A Stochastic Formulation for the Dig-Limit Definition Problem in Short-Term Mine Planning Under Grade Uncertainty

Uncertainty in short-term grade estimations can significantly affect destination policies and dig-limit definitions in open-pit mining. However, most dig-limit techniques still rely on deterministic methods and manual procedures. This study proposes a stochastic optimization model for the dig-limit definition problem that incorporates geological uncertainty through multiple grade scenarios and explicitly controls deviations from production targets. Two real case studies were evaluated to compare the stochastic formulation against deterministic and manual definitions. Results show that the stochastic model systematically improves economic performance, with profit increases of up to 2.3% over deterministic policies and up to 4.3% when compared against manual solutions. The stochastic solution also reduces deviations from metal and grade targets, producing more stable outcomes across scenarios. The model is computationally efficient, with solution times below 25 s for all case studies, which are compatible with practical short-term planning workflows. Overall, our findings demonstrate that incorporating grade variability into the dig-limit definition improves profitability and reliability in short-term mine planning horizons.