This study is focused on Direct Block Scheduling testing (Direct Multi-Period Scheduling methodology) which schedules mine production considering the correct discount factor of each mining block, resulting in the final pit. Each block is analyzed individually in order to define the best target period. This methodology presents an improvement of the classical methodology derived from Lerchs-Grossmann's initial proposition improved by Whittle. This paper presents the differences between these methodologies, specially focused on the algorithms' avidity. Avidity is classically defined by the voracious search algorithms, whereupon some of the most famous greedy algorithms are Branch and Bound, Brutal Force and Randomized. Strategies based on heuristics can accentuate the voracity of the optimizer system. The applied algorithm use simulated annealing combined with Tabu Search. The most avid algorithm can select the most profitable blocks in early periods, leading to higher present value in the first periods of mine operation. The application of discount factors to blocks on the Lerchs-Grossmann's final pit has an accentuated effect with time, and this effect may make blocks scheduled for the end of the mine life unfeasible, representing a trend to a decrease in reported reserves.

Geologic modeling is an important step in determining the benefits and final pit dimensions for mining operations. Geostatistical models and distance-based functions are the main methods used to estimate the grade behavior. However, these two methods, despite their similar mean values, differ in spatial variability. The objective of this article is to prove, by comparing the two methodologies, that models with different spatial variability using the Lerchs-Grossmann algorithm will output subtly different final pit dimensions and scheduling. Furthermore, with the direct block schedule (DBS), these differences can be considerable. The tests compared the methodologies using the following three models: inverse distance (ID), ordinary kriging (OK) and turning bands simulation (TBS). The results demonstrate that the Lerchs-Grossmann algorithm is only slightly sensitive to the spatial variability of the grade; however, DBS requires the model populations to be better defined because of its greater sensitivity to spatial variability.

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In a mining context, production scheduling's main objective is to determine the best mining sequence of blocks to achieve the largest net present value and to maximize ore reserve exploitation. Stockpiling and blending procedures may represent very helpful alternatives for mine planning to ensure the ore quality and amount required by the processing plant. In order to satisfy industrial requirements of grades and tones, reducing stockpile fluctuations may represent a very important tool especially for medium and short term mine planning. Classical linear programing has been widely used to model blending problems at the mining industry, however this formulation allows only one objective formulation. The current work describes a system based on goal programing able to reach blending constraints desired by short/medium term planning. The proposed formulation achieves the best schedule scenario, ensuring cost constrains are respected. Hence, this study aims to provide support for both short and long term mine planning.Keywords: stockpile; goal programing; blending constraints; stockpile scheduling; bulk ore blending. Programación directa de pilas de acopio: Formulación matemáticaResumen Según el contexto de industria minera la programación de producción es la mejor metodología para determinar la mejor secuencia de explotación y asi obtener el mejor valor presente líquido y explotar la reserva máxima. La construcción de pilas de acopio y de mezcla representa una alternativa valiosa para la planificación de minado permitiendo garantizar la calidad del concentrado y las especificaciones de la planta de tratamiento. Para satisfacer las especificaciones de leyes y tonelaje, y reducir las variaciones las pilas de acopio y mezcla cumplen un papel importante para la planificación de corto y largo plazo. La programación linear clásica viene siendo ampliamente utilizada en problemas de mezcla presentes en la industria minera entretanto esta formulación permite apenas trabajar con una sola función objetivo en su formulación. El presente trabajo describe un sistema basado en goal programing, capaz de alcanzar las restricciones requeridas en la planificación a corto y largo plazo de forma simultánea. La formulación propuesta obtiene el mejor escenario operacional garantizando que las restricciones de costos sean respetadas. Esta formulación es útil pues da soporte a la toma de decisiones en las actividades de planificación a largo y corto plazo Palabras clave: pilas de acopio; goal programing; restricciones de mezcla; agendamiento de pilas; mezcla de concetrado.

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