the project, subject to spatial precedence and various operational constraints (Espinoza , 2012).It is common practice in the mining industry to represent a mineral deposit as a set of three-dimensional blocks, known as a block model. The production scheduling then consists of defining when, if ever, to extract each of these blocks and the destination to which they should be sent.There are two methodologies that are mainly used to optimize this form of scheduling, namely 'block-level resolution ' and 'aggregation' (Elkington and Durham, 2011). The block-level resolution optimization approach was first proposed by Thys Johnson (1968) and evolved to be known as direct block scheduling (DBS). The aggregation approach splits the scheduling problem into several smaller sub-processes which include, for example, the definition and optimization of the ultimate pit, intermediate pushback selection, and finally, production scheduling. This last approach became known as the conventional planning approach (Elkington and Durham, 2011;Morales et al., 2015).Research into DBS and its use as a method for solving scheduling problems in open pit mine planning has recently been gaining increasing interest as an alternative to the conventional methodology, which is based on nested pits. In DBS, however, an entire production plan can be obtained in only one step, which can maximize the economic value of a mining project.Among the advantages offered by this method is that it considers the temporality of the problem and the opportunity cost when sequencing mining blocks, i.e., it searches for the next best block to mine considering its implication for other periods. As such, it is able to present users with the best NPV possible, subject to constraints such as operation, capacity, and metallurgy.However, this methodology is still being developed, and all of the existing operational constraints have not yet been fully implemented in the method, which can result in unfeasible long-term production plans. To address this gap, this paper proposes using DBS as a tool for medium-term planning.Medium-term planning is important for operational purposes; it also encompasses the quality and quantity of intermediate-period Three different approaches to medium-term planning were compared. First, a renowned software package that is used in the mineral industry was used to execute conventional medium-term scheduling. Then, DBS was used to perform the same task. Finally, a combination of DBS and conventional scheduling was tested. Using the results provided by DBS, sectorization of specific areas was included in the conventional methodology to guide the scheduling and thus allow this combination to produce real benefits, even for large projects.Block scheduling, open pit mining, mine planning, production scheduling.

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.