Heuristic and exact approaches to optimize the production scheduling of mines transitioning from open-pit to block caving

Mine planning engineers perform production schedule optimization to determine the sequence in which ore blocks should be extracted to maximize value. For mines transitioning from a surface mining method to an underground extraction method, production schedule optimization is a complex problem with no existing solution. We developed two optimization approaches for the transition mine production scheduling problem (TMPSP) – a disintegrated heuristic approach, and an integrated exact approach – and investigated the situations where the integrated approach outperforms the disintegrated approach. The computational results of a case study showed that the integrated model achieves 5 percent higher net present value (NPV) than the disintegrated approach in the base scenario when determining the transition depth. The integrated solution also outperforms the disintegrated solution for many other scenarios with combinations of planning horizon, grade distribution, copper price and cost. Background Mineral deposits are mined using two main methods: surface and underground. Depending on the characteristics of the deposit, one of these two methods is selected to extract the ore. In certain cases, deposits start near the surface and continue deep within the Earth’s crust. In the past, most mines abandoned their operations after employing surface methods up to the point where they were no longer economically profitable. In the 1950s, mine operations began exploring the possibility of combining both extraction methods (Fig. 1). Deposits were mined with surface mining methods until it was no longer feasible to mine the ore at a particular depth (transition depth), then the remaining deposit can be mined with an underground mining method to maximize profit [1]. However, the differences in surface and underground mining methods make the transition challenging and capital-intensive [2]. There are two general approaches to the TMPSP in the literature: the disintegrated and integrated approaches. The objective of this study is to investigate if there are certain conditions under which an integrated approach to determining the transition mine depth outperforms a disintegrated approach. Methods To determine the transition depth from an openpit method to a block caving method that optimizes the production schedule and maximizes the NPV, we first describe both the openpit and underground mining problems that underpin the TMPSP. We then present the disintegrated approach with two mixed-integer linear programming (MILP) models for the openpit and underground mining problems, respectively. An integrated model is then presented to optimize the decisions for the openpit and underground problems simultaneously, and a comparative analysis is conducted to compare the integrated and disintegrated solutions based on the NPV, the planning horizon, grade distribution, copper price and cost. Fig. 2 Ore production using (a) openpit and (b) block caving extraction methods for the disintegrated and integrated models. Results We analyzed four experimental levels of the undercut level parameters in the underground model instance and 16 levels of the annual production targets for the openpit model instance. The highest NPV, 1194.85 MUSD ($1,194.85 million), was observed at an undercut level at elevation 830 m for the underground instance. In the case of the surface model, the highest NPV of 298.56 MUSD is observed for the annual production of 115.78MTon (115.78 Mt) with a corresponding pit limit at elevation 945 m. The integrated model obtained an NPV of 1,314 MUSD, 5 percent higher than the disintegrated approach.An experiment was run for six levels with time horizons ranging from two to 12 periods. As the number of extraction periods increases, the NPV decreases. Compared to the results obtained from the disintegrated approach, the NPV for the integrated approach was higher for varying combinations of the scheduling horizon. The minimum and maximum NPVs obtained for the integrated model are 661 MUSD and 1,312 MUSD, respectively, which are considerably higher than the scenarios evaluated for the disintegrated case. Fig. 1 A simple design of the transition mine problem. The average waste and ore tonnages obtained in each period for the disintegrated and integrated models were also evaluated. Two best-case scenarios — undercut levels 830 m (scenario 1) and 730 m (scenario 4) — of the disintegrated model were compared to the integrated model (Fig. 2). The tonnages generated in each period from the integrated model are similar, with 0.8 to 4 percent difference, to that of scenario 4 of the disintegrated model for the surface method (Fig. 2). We also compared the computation times for the integrated and disintegrated approaches for one and four periods. The disintegrated approach took more computational time on average than the integrated approach to achieve a comparable optimality gap. Discussion We employed a disintegrated heuristic approach to select the combination of openpit and block caving strategies to extract the deposit considering crown pillar placement. Based on the production rate, production schedules, operational constraints and the combined NPV, we determined that a block caving method with an undercut level of 830 and a pit limit of 1185 should be used to extract the deposit. For the scenarios evaluated, we found that starting the underground portion too early or too late can result in a loss of revenue: therefore, reiterating the argument presented by previous studies that value could be lost if the underground method were not incorporated into the transition depth decision process in earlier stages of mine planning. By considering both methods and crown pillar placement in the integrated approach, the overall NPV was 5 percent higher than in the disintegrated approach. Conclusions We developed and applied two optimization approaches to the TMPSP: a disintegrated heuristic approach, and an exact integrated approach. Our work provides insights into the conditions under which an integrated approach to solving the transition mine problem is superior to the disintegrated approach. Selected references Tokarev OV, Kuzenkov MV, Udalov AE (2015) Underground mining technology for the transition from open-pit to underground operation at the Zhdanov copper–nickel ore deposit. Gornyi Zhurnal 2015(6):60–64 Opoku S (2013) Modelling the optimum interface between open pit and underground mining for gold mines (Doctoral dissertation, University of the Witwatersrand)

Heuristic and exact approaches to optimize the production scheduling of mines transitioning from open-pit to block caving

Authored by: Angelina Anani1, Ignacio Ortiz Flores, Haitao Li and Afrooz Jalilzadeh

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