Efficient optimization of open pit mining is possible, according to Marcos Goycoolea and Eduardo Moreno of Universidad Adolfo Ibañez in Santiago, Chile. The duo explained their research in this topic in their presentation, “Pushing Optimization to the Limit: Challenges in Open Pit Mining” at the Division of Economics and Business Seminar November 18.
Goycoolea began by explaining a bit about the mine planning process. “It’s about deciding where to dig the hole, when to dig it, and what to do with the stuff that you dig up – those are the three main questions that as a mine planner you have to answer.” As that is “a big, complex problem,” the only way to analyze it is to “break it down into small, simple problems we can understand” and then recombine these pieces.
Traditionally, a block model of the site is sculpted first. From this model, a production schedule can be constructed based upon capacity, priority, and timing. The third step is to “make the solution operational,” and actually initiate the project.
“What we’ve been trying to do is to change this classic approach… we like to use some kind of optimization process to solve all these problems concurrently… and do it in such a way that we get better solutions,” Goycoolea said. The research team believes this is possible and practical and can be accomplished by developing new algorithms and programs to conduct this optimization.
The goal is to actually take the input block models and be able to tell companies which blocks should be extracted when and in what order in order to maximize net present value. The issue is that the problems are very large. By Goycoolea’s approximations, for “a typical problem, it’s very easy that you’ll have five million different blocks.” Each of these blocks can have three variables, totaling 15 million different variables that cover upwards of fifty years. The amount of memory necessary to solves these problems often exceeds the amount of memory available. In fact, when provided a large variety of data sets, only five were able to be solved with standard methods and even these five took substantial time.
“The first thing we started developing was… some special linear programming technology,” said Goycoolea. However, this was easier than might be supposed because “We’re developing a linear programming structure for a very specific problem.” The team began with a heavily simplified model mine and continued to make modifications. Ultimately, they can make approximations by taking a convex combination of the pits closest in size to the goal. These approximations, known as the critical multiplier algorithm, allow most of the problems to be solved. “We set out and looked at the same data set… It turns out we can solve a big majority of the problems,” Goycoolea said.
The team also investigated with great success the independently developed Bienstock-Zuckerburg algorithm. This other algorithm offered a more general solution, and could model multiple constraints. When the research team applied this algorithm with some modifications, it also accurately and efficiently approximated results. This method was able to solve six previously un-solved problems without modifications and with modification was able to solve even more problems.
The researchers also offered three case studies, showing that problems could be run more efficiently and better results achieved with these new algorithms. The first example was a large production mine, which showed a higher total revenue with their Opt-Maths approximations than with other figures. The second mine had two different products, with different values. The Opt-Maths model was able to eliminate cash-flow gaps and help decide which products should be produced when and in what quantities. Finally, the third mine had to manage high arsenic levels, which was also shown to be possible with the new methods.
Moren and Goycoolea concluded that managing large scale data sets such as those for open pit mining optimization was possible. They also added that these processes would be effective in non-mining industries as well.