Network Linear Programming Optimisation of an Integrated Mining and Metallurgical Complex

Abstract

Mining companies seek to mine, route and process ore to make the most efficient use of capital equipment during the life of the mine. The situation analysed in this paper relates to optimisation of medium-term production strategy for a group of mines and metallurgical plants. Typical operations under this scenario involve mining of crude ore from shafts and/or open pits; transportation of ore to the milling plants, run-of-mine stockpiles and leach-pads. The concentrate from the mill(s) is sent to the smelters and refineries, from where the finished metal is sent to the markets. If one assumes that the grade of run-of-mine ore varies according to source and that the milling plants are designed to handle different types of ore, plus the fact that mines and plants may separate by considerable distances, optimisation of the production plan becomes imperative. Most of the publications dealing with the subject of mine production planning are limited to mine scheduling optimisation and do not include metallurgical plants. However, the nature of the problem requires the application of a model that incorporates all the elements of the mineral production system. The methodology outlined in this paper is based on a Network Linear Programming formulation of the production-planning problem for a mining and metallurgical complex. Network LP models are particularly useful in analysing production-distribution type systems such as the one involving a group of mines and metallurgical plants. The problem is formulated using the theory of dual-primal relationships in linear programming. The solution algorithm finds the minimum cost of production and distribution, hence the optimal production and material routing plan for a group of mines and metallurgical plants. The graphs of optimality conditions for each arc in the network could be exploited as a tool for strategic mine planning. The advantages of this formulation are outlined and its application is demonstrated using a hypothetical situation involving an integrated mining and metallurgical complex, specifically six mines, five concentrators, three smelter and two copper refineries. A computer program called Linear Integer Discrete Optimiser (LINDO) is used to solve the network linear programming model. This program allows the user to quickly input an LP formulation, solve it and perform ‘what if’ type analyses.