Application of network flow and zero-one programming to open pit mine design problems.

Abstract

An algorithm which adopts a moving cone approach but is guided by maximal network flow principles is developed. This study argues that from a network flow point of view, the re-allocation problem is a major obstacle to prevent a simulation oriented pit design algorithm from reaching the optimum solution. A simulation oriented pit design algorithm can not resolve the re-allocation problem entirely without explicit definition of predecessors and successors. In order to preserve the advantages of moving cone algorithm and to improve the moving cone algorithm, the new algorithm trys to avoid the re-allocation situations. Theoretical proof indicates that the new algorithm can consistently generate higher profit than the popular moving cone algorithm. A case study indicates that the new algorithm improved over the moving cone algorithm (1% more profit). Also, the difference between the new algorithm and the rigorous Lerchs-Grossmann algorithm in terms of generated profit is very insignificant (0.015% less). The new algorithm is only 2.08 times slower than the extremely fast moving cone algorithm. This study also presents a multi-period 0-1 programming mine sequencing model. Once pushbacks are generated and the materials between a series of cutoffs are available for each bench of every pushback, the model can quickly answer, period by period, what is the best (maximum or minimum) that can be expected on any one of these four items: mineral contents, ore tonnages, waste tonnages and stripping ratios. This answer is based on a selected cutoff and considers the production capacity defined by the ore tonnage, the desired stripping ratio and the precedence constraints among benches and pushbacks. The maximization of mineral contents is suggested to be the direct mine sequencing objective when it is permissible. Suggestions also are provided on how to reduce the number of decision variables and how to reduce the number of precedence constraints. A case study reveals that the model is fast and operational. The maximization of mineral contents increases the average grades in early planning periods.