Fundamental tree algorithm in optimising production scheduling for open pit mine design

Mathematical programming models are well suited to optimising long-term production scheduling of open pit mine designs; however, it is not possible in most cases to solve the scheduling problem as a mathematical programming model because the number of integer variables required becomes too large. New methods are required that will reconstruct the mining blocks and decrease the number of integer variables in scheduling without reducing the resolution of the model or optimality of the results. The fundamental tree algorithm proposed herein addresses this issue effectively. A fundamental tree is defined as any combination of blocks such that the blocks can be profitably mined, the blocks obey the slope constraints, and the chosen blocks do not have a proper subset that meets the first two conditions. A set of linear programming (LP) formulations is developed to find a set of fundamental trees (FTs) that exist for a given mine deposit. It is shown in this paper that the LP model generates FTs with the defined properties. The proposed method is illustrated in optimisation of the long-term production schedule of a multi-element large open pit copper deposit in Peru, South America. The results show that after generating FTs, the mixed integer programming (MIP) model can be used to optimise large open pit mines. The case study presented shows the financial benefits of the capabilities of MIP to consider multiprocessors and multi-elements in mine optimisation.