented as directed graphs where nodes are associated with blocks, while arcs correspond to the precedence of these blocks, induced by physical and operational requirements derived from the geomechanics of slope stability. This discrete approach gives rise to huge combinatorial problems, the mathematical formulations of which are special large-scale instances of integer programming (IP) optimization problems; see for instance Caccetta (2007). Precedence between blocks is one of the most important sets of constraints, as the extraction process proceeds from surface down to the bottom of the mineralization. This idea applies to every block in the model: it is not possible to access a given block in a certain time unless the blocks that are above have already been extracted, because stability of the pit walls Optimizing open-pit block scheduling with exposed ore reserve by J. Saavedra-Rosas*, E. Je lvez † , J. Amaya ‡ , and N. Morales † A crucial problem in the open pit mining industry is to determine the optimal block scheduling, defining how the orebody will be sequenced for exploitation. An orebody is often comprised ...

Advanced mine optimisation under uncertainty using evolution

“…In the following, we describe a basic model of the open pit scheduling problem similar to the one given in [20] and it should be noted that the actual implementation might require the consideration of additional constraints and/or variations of the objective function. A block model is given by a set of blocks B and a set of destinations D. Each block i ∈ B has a certain number of parameters such as density, tonnage, ore grade, etc.…”

Methodological approach to creation of the 3D model of an oval-shaped open pit mine

“…The scientific work [14] presents an integer programming (IP) model that generates open pit projects in accordance with the requirements of the ore reserve, as an extension of the classical optimization models for planning of mining. A set of new binary variables is introduced for this purpose, representing blocks that can be taken as an open ore reserve, in addition to mining and processing decisions.…”

Application of optimized models through direct block scheduling in traditional mine planning

“…Jélvez et al (2016) used heuristics based on incremental and aggregation approaches to solve the problem. Saavedra-Rosas et al (2016) developed a block scheduling technique for an exposed ore reserve. Morales and Reyes (2016) proposed an approach that takes the mining system into account to solve mine scheduling issues related to short-term planning.…”