This article was first published in the Snowden newsletter in July 2011 and we believe many of the ideas presented are still relevant today.
There are typically three approaches to determining the cut-over point. They are discussed below.
Biggest economic pit
A common approach to determining open pit to underground cut-over,is to focus on the economic size of the open pit. Consideration of underground mining is secondary and is based on the remaining resource outside this pit. This is the simplest approach. It can be determined using any one of a number of commercially available pit optimization software packages. The pit will terminate at the point that the marginal cost of waste stripping outweighs the marginal revenue generated by additional ore processing.
Incremental undiscounted cash flow
The marginal profit derived from the pit decreases with depth. Given that underground mining profits are less dependent on depth there will likely be a point where the marginal profit of the underground exceeds that of the open pit. Using this method the cut-over point is the depth at which the marginal profit from the open-pit is equal to the marginal profit from the underground. This is usually shallower than the largest economic pit method. This method can also be undertaken using commercially available software.
Automated scenario analysis
The methods mentioned above do not account for discounting. As the underground mine operates at a higher cut-off grade than the open pit, it will deliver a higher grade and normally higher cashflow for the same throughput. Therefore there is likely a discounted cash flow to benefit generating this cash-flow early that may elevate the optimal transition point. The only way to test this is to complete schedules (which include open-ut and underground mining) and derive an NPV for each potential transition point. Depending on the complexities of the mine deriving a new schedule for each transition point can be very time consuming, and to test a reasonable number of transition points in a reasonable time automated optimising scheduling software should be used
The software should be able to handle both underground and open-pit mine scheduling simultaneously, and should be able to develop an optimised schedule for each transition point. In this way each schedule generated reflects the best possible schedule for a given transition point. Using this kind of software a suite of transition points can be evaluated, and their results compared so that the point that offers the highest value can be chosen.
There are a range of parameters (price, production rate, open pit mining cost, underground mining cost, and open pit cut-off grade) that can be tested to identify the sensitivity of the optimal transition point. Snowden has undertaken some case studies on the sensitivity of the transition point using its Evaluator software; these are presented in the charts below.
NPV curve sensitivity analysis
Factors such as price, production rate, and open pit and underground mining costs where shown not to materially affect the transition point decision. The only parameters to affect the transition point decision were the cut-off grades of the open pit and the underground.
The typical approaches to consider in the open pit to underground transition point optimisation problem can lead to appreciably sub-optimal solutions. When considering discounting, the optimal transition point elevates significantly as does the achieved value.
It is rarely practical to analyse every possible transition point. Only in simple examples, such as the one demonstrated here, is an enumeration of transition points feasible. In most cases it is sufficient to consider a range of possible transition points within the largest economic pit. Schedules and cash flows developed for each option can be compared to find the best alternative.
The effort of generating open pit and underground schedules for all likely transition points at all likely processing rates (and by inference cut-off grades) can be costly and time consuming. This often means that as a consequence, the problem is not thoroughly explored and therefore the result may be sub-optimal. By applying modern automated optimisation software solutions to this problem, the effort can be significantly reduced and the likelihood of developing an optimal result in a palatable time frame at an acceptable cost is dramatically increased.
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