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Boland N.,University of Newcastle | Bley A.,TU Berlin | Fricke C.,TSG Consulting | Froyland G.,University of New South Wales | Sotirov R.,University of Tilburg
Mathematical Programming | Year: 2012

We consider a knapsack problem with precedence constraints imposed on pairs of items, known as the precedence constrained knapsack problem (PCKP). This problem has applications in manufacturing and mining, and also appears as a subproblem in decomposition techniques for network design and related problems. We present a new approach for determining facets of the PCKP polyhedron based on clique inequalities. A comparison with existing techniques, that lift knapsack cover inequalities for the PCKP, is also presented. It is shown that the clique-based approach generates facets that cannot be found through the existing cover-based approaches, and that the addition of clique-based inequalities for the PCKP can be computationally beneficial, for both PCKP instances arising in real applications, and applications in which PCKP appears as an embedded structure. © 2011 Springer and Mathematical Optimization Society. Source


Volz M.G.,TSG Consulting | Brazil M.,University of Melbourne | Ras C.J.,University of Melbourne | Swanepoel K.J.,The London School of Economics and Political Science | Thomas D.A.,University of Melbourne
Networks | Year: 2013

We investigate the problem of designing a minimum-cost flow network interconnecting n sources and a single sink, each with known locations in a normed space and with associated flow demands. The network may contain any finite number of additional unprescribed nodes from the space; these are known as the Steiner points. For concave increasing cost functions, a minimum-cost network of this sort has a tree topology, and hence can be called a Minimum Gilbert Arborescence (MGA). We characterize the local topological structure of Steiner points in MGAs, showing, in particular, that for a wide range of metrics, and for some typical real-world cost functions, the degree of each Steiner point is 3. © 2012 Wiley Periodicals, Inc. Source


Sandeman T.,TSG Consulting | Fricke C.,TSG Consulting | Bodon P.,TSG Consulting | Stanford C.,PT Kaltim Prima Coal
Proceedings - Winter Simulation Conference | Year: 2010

This paper describes the benefits of integrating optimization formulations within simulation models. Two different case studies in mining are presented, both requiring a blending optimization. The primary problem at hand is to model a complex supply chain involving blending of multiple inputs to produce a number of potential products for customers. The first approach involves solving an optimization model to produce a long term plan, then simulating this plan over time without the ability to change the plan as time progresses. The second approach involves a more integrated system where multiple instances of an optimization model are run throughout the simulation using updated inputs. A description of the problem is supplied, providing the need for both optimization and simulation, and then the two case studies are compared to show the benefits of integrating the optimization within the simulation model. ©2010 IEEE. Source


Bodon P.,TSG Consulting | Fricke C.,TSG Consulting | Sandeman T.,TSG Consulting | Stanford C.,PT Kaltim Prima Coal
Journal of Mining Science | Year: 2011

This paper describes a method for modeling a complex export supply chain using a combination of optimization and Discrete Event Simulation techniques to enable capacity analysis and evaluation of expansion options. A description of the modeling process is presented along with a case study of a successful implementation of the approach to analyze the export supply chain of PT Kaltim Prima Coal in Indonesia. © 2011 Pleiades Publishing, Ltd. Source

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