Stochastic integer programming for optimising long term production schedules of open pit mines: methods,application and value of stochastic solutions

Abstract

The production scheduling of open pit mines is an intricate, complex and difficult problem to address due to its large scale and the unavailability of a truly optimal net present value (NPV) solution, as well as the uncertainty in key parameters involved. These key factors are geological and mining, financial and environmental. Geological uncertainty is a major contributor in failing to meet production targets and the financial expectations of a project especially in the early stages of a project. Stochastic integer programming (SIP) models provide a framework for optimising mine production scheduling considering uncertainty. A specific SIP formulation is shown herein that generates the optimal production schedule using equally probable simulated orebody models as input, without averaging the related grades. The optimal production schedule is then the schedule that can produce the maximum achievable discounted total value from the project, given the available orebody uncertainty described through a set of stochastically simulated orebody models. The proposed SIP model allows the management of geological risk in terms of not meeting planned targets during actual operation, unlike the traditional scheduling methods that use a single orebody model and where risk is randomly distributed between production periods while there is no control over the magnitude of the risks on the schedule. Notably, the testing of the SIP formulation in two cases, a gold and a copper deposit, shows that the expected total NPV of the schedule using the SIP approach is significantly higher (10 and 25% respectively) than the traditional schedule developed using a single estimated orebody model.