A simulated annealing approach to mine production scheduling

Increasing global competition, quality standards, environmental awareness and decreasing ore prices impose new challenges to mineral industries. Therefore, the extraction of mineral resources requires careful design and scheduling. In this research, simulated annealing (SA) is recommended to solve a mine production scheduling problem. First of all, in situ mineral characteristics of a deposit are simulated by sequential Gaussian simulation, and averaging the simulated characteristics within specified block volumes creates a three-dimensional block model. This model is used to determine optimal pit limits. A linear programming (LP) scheme is used to identify all blocks that can be included in the blend without violating the content requirements. The Lerchs–Grosmann algorithm using the blocks identified by the LP program determines optimal pit limits. All blocks that lie outside of the optimal pit limit are removed from the system and the blocks within the optimal pit are submitted to the production scheduling algorithm. Production scheduling optimization is carried out in two stages: Lagrangean parameterization, resulting in an initial sub-optimal solution, and multi-objective SA, improving the sub-optimal schedule further. The approach is demonstrated on a Western Australian iron ore body.     

Informational processing of complex sound. III: interference.

In this study, theoretical results from information theory and detection theory are applied to provide a formal analysis of the interaction of target and context uncertainty on the discrimination of brief multitone sequences. The experiments employ a sample-discrimination task in which the performance of an ideal observer is held constant while the relative variability of the target sigmaT and context sigmaC is varied. Listener performance in these experiments was less than ideal but increased monotonically with sigmaT/sigmaC whether the task was to discriminate the frequency or the intensity of the target. Performance was also constant for a constant sigmaT/sigmaC regardless of the target's position in the sequence. The results are consistent with a class of models in which the decision variable is a weighted sum of the tone values comprising the sequence. Weighting functions computed from the trial-by-trial date suggest that limits in performance result from trial-by-trial variability in the weights. The decision variable also serves as the basis for an analysis in which performance is linearly related to the information rate of the context independent of target position or task. In this analysis, target and context uncertainty contribute additively to the overall uncertainty associated with the decision variable.     

Incorporating geo-metallurgical information into mine production scheduling

Economic characterization of mining parcels depends upon geo-metallurgical properties, which vary throughout orebody. Mine production scheduling should aim to obtain maximum utility from orebody in such a way as to ensure mine–mill reconciliation. As heterogeneity of geo-metallurgical variables increases, the scheduling will be a very complicated task. Geo-metallurgical and financial data used in the mine production scheduling are based on simulation and/or estimation generated from sparse drilling and unknown future events. Therefore, the scheduling process involves a significant degree of uncertainty. In order to deal with the uncertainty stemmed from geo-metallurgical and financial variables, two approaches are recommended in this paper. Firstly, mine production scheduling is formulated as a problem of stochastic programming with recourse. The extraction periods of mining blocks are treated as the first-stage variables and the block destinations represents a recourse vector. It is observed that the solution is implicitly robust. Secondly, the scheduling is expressed as a maximin problem to extract more uniform metal quantity in periods to coincide with mill requirements instead of maximization of net present value because the blending constraint in the traditional approach forces more uniform production. In the case where there is correlation between grade and geo-metallurgical variables, this model generates reasonably good results.