496 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. 2. METHOD The methodology described herein combines short-term shovel allocation optimization, extraction sequencing, and truck dispatch decisions, integrating two commonly separated optimization models in a single simultaneous analysis. The stochastic modelling primarily focuses on the uncertainty in the input parameters related to the geological risk (grade uncertainty). However, the stochastic analysis is also extended to operational parameters that impact lower-stage decisions related to truck tasks. 2.1. Stochastic Formulation The optimization model designs the open pit mine as a set of locations subdivided in recently blasted work benches represented as muck piles ï∈∏ (mining areas) and destinations 4 ∈π. In this system, a set of shovels j ∈∫ make use of trucks M ∈ª to transfer material through the mine. Muck piles are sequenced for extraction so that each truck performs an T ∈ º number of trips (back and forth) in each period 1∈ℙ as part of the dynamic dispatch process. The stochastic nature is represented by a set of scenarios jW ∈∫ℂ, encompassing the data distribution and uncertainty of the muck piles’ combined grades. The details of the model follow. 2.1.1. Objective Function and Uncertainty Policies The methodology evaluates an objective function that focuses on the maximization of the overall revenue of the fleet operation, material transportation, and processing activities. B#D e = ‖f 1 ℂ‖ h hUij.$$ AG1G/kG!",6Y !"∈9ℂ6∈ℙ − ‖f1ℂ‖ h hUl.$%$!",6 + 8G/#"%&G$!",6Y !"∈9ℂ6∈ℙ (1) As shown in Equation 1, the objective function is established around the profit created from the difference between the gross revenue from the sales of the processed material and the sum of all operating costs, processing costs, and the economic penalties generated from not meeting the tonnage and grade targets, for all periods 1∈ℙ (shifts) under analysis.
RkJQdWJsaXNoZXIy MTM0Mzk2