Mathematical relationship between ultimate pit limits generated by discounted and undiscounted block value maximization in open pit mining

Abstract

Ultimate pit limit is an important aspect of open pit mining. The optimal ultimate outline determines the tonnage of extractable ore, the volume of waste to be removed, the location of the subsidiary facilities, the location of ore and waste stockpiles, the life time of the mine and the estimated net present value (NPV) of the entire mining operation. Traditionally, there are two major approaches to optimizing the ultimate pit limit. One seeks to determine the ultimate pit using undiscounted profit maximization and the other by determining the optimal mining sequence of all blocks and discounting the value of the blocks. The outline with the highest cumulative NPV will be chosen as the final pit limit. For each of these approaches, different algorithms are presented. The aim of this paper is to present an analytical investigation about the mathematical relationship between sets of blocks of ultimate pits generated by each of these approaches in an ore body. This investigation is in fact the mathematical proof of the theorem that a discounted ultimate pit is smaller than or equal to the undiscounted pit. The results show that the discounted pit is always a subset of the undiscounted pit. Keywords: Open pit mines, Ultimate pit limit, Net present value, Discount rate