86 grade uncertainty through binary stochastic programming, integrating precedence constraints and extraction capacity constraints; however, such extensions typically entail high computational complexity and often leave out economic uncertainties (prices/costs) or other non-technical dimensions In summary, existing transition models converge toward a relatively consistent set of key decision variables: (1) economic/financial variables (costs, prices, NPV/BEV, discount rate, development investment), (2) operational variables (sequencing, period capacities, precedences, blending, delays, and continuity), (3) geotechnical and design variables (slope angle, slope stability, crown pillar location/thickness/stability, rock mass parameters), and (4) geological and metallurgical variables (grade and recovery), with some explicit incorporation of technical uncertainty in recent studies. Nevertheless, even in advanced formulations, socio-environmental dimensions are rarely incorporated as quantified criteria with traceable weights within the decision framework and, when considered, they are typically treated indirectly (e.g., through regulatory constraints) or as external considerations to the optimization model; this gap motivates complementing traditional approaches with multi-criteria decision-making methods, particularly the Analytic Hierarchy Process (AHP) (Saaty, 1990), which structures heterogeneous criteria through pairwise comparisons, derives consistent weights, and produces a transparent ranking to integrate socio-environmental variables as explicit inputs to strategic assessments, complementing (rather than replacing) the techno-economic core of existing transition models. 3.- METHODOLOGY MCDM methods provide a suitable framework for addressing problems that involve multiple heterogeneous and potentially conflicting dimensions, as they enable the structuring of the decision problem, the comparison of the relative importance of criteria, and the derivation of explicit rankings to support decision-making (Mardani et al., 2015). Within these approaches, the AHP is one of the most widely used methods for criteria prioritization in complex contexts, due to its formulation based on pairwise comparisons, its ability to systematically incorporate expert judgment, and the possibility of assessing the internal consistency of the evaluations (Saaty, 1977; Saaty & Tran, 2007). In this study, AHP is used to derive relative weights for socio-environmental criteria and to define the structure of an integrated socio-environmental risk indicator, based on a group-aggregated pairwise comparison matrix. 3.1 Criteria definition The AHP is used to structure and prioritize socio-environmental criteria relevant to strategic decisions associated with the transition from open-pit to underground mining. The hierarchy considered corresponds to a single-level hierarchy consisting of one goal and six criteria, defined as: (C1) surface disturbance, (C2) extreme climate events, (C3) energy consumption, (C4) mine-to-water-resources distance, (C5) mine-to-population-centers distance, and (C6) distance between water resources and population centers. This structure enables the
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