Global supply chains of high value low volume products

Imperial Users onl

An odyssey into local refinement and multilevel preconditioning III: Implementation and numerical experiments

In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform refinement-based discretizations of elliptic equations, they tend to be less effective for algebraic systems, which arise from discretizations on locally refined meshes, losing their optimal behavior in both storage and computational complexity. Our primary focus here is on Bramble, Pasciak, and Xu (BPX)-style additive and multiplicative multilevel preconditioners, and on various stabilizations of the additive and multiplicative hierarchical basis (HB) method, and their use in the local mesh refinement setting. In parts I and II of this trilogy, it was shown that both BPX and wavelet stabilizations of HB have uniformly bounded condition numbers on several classes of locally refined two- and three-dimensional meshes based on fairly standard (and easily implementable) red and red-green mesh refinement algorithms. In this third part of the trilogy, we describe in detail the implementation of these types of algorithms, including detailed discussions of the data structures and traversal algorithms we employ for obtaining optimal storage and computational complexity in our implementations. We show how each of the algorithms can be implemented using standard data types, available in languages such as C and FORTRAN, so that the resulting algorithms have optimal (linear) storage requirements, and so that the resulting multilevel method or preconditioner can be applied with optimal (linear) computational costs. We have successfully used these data structure ideas for both MATLAB and C implementations using the FEtk, an open source finite element software package. We finish the paper with a sequence of numerical experiments illustrating the effectiveness of a number of BPX and stabilized HB variants for several examples requiring local refinement

Planning complex engineer-to-order products

The design and manufacture of complex Engineer-to-Order products is characterised by uncertain operation durations, finite capacity resources and multilevel product structures. Two scheduling methods are presented to minimise expected costs for multiple products across multiple finite capacity resources. The first sub-optimises the operations sequence, using mean operation durations, then refines the schedule by perturbation. The second method generates a schedule of start times directly by random search with an embedded simulation of candidate schedules for evaluation. The methods are compared for industrial examples

The integrated use of enterprise and system dynamics modelling techniques in support of business decisions

Enterprise modelling techniques support business process re-engineering by capturing existing processes and based on perceived outputs, support the design of future process models capable of meeting enterprise requirements. System dynamics modelling tools on the other hand are used extensively for policy analysis and modelling aspects of dynamics which impact on businesses. In this paper, the use of enterprise and system dynamics modelling techniques has been integrated to facilitate qualitative and quantitative reasoning about the structures and behaviours of processes and resource systems used by a Manufacturing Enterprise during the production of composite bearings. The case study testing reported has led to the specification of a new modelling methodology for analysing and managing dynamics and complexities in production systems. This methodology is based on a systematic transformation process, which synergises the use of a selection of public domain enterprise modelling, causal loop and continuous simulationmodelling techniques. The success of the modelling process defined relies on the creation of useful CIMOSA process models which are then converted to causal loops. The causal loop models are then structured and translated to equivalent dynamic simulation models using the proprietary continuous simulation modelling tool iThink