This paper proposes a stochastic integer programming (SIP) formulation to address the optimization of long-term mine production schedules, whereby the supply of metal from a mineral deposit is considered uncertain and can be described by a set of equally probable orebody representations. The proposed SIP formulation maximizes the expected net present value of the production over the life of the mine while reducing the risk of deviating from production targets. The proposed modelling methodology considers a set of limiting surfaces to facilitate the scheduling of larger size deposits, where a surface defines a limit that separates mining blocks assigned to two consecutive production periods, and is represented by a discrete set of elevations. A key characteristic of the formulation is that it facilitates a divide-and-conquer approach to scheduling, where the scheduling can be performed sequentially, thus controlling the number of binary variables in multi-period production scheduling, which in turn facilitates production scheduling for large mineral deposits.
The proposed SIP production scheduling formulation is tested at a copper deposit. First, scheduling with the proposed SIP shows the intricacies and performance of the formulation. Subsequently, the method is applied sequentially to show the equivalence of solutions while assessing computational requirements and demonstrates empirically that the proposed SIP formulation can reduce the processing time from days to minutes.
Published September 2013 , 22 pages