Managing risk and waste mining in long-term production scheduling of open-pit mines

Open pit mine design and production scheduling deals with the quest for the most profitable mining sequence over the life of a mine. The dynamics of mining ore and waste and the spatial grade uncertainty make predictions of the optimal mining sequence a challenging task. A new optimization approach to production scheduling based on the effective management of waste mining and orebody grade uncertainty is presented. The approach considers an economic model, mining specifics including production equipment and the integration of multiple equally possible representations of an orebody. The utilization of grade uncertainty and optimal mining rates leads to production schedules that meet targets whilst being risk resilient and generating substantial improvements in project net present value. A case study from a large gold mine demonstrates the approach. Introduction Valuation and related decision-making in surface mining projects require the assessment and management of orebody risk in the generation of a pit design and a long-term production schedule. As the most profitable mining sequence over the life of a mine determines both the economic outcome of a project and the technical plan to be followed from mine development to mine closure, the effect of orebody risk on performance is critical (Ravenscroft, 1992; Dowd, 1994; Rendu, 2002). Geological risk is a major contributor in not meeting expectations in the early stages of a project (Vallee, 2000), when repayment of development capital is vital, as well as to production shortfalls in later years of operation (Rossi and Parker, 1994). The adverse effects of orebody uncertainty on the traditional optimization of pit designs and corresponding key project performance indicators are documented in various studies (e.g., Dowd, 1997; Dimitrakopoulos et al., 2002; Farrelly, 2002). These past efforts deal with the use of stochastic simulation methods in assessing project risk for a given mine design and mining sequence. They do not, however, address the generation of optimal conditions under uncertainty, long-term production schedules or operational issues and interactions of ore and waste within the orebody space over the life of the mine. New integrated approaches can be developed to effectively deal with orebody uncertainty in production scheduling while maximizing cash flows, and may be based on two elements. The first element is the ability to represent orebody uncertainty through the stochastic simulation of multiple, equally probable deposit models. Although the technologies are available (e.g., Dimitrakopoulos, 2002), the use of multiple orebody models for production scheduling, instead of a single model, is not a trivial exercise. Generally, traditional optimization formulations are not compatible with stochastic modeling approaches. The second element in dealing with risk is a modified optimization framework that, while compatible with orebody uncertainty, integrates a variety of mining issues, particularly management of waste, equipment utilization, mill demand, and technological, financial and environmental constraints. This paper presents a novel optimization approach that is shown to effectively integrate grade uncertainty into the optimization of long-term production scheduling in open pit mines. The approach is founded on the following two key elements: • a framework for long-term production scheduling based on the concept of a “stable solution domain” and • a new scheduling algorithm based on simulated annealing. The approach generates “100% confidence” in the contained ore reserves, given the understanding of the orebody and minimizes deviations from production targets to acceptable ranges. Related to the approach presented herein are concepts in Tan and Ramani (1992) and in Rzhenevisky (1968), where open pit production scheduling is seen as the determination of a sequence of depletion schedules in which at least two types of products, ore and waste, are removed to meet the mine’s demand. The optimal schedule maximizes the net present value (NPV) of the project subject to constraints, including: • feasible combinations of ore and waste production (stripping ratio) and • ore production rates that meet mill feed requirements. At the same time, an optimal schedule defers waste mining as long as possible and, in doing so, considers the mining equipment and capacity available. This approach is limited in Nonmeeting paper number 03-327. Original manuscript submitted for review August 2003 and accepted for publication January 2004. Discussion of this peer-reviewed and approved paper is invited and must be submitted to SME Publications Dept. prior to Sept 30, 2005. Copyright 2004, Society for Mining, Metallurgy, and Exploration, Inc.