Conventional underground long-term mine planning is based on a deterministic stepwise framework, which is unable to effectively manage the synergies between the mine planning components or to manage the orebody risk i...
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Conventional underground long-term mine planning is based on a deterministic stepwise framework, which is unable to effectively manage the synergies between the mine planning components or to manage the orebody risk in production schedules and forecasts. The present study enhances prior integrated optimisation approaches to a variation of the sublevel longhole open stoping mining method using backfilling, through a new two-stage stochastic integer programming formulation. A comparison to a sequential stochastic approach shows different stope layouts and extraction sequences for a copper mine with secondary elements being gold and uranium. The integrated approach shows lower horizontal development costs and 6% higher net present value.
It is common practice for underground mine plans to be created sequentially, where results from one planning process form the input data for another. While this is practical for manual methods, computerized optimizati...
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It is common practice for underground mine plans to be created sequentially, where results from one planning process form the input data for another. While this is practical for manual methods, computerized optimization techniques should consider an integrated approach to creating the global mine plan. This is because optimizing an individual mine planning process, such as stope layouts, introduces a likelihood of increasing costs or decreasing revenues associated with other areas, such as production scheduling, as harmful decisions must be balanced. Considering the interaction and influence that individual underground mine planning processes have on each other during optimization will provide more profitable results than if these are ignored. Optimization techniques for stope layouts and production scheduling are reviewed. An integer programming model is proposed that allows for either integrated or isolated optimization. Both approaches are separately applied to a block model. The results demonstrate the model's ability to produce optimal long-term sublevel stoping mine plans and the benefits of using an integrated approach.
Mixed integer programming (MIP) has been used for optimizing production schedules of mines since the 1960s and is-recognized as having significant potential for optimizing production scheduling problems for both surfa...
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Mixed integer programming (MIP) has been used for optimizing production schedules of mines since the 1960s and is-recognized as having significant potential for optimizing production scheduling problems for both surface and underground mining. The major problem in long-term production scheduling for underground orebodies generally relate to the large number of variables needed to formulate a MIP model, which makes it too complex to solve. As the number of variables in the model increase, solution times are known to increase at an exponential rate. In many instances-the more extensive use of MIP models has been limited due to excessive solution times. This paper reviews production schedule optimization studies for underground mining operations. It also presents a classical MIP model for optimized production scheduling of a sublevel stoping operation and proposes a new model formulation to significantly reduce solution times without altering results while maintaining all constraints. A case study is summarized investigating solution times as five stopes are added incrementally to an initial ten stope operation, working up to a fifty stope operation. It shows substantial improvement in the solution time required when. using the new formulation technique. This increased efficiency in the solution time of the MIP model allows it to solve much larger underground mine scheduling problems within a reasonable time frame with the potential to substantially increase the net present value (NPV) of these projects. Finally, results from the two Models are also compared to that of a manually generated schedule which show the clear advantages of mathematicalprogramming in obtaining optimal solutions.
The sales territory alignment problem may be viewed as the problem of grouping small geographic sales coverage units into larger geographic clusters called sales territories in a way that the sales territories are acc...
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The sales territory alignment problem may be viewed as the problem of grouping small geographic sales coverage units into larger geographic clusters called sales territories in a way that the sales territories are acceptable according to managerially relevant alignment criteria. This paper first reviews sales territory alignment models which have appeared in the marketing literature. A framework for sales territory alignment and several properties of a good sales territory alignment are developed in the course of the review. A general sales territory alignment model which accommodates these properties is developed. A solution procedure for the general model is presented. Finally, an actual implementation of the general model is described. The implementation provides a comparison of the general model with a similar model which has been frequently cited in the marketing literature.
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