Optimización de la limitación del Pit final mediante el Algoritmo Lerchs & Grossmann en Python

Abstract

La optimización del límite final del tajo (UPL) es una etapa desisiva al momento de planficar la explotacion de minas a tajo abierto, debido a que afecta directamente la rentabilidad del proyecto. Este estudio busca determinar el UPL usando el algoritmo de Lerchs y Grossmann (LG). Se maximiza el Valor Actual Neto (VAN) a través de una implementación computacional reproducible en Python. La metodología se basa en un modelo de bloques sintético que incluye 151,898 bloques de 5 × 5 × 5 m. Este modelo tiene información espacial (X, Y, Z), leyes de cobre variables, una densidad constante y parámetros económicos definidos. El análisis se realizó en Google Colab con Python 3.12.12. Se consideró un precio del cobre de 2.26 USD/lb, un costo de venta de 0.12 USD/lb, un costo de minado de 6.15 USD/t y supuestos económicos constantes, sin descuento temporal, para un escenario de planificación de tajo final. Los resultados indican que la optimización mediante LG crea un tajo final con 18,393 bloques, un tonelaje de mineral de 6,295,982.75 t, 106,322.86 t de material estéril, una profundidad máxima de 110 m y un volumen total de 3,523,275 m³. Esto resulta en un VAN de 239.92 millones de USD. El algoritmo de LG es un método sólido y eficiente para optimizar el UPL. Ofrece soluciones económicamente óptimas y técnicamente consistentes para estudios de planificación minera estratégica.

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