Influence of the faces relative arrangement on the optimal reloading station location and analytical determination of its coordinates

The purpose of this study is to develop a methodology of the optimal rock mass run-of-mine (RoM) stock point determination and research of the influence of faces spatial arrangement on this point. The research represents an overview of current researches, where algorithms of the Fermat-Torricelli-Steiner point are used in order to minimize the logistic processes. The methods of mathematical optimization and analytical geometry were applied. Formulae for the optimal point coordinates determination for a 4 faces were established using the latter methods. Mining technology with use of reloading stations is rather common at the deep iron ore pits. In most cases, when deciding on location of RoM stock, its high-altitude position in space of the pit is primarily taken into account. However, the location of the reloading station in a layout also has a significant influence on technical and economic parameters of open-pit mining operations. The traditional approach, which considers a point of the center of gravity as an optimal point for RoM stock location, does not guarantee the minimum haulage. In mathematics, the Fermat-Torricelli point that provides a minimum distance to the vertices of the triangle is known. It is shown that the minimum haulage is provided when the point of RoM stock location and Fermat-Torricelli point coincide. In terms of open pit mining operations, the development of a method that will determine an optimal point of RoM stock location for a working area with respect to the known coordinates of distinguished points on the basis of new weight factors is of particular practical importance. A two-stage solution to the problem of determining the rational point of RoM stock location (with a minimal transport work) for any number of faces is proposed. Such optimal point for RoM stock location reduces the transport work by 10–20 %