2053 term plan is then divided into distinct stages, called pushbacks. Each pushback is then executed using the short-term schedules. A visual schematic of mine planning processes is presented in Figure 1. Figure 1 – Schematic representation of an open-pit mine planning process One of the fundamental methods widely adopted by the industry is the Lerchs-Grossman algorithm, developed in 1965, used to define the ultimate pit limit based on graph theory (Lerchs and Grossman 1965). The technique relies on the definition of the economic value of the constituent blocks comprising the orebody model, which are then classified as economically feasible to extract or to be discarded as waste. Given the reliance of the technique on geological knowledge of the mineralogy of the deposit, the underlying geostatistical model used to spatially predict the composition of the deposit from the borehole data is fundamental to the economic success of the mining operation. The main drawback of the traditional planning approach is its initial assumption of perfect knowledge of the deposit based on the conducted modelling stage. In reality, popular estimation techniques, such as ordinary kriging, produce overly smooth models that fail to capture the in-situ variability of the deposit (Smith and Dimitrakopoulos 1999). The lack of acknowledgement of uncertain variables can be detrimental in other areas as well. For example, developing a rigid cut-off grade (CoG) policy that fails to address fluctuations in the price of extracted commodities can pose significant economic risk to the operation (Muttaqin, Ciptomulyono, and Siswanto 2025). To address the issues of uncertain parameters in a highly variable and dynamic mine environment, stochastic mine planning and scheduling techniques have been developed. These solutions rely on multiple equally probable realizations of the orebody utilized to quantify the probability functions associated with geological variables of interest, such as grade, and optimize production schedules. This approach was pioneered by Dimitrakopoulos and Ramazan (2004) in a long-term planning of single open pit mines, and extended over the years to address mining complexes (Goodfellow and Dimitrakopoulos 2016). Since then, multiple applications of these formulations have been developed, some of which are discussed in more detail in this work. Regardless of the chosen optimization method, the primary objective of the mine planning and scheduling process is to ensure the operation is economically viable and provides a financial return to the stakeholders of the company. In order to fulfill this goal, modern methodologies focus on maximizing the net present value (NPV) of the project, often including other economic evaluation parameters such as conditional value at risk (CVaR) or discounted cash flow (DCF). However, focusing exclusively on economic measures ignores the potential to address other aspects of the mine planning process, such as the social and environmental impact that mining operations exert on the local populations and ecosystems. Despite the fact that, depending on legislative frameworks in place, these issues need to be taken into account to comply with legal requirements, the inclusion of said aspects often comes as an afterthought (Aghdamigargari et al. 2024). For example, Burgher and Erickson (1984) point out that the maximization of NPV as a primary goal, coupled with high discount rates, delays reclamation efforts, as postponing such operations effectively discounts their cost from a perspective of the life-of-mine plan. Conversely, developing an extraction sequence that actively addresses the quantity and characteristics of extracted waste can significantly decrease the environmental impact and decrease the reclamation cost, ultimately leading to a more robust solution (Levinson and Dimitrakopoulos 2024). Additionally, expressing active interest in the more sustainable development of mining projects may, in turn, result in less public opposition to individual operations and the sector as a whole. This work aims to highlight recent developments in the field of sustainable stochastic mine planning and pinpoint promising areas in which these types of techniques can prove themselves useful in the future.
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