Application of mathematical modelling for draw control under material flow uncertainty

Abstract

Production scheduling is one of the key steps in the decision-making process of any mining operation. In block caving, it is the choice of the amount of caved rock to extract from drawpoints in different periods. One of the main differences between block caving and other mining methods is the influence of the material flow on production, and draw control in general. Achieving an optimum production schedule without consideration of the cave rate and material flow could be unrealistic and impractical as the movements of material between drawpoints will result in unexpected production grades and tonnages. In this paper, a stochastic mixed integer optimisation model is proposed to optimise the production schedule during the life of the mine. The uncertainties of production grades and tonnages are captured by defining a number of scenarios that represent the probable movements of fragmented rock between drawpoints in the same neighbourhood. The decision variables in the formulation are based on the slice model, which means that the mathematical solution determines which slices are extracted from drawpoints in each period of production. The goal is to maximise the net present value of the project during the life of the mine and minimise the deviations of production grades and tonnages from the defined goals in all probable scenarios resulting from the movements of the fragmented rock between drawpoints. Application of the proposed model in caving operations can not only improve the profitability of the project, but also increase the confidence of the production schedule. MATLAB was used for programming and CPLEX for solving the model. The designed graphical user interface, with the capability of adding different technical and operational constraints, will be a flexible tool for mine planners to control the draw based on the company's goals during the life of the mine.

Long-term production scheduling optimization and 3D material mixing analysis for block caving mines

“…Many researchers have used mathematical programming to optimize the production schedule in block-cave mining. They have been trying to either maximize the NPV (Guest et al 2000;Rubio Enrique 2002;Diering 2004;Rubio and Diering 2004;Weintraub et al 2008;Smoljanovic et al 2011;Epstein et al 2012;Pourrahimian et al 2013;Alonso-Ayuso et al 2014;Khodayari and Pourrahimian 2014;Nezhadshahmohammad et al 2017;Khodayari and Pourrahimian 2017), to minimize the mining cost (Song 1989), or to minimize deviations from operating goals (Chanda 1990;Rahal 2008;Diering 2012;Khodayari and Pourrahimian 2016;Khodayari and Pourrahimian 2017;Sepúlveda et al 2018). Mixed integer linear programming (MILP) is the most common methodology that has been used for the purpose of production scheduling optimization.…”

“…2013; Alonso-Ayuso et al. 2014; Khodayari and Pourrahimian 2014; Nezhadshahmohammad et al. 2017; Khodayari and Pourrahimian 2017), to minimize the mining cost (Song 1989), or to minimize deviations from operating goals (Chanda 1990; Rahal 2008; Diering 2012; Khodayari and Pourrahimian 2016; Khodayari and Pourrahimian 2017; Sepúlveda et al.…”