March/April 2006 1 INTRODUCTION Grade uncertainty and in situ variability continue to be major obstacles for optimizing open pit mine design, as shown in recent studies. Dimitrakopoulos et al. (2002) and Dimitrakopoulos (2005) show that there are substantial conceptual and economic differ- ences between risk-based frameworks and traditional approaches. Ramazan and Dimitrakopoulos (2004a) show that the scheduling patterns generated by con- ventional mixed integer programming (MIP) models that use multiple simulated orebody input models may be significantly different from each other, as well as from the scheduling pattern generated by using an estimated input model. These significant variations in the scheduling patterns suggest that a new mathe- matical scheduling method is needed—one that can account for orebody variability in optimization. Past efforts to deal with uncertainty attempt to sequentially link stochastic orebody models with con- ventional optimization formulations (Ravenscroft, 1992; Dowd, 1997). This sequential process is ineffi- cient and, although it allows the assessment of risk in a schedule, it does not produce optimal scheduling solutions in the presence of uncertainty as shown in Dimitrakopoulos et al. (2002). In addition, these efforts do not consider multi-element deposits that have complex ore quality constraints, such as nickel laterites, iron ore, or magnesium deposits. Further- more, dealing with orebody uncertainty and in situ grade variability accentuates the need to consider issues of equipment access and mobility on the related stochastic optimization formulations. The Probabilistic practical optimization of production scheduling for multi-element deposits S. Ramazan, Rio Tinto, Perth, Western Australia, Australia, and R. Dimitrakopoulos, McGill University, Montreal, Quebec ABSTRACT Optimizing production scheduling in open pit mines is important for managing cash flows of mining operations. This paper describes a new, probabilistic, mixed integer programming (MIP) formulation which has been developed to minimize the risk of not achieving planned pro- duction targets, in terms of metal production and ore tonnage feed for the mill during production, while considering maximization of total discounted economic value. The new MIP model also rec- ognizes that to minimize movement of excavators over long distances and accommodate equip- ment access, the blocks scheduled for mining within a period cannot be spread too widely. The model is applied to a laterite nickel-cobalt deposit, as an example of multi-element deposits that have complex ore quality constraints. The results show that the proposed model generates feasible schedules. When compared with traditional optimization techniques, the new model is superior in terms of minimizing the risk of not meeting production targets, especially at the early stages of pro- duction, and in terms of generating practical scheduling patterns. KEYWORDS Probabilistic schedule, Uncertainty, Mathematical programming, Mine planning number of binary variables required in mathematical modelling for open pit mine planning (Ramazan, 2001; Ramazan and Dimitrakopoulos, 2004b) is also one of the major obstacles for application of MIP-type models for large open pit mines. Godoy and Dimi- trakopoulos (2004) developed a long-term produc- tion scheduling model that is based on simulated annealing, is robust to risk, and is focused on meet- ing the optimized ore production targets to maximize the total achievable net present value (NPV) of the project, using multiple simulated orebody models to deal with grade uncertainty. Dimitrakopoulos and Ramazan (2004) developed a long-term production scheduling method that is based on a linear pro- gramming (LP) model. The LP formulations eliminate partial block mining problem in using linear variables instead of binaries to improve the efficiency in solu- tion time, and the model also considers orebody uncertainty integrating the issue of equipment access and reduced movement of large equipment. They proposed the use of grade probabilities integrated with a parameter that discounts orebody risk for meeting production targets. Two windows generating two sets of constraints for each block in the model are implemented for handling equipment access and mobility, but these multiple windows and constraints increase the size of the models. In addition, the reader is referred to recent developments and prac- tices in the industry, presented in Dimitrakopoulos (2005). This paper presents an application of a new, probabilistic, production scheduling formulation for complex, multi-element deposits. The formulation is Paper 6 Metal Mining