evaluating plant feed rate, shovel utilization, and truck queuing, observing some improvements in the behavior of the fleet. The topic of geological and equipment uncertainty was later reviewed by Quigley & Dimitrakopoulos (2020), incorporating the shovel sequencing and truck performance under unplanned events, and was the first to note the complexity hurdles for commercial solvers when handling large case studies. One common problem observed in most approaches is the disconnection of the simultaneous optimization between shovel utilization, truck utilization, and plant feed rate, which was assessed by Moradi-Afrapoli and Askari-Nasab (2020) against the performance of commercial software Modular Mining DISPATCH®, identifying several shortcomings in the optimization process for the current commercial implementations. Other optimization approaches that include shovel allocation and sequencing (Both & Dimitrakopoulos, 2020, and De Carvalho & Dimitrakopoulos, 2023) reinforce learning applied to truck tasks (De Carvalho & Dimitrakopoulos, 2021), dynamic dispatching policy selection (Mirzaei-Nasirabad et al., 2023), and grade control to update diglines (De Carvalho & Dimitrakopoulos, 2024). Considering the advances made up to this point, the next step is to analyze the likelihood of changes occurring in the initial plan in response to individual and combined uncertainties. This entails identifying differences from a baseline plan when uncertainty impacts upper-level (shovel allocation) and lower-level (truck dispatching) decisions for a variety of equally-probable scenarios. The formulation of the problem must also consider the possibility of parameter reselection, depending on the complexity of the problem, similar to the parametric-dependent policies suggested by Paduraru & Dimitrakopoulos (2018), such as material recategorization (ore/waste) and destination changes (to process, to store, or to dispose). Existing commercial implementations are bounded by the limitations of the conventional deterministic calculations, the computational cost associated with the size and complexity of the problem, and the degree to which any decisions rendered can actually be implemented. Therefore, they can only evaluate one scenario of simulated parameters at a time. In contrast, a mining operation would require a wider range of solutions for any possible operational condition to be encountered. These solutions can be obtained from a simultaneous optimization for a set of scenarios that cover the uncertainty distribution of the operational parameters. Stochastic solutions must account for multiple consecutive periods, sequenced shovel allocations, dynamic truck tasks (observed by Li, 1990, and Ta et al., 2005, as the most cost efficient method for truck dispatching), travel times, number of trips for each unit, blasted muck piles depletion rates, delivered material at each destination, average grades, and any deviation from the operational targets. In this sense, the integration between short-term planning and live dispatching is guaranteed during the optimization process. The possibility of knowing what to do in advance of the reconciliation process can greatly reduce the risks of misallocation or overestimation of system efficiency. As such, it offers a considerable reduction of operational contingencies, while also reducing the impact of geologic risks (Hazrathosseini & Afrapoli, 2023) in most mining operations. This paper describes the design and implementation of a stochastic optimization model to solve combined dispatch problems and short-term shovel allocations. The methodology includes the analysis of the parameters dataset, the general mathematical formulation, the conditional objective function based on the type of uncertainty, and the interpretation of results from simultaneous optimization. The implementation evaluates a case study at an open-pit copper mine for multiple consecutive periods and equally-possible scenarios of occurrence. Conclusions and future work follow.
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