Análise comparativa da otimização de cava através do algoritmo de lerchs & grossmann e da metodologia do sequenciamento direto de blocos aplicados por softwares especializados

Abstract

The strategic mine planning is a fundamental step of any mining enterprise and the main responsible for choosing the optimization method that will define the final pit design. This directly influences the technical and economic feasibility of the mining operations. The final pit can be obtained through optimization methods that aim to maximize the economic value of that mining project which, when discounted to the present time, is used as a financial parameter for the project’s investment decision. One classic pit optimization method is the Lerchs & Grossmann Algorithm, formulated in 1965 and widely used in the mining industry since its inception. It has two branches, one two-dimensional, based on dynamic programming, and another three-dimensional, formulated based on graph theory and the construction of a normalized tree. The method presents optimal results for maximizing the economic value of the pit, requiring subsequent steps to generate the best production schedule and discount the economic value. Another approach to optimizing the pit is Direct Block Sequencing, formulated in 1968 by Johnson. This method uses mixed-integer programming to maximize the discounted economic value and simultaneously consider a series of constraints to generate the final pit and the mining sequence in a single step. Due to the computational limitations of the time, this approach only became feasible for real models in recent times. Therefore, the present work aims to comparatively analyze the results obtained from the application of the two aforementioned optimization approaches in a block model. This application occurs for two distinct scenarios: scenario 01, without a maximum total extraction capacity restriction, and scenario 02, limiting the annual maximum extraction capacity to 6 million tons. To achieve this objective, the development was carried out using specialized software: Studio NPVS, which incorporates the Lerchs & Grossmann Algorithm with the implementation of nested pits, integrated with the traditional mine planning approach, consisting of sequential and interdependent stages known as Ultimate Pit, Pushbacks, and Scheduler; and the MiningMath software, which adopts the Direct Block Sequencing methodology and performs the entire workflow in a single step simultaneously. Based on the analysis performed, considering the results of both approaches, it was found that in both scenarios, the net present value obtained through Direct Block Sequencing was higher, indicating greater profitability, while the Lerchs & Grossmann Algorithm showed greater efficiency in reducing the waste/ore ratio.