Open Pit Mine Scheduling Based On Fundamental Tree Algorithm

Long-term production scheduling design is a very important part of mining because it determines the economic outcome of a project There have been many attempts to solve the optimum pit scheduling problem, but there has been no success in developing a scheduling method to give optimum results in maximizing net present value of a mining project. Open pit production scheduling problem can be formulated as a mathematical programming problem and solved using Mixed Integer Programming technique. However, it is not possible to solve the formulation within a reasonable time since the number of integer variables required for the mathematical model is too great to do that by today's available computer technology. There- fore, a methodology is required to combine, or aggregate, the mining blocks and to decrease the number of integer variables in scheduling without losing the optimality. Therefore, the fundamental tree concept was developed in this paper to combine the blocks. A fundamental tree is defined as any combination of blocks such that: 1. the blocks can be profitably mined, 2. the blocks obey the slope constraints and, 3. there is no subset of the chosen blocks that meets 1 and 2. A Linear Programming (LP) formulation is developed as a mathematical model to find a set of fundamental trees that exist for a deposit. Since the blocks are combined to form the fundamental trees, the number of variables required for the scheduling model is decreased significantly. This decrease in the number of variables makes it possible to mathematically formulate the multi-time period scheduling problem as a Mixed Integer Programming (MIP) model. A case study is performed on a multi-mineral copper deposit in Peru, South America. NPVs of annual after-tax cash flows generated based on the schedule provided by the "Fundamental Tree Algorithm" is compared with NPVs resulted from the schedules coming from three of the computer packages presently available to the mining industry. These are Mintec's M821V, Earth- work's NPV Scheduler, and Whittle's Milava open pit mine schedulers.