Performance evaluation of a new stochastic network flow approach to optimal open pit mine design–application at a gold mine

An orebody model constitutes a threedimensional accumulation of mining units (blocks). The available metal content in a mining unit and the economic parameters, such as metal price, mining cost, processing cost, marketing or selling cost, as well as the metallurgical recovery, are used to calculate the economic value of a particular mining block. A mining block with a positive value is classified as an ore block, while a mining block with a negative value is identified as a waste block. Usually, an orebody model consists of millions of blocks, and the economic value of these blocks becomes the basic input for the development of the optimal production phase design and determination of the optimal ultimate pit limit1. An optimal phase design refers to the sequence of extraction that reaches the ultimate pit limit or the extent of extraction2. It is well established that the phase design and ultimate pit limit may be accomplished using conventional and stochastic approaches3,4. The conventional optimization approaches may not account for the expected variations or uncertainty in all pertinent inputs, assuming that inputs (grade or metal content) of mining blocks and all other parameters are constant and in fact the actual values. More specifically, conventional optimization methods consider input from an estimated ’average’-type representation of the orebody model5,6. However, the utilization of the estimated block values may result in an unrealistic mine design and production schedules, leading to the possible failure of capital-intensive mining projects7,8. The stochastic approach, on the other hand, quantifies the inherent uncertainty in geological parameters (grade or metal content), anticipating the possibility of a block incorrectly identified as an ore block, thus accounting for and managing risk in the possible economic value at the time of extraction. Stochastic optimization in mine planning considers a set of simulated realizations of the orebody as an input9–12, and each of these realizations constitutes economic values of mining blocks of its own. Generally, optimization of production phase design and ultimate pit limit may be described by a directed graph13, represented as G = (N, A). A mining block i carrying a value vi is represented as a node in N. Also, an arc directed from node i to node i′ exists in A, representing the extraction precedence of block i′ over block i. The solution to this graph problem maximizes ∑i∈N vi by finding a set N′ N that contains all predecessors related to the nodes with the maximum value. Here, N′ is referred as the maximum closure on the Performance evaluation of a new stochastic network flow approach to optimal open pit mine design–application at a gold mine