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1.
An Application of Branch and Cut to Open Pit Mine Scheduling 总被引:5,自引:0,他引:5
The economic viability of the modern day mine is highly dependent upon careful planning and management. Declining trends in average ore grades, increasing mining costs and environmental considerations will ensure that this situation will remain in the foreseeable future. The operation and management of a large open pit mine having a life of several years is an enormous and complex task. Though a number of optimization techniques have been successfully applied to resolve some important problems, the problem of determining an optimal production schedule over the life of the deposit is still very much unresolved. In this paper we will critically examine the techniques that are being used in the mining industry for production scheduling indicating their limitations. In addition, we present a mixed integer linear programming model for the scheduling problems along with a Branch and Cut solution strategy. Computational results for practical sized problems are discussed. 相似文献
2.
André Kündgen 《Discrete Mathematics》2005,296(1):121-128
A cycle cover (cut cover) of a graph G is a collection of cycles (cuts) of G that covers every edge of G at least once. The total size of a cycle cover (cut cover) is the sum of the number of edges of the cycles (cuts) in the cover.We discuss several results for cycle covers and the corresponding results for cut covers. Our main result is that every connected graph on n vertices and e edges has a cut cover of total size at most 2e-n+1 with equality precisely when every block of the graph is an odd cycle or a complete graph (other than K4 or K8). This corresponds to the result of Fan [J. Combin. Theory Ser. B 74 (1998) 353-367] that every graph without cut-edges has a cycle cover of total size at most e+n-1. 相似文献
3.
We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φω (0) (while that of PA or of Kirby-Paris' Game is φ1 (0) = ?0) in the Veblen hierarchy of ordinals. 相似文献
4.
In this paper, we develop a novel adjacency matrix, He-matrix, corresponding to the dualist graph. Without using the graph center concept, we advance a novel nomenclature of polycyclic aromatic hydrocarbons. Further, we derive some distinguishing theorems about PAH molecules and present some results of our automatic derivatization and automatic classification counting of fused PAH molecules. 相似文献
5.
Flow field-flow fractionation (flow FFF), a separation technique for particles and macromolecules, has been used to separate carbon nanotubes (CNT). The carbon nanotube ropes that were purified from a raw carbon nanotube mixture by acidic reflux followed by cross-flow filtration using a hollow fiber module were cut into shorter lengths by sonication under a concentrated acid mixture. The cut carbon nanotubes were separated by using a modified flow FFF channel system, frit inlet asymmetrical flow FFF (FI AFIFFF) channel, which was useful in the continuous flow operation during injection and separation. Carbon nanotubes, before and after the cutting process, were clearly distinguished by their retention profiles. The narrow volume fractions of CNT collected during flow FFF runs were confirmed by field emission scanning electron microscopy and Raman spectroscopy. Experimentally, it was found that retention of carbon nanotubes in flow FFF was dependent on the use of surfactant for CNT dispersion and for the carrier solution in flow FFF. In this work, the use of flow FFF for the size differentiation of carbon nanotubes in the process of preparation or purification was demonstrated. 相似文献
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We consider the Robust Network Design problem, i.e. the problem of dimensioning the capacities on the edges of a graph to serve point-to-point traffic demands subject to uncertainty. The scope of the paper is to investigate when the cut condition is sufficient to guarantee the feasibility for such problem. 相似文献
8.
This paper investigates the integration of the employee timetabling and production scheduling problems. At the first level, we manage a classical employee timetabling problem. At the second level, we aim at supplying a feasible production schedule for a set of interruptible tasks with qualification requirements and time-windows. Instead of hierarchically solving these two problems as in the current practice, we try here to integrate them and propose two exact methods to solve the resulting problem. The former is based on a Benders decomposition while the latter relies on a specific decomposition and a cut generation process. The relevance of these different approaches is discussed here through experimental results. 相似文献
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