•Workload smoothing in simple assembly line balancing is analyzed.•A station-oriented branch-and-bound procedure is developed.•Novel workload generation scheme based on dynamic ...programming.•Computational results attest to SALSA’s superiority over existing procedures.•Particularly good performance on realistic problem instances.
We consider a version of the well-known simple assembly line balancing problem (called SALBP-SX) where, given the cycle time and the number of stations, the workloads of the stations are to be leveled according to an adequately defined smoothness index SX. Our index SX involves for each station the quadratic deviation of its workload from the average (or ideal) workload and is therefore closely related to the variance, which is a common measure of dispersion in statistics. Contrary to the existing literature on workload smoothing in ALB, which often treats the optimization of a prespecified smoothness index as a secondary objective, we consider our SX-objective as the single one in order to account for the practical relevance of fair workload distributions and avoiding overloaded bottleneck stations.
To optimally solve SALBP-SX, we develop a tailored branch-and-bound procedure. It contains a new station-oriented branching scheme, new lower bound arguments, logical tests and, in particular, a dynamic programming scheme for the pre-calculation of potential workloads, which accelerates the procedure greatly. In comprehensive computational experiments, we show that our method clearly outperforms a class of recently developed task-oriented branch-and-bound procedures and also the mathematical programming solver Gurobi.
•The workload smoothing problem on simple assembly lines is studied.•A bidirectional branch, bound, and remember algorithm is developed.•Several new and enhanced subroutines are developed and ...implemented.•The broad applicability of our solution method is demonstrated.•R-SALSA clearly outperforms all former procedures.
We consider a simple assembly line balancing problem with given cycle time and number of stations. A quadratic objective function based on a so-called smoothness index SX levels the workloads of the stations. For this problem, called SALBP-SX, only a few solution procedures have been proposed in literature so far. In this paper, we extend and improve the branch-and-bound procedure SALSA (Simple Assembly Line Smoothing Algorithm) of Walter et al. (2021) to a bidirectional branch, bound, and remember algorithm called R-SALSA (R for remember). Like SALSA, it is based on a dynamic programming scheme which pre-determines potential workloads of the stations and provides a construction plan for possible station loads. This scheme is extended by the new concept of supporters and preventers which significantly enhances branching, bounding, and logical tests. Furthermore, a tailored heuristic that searches for improved initial solutions, a bidirectional branching scheme and additional dominance rules are integrated. In extensive computational experiments, we find out that our new procedure clearly outperforms all former exact solution procedures on benchmark data sets with up to 1000 tasks.
We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs time-dependent transformation operators ...and, especially, generalizes MFEM to arbitrary basis functions. The new framework is suitable to obtain a low-dimensional approximation with small errors even in situations where classical model order reduction techniques require much higher dimensions for a similar approximation quality. Analogously to the MFEM framework, the reduced model is designed to minimize the residual, which is also the basis for an
a posteriori
error bound. Moreover, since the dependence of the transformation operators on the reduced state is nonlinear, the resulting reduced order model is obtained by projecting the original evolution equation onto a nonlinear manifold. Furthermore, for a special case, we show a connection between our approach and the method of freezing, which is also known as symmetry reduction. Besides the construction of the reduced order model, we also analyze the problem of finding optimal basis functions based on given data of the full order solution. Especially, we show that the corresponding minimization problem has a solution and reduces to the proper orthogonal decomposition of transformed data in a special case. Finally, we demonstrate the effectiveness of our method with several analytical and numerical examples.
We study linear quadratic Gaussian (LQG) control design for linear port-Hamiltonian systems. To this end, we exploit the freedom in choosing the weighting matrices and propose a specific choice which ...leads to an LQG controller which is port-Hamiltonian and, thus, in particular stable and passive. Furthermore, we construct a reduced-order controller via balancing and subsequent truncation. This approach is closely related to classical LQG balanced truncation and shares a similar a priori error bound with respect to the gap metric. By exploiting the non-uniqueness of the Hamiltonian, we are able to determine an optimal pH representation of the full-order system in the sense that the error bound is minimized. In addition, we discuss consequences for pH-preserving balanced truncation model reduction which results in two different classical H∞-error bounds. Finally, we illustrate the theoretical findings by means of two numerical examples.
Smoothing the workloads among the stations of an already installed assembly line is one of the major objectives in assembly line (re-)balancing. In order to find a feasible task-station assignment ...that distributes the total workload as equal as possible, two exact task-oriented branch-and-bound algorithms have recently been proposed. In this paper, we systematically analyse their effectiveness in solving the workload smoothing problem on simple assembly lines. In our experiments, we also examine the performance of a state-of-the-art mathematical programming solver and a 'combined' exact branch-and-bound procedure that integrates components of the two algorithms from the literature. In terms of theory, we show the equivalence of two recently developed local lower bounding arguments and suggest a slight improvement of the bound. We also propose an enhanced feasibility test.
Data-driven structured realization Schulze, Philipp; Unger, Benjamin; Beattie, Christopher ...
Linear algebra and its applications,
01/2018, Letnik:
537
Journal Article
Recenzirano
Odprti dostop
We present a framework for constructing structured realizations of linear dynamical systems having transfer functions of the form C˜(∑k=1Khk(s)A˜k)−1B˜ where h1,h2,...,hK are prescribed functions ...that specify the surmised structure of the model. Our construction is data-driven in the sense that an interpolant is derived entirely from measurements of a transfer function. Our approach extends the Loewner realization framework to a more general system structure that includes second-order (and higher) systems as well as systems with internal delays. Numerical examples demonstrate the advantages of this approach.
Herein, we summarize the current status of native fluorescence detection in microchannel electrophoresis, with a strong focus on chip-based systems. Fluorescence detection is a powerful technique ...with unsurpassed sensitivity down to the single-molecule level. Accordingly fluorescence detection is attractive in combination with miniaturised separation techniques. A drawback is, however, the need to derivatize most analytes prior to analysis. This can often be circumvented by utilising excitation light in the UV spectral range in order to excite intrinsic fluorescence. As sensitive absorbance detection is challenging in chip-based systems, deep-UV fluorescence detection is currently one of the most general optical detection techniques in microchip electrophoresis, which is especially attractive for the detection of unlabelled proteins. This review gives an overview of research on native fluorescence detection in capillary (CE) and microchip electrophoresis (MCE) between 1998 and 2008. It discusses material aspects of native fluorescence detection and the instrumentation used, with particular focus on the detector design. Newer developments, featured techniques, and their prospects in the future are also included. In the last section, applications in bioanalysis, drug determination, and environmental analysis are reviewed with regard to limits of detection.
•The Singapore state changed its strategic role in engaging with foreign universities.•Singapore moved from importing global knowledge to fostering local skill formation.•More recently set up ...offshore campuses are more embedded in local skill formation.•Offshore campuses with high levels of embeddedness serve specifically local functions.
With operating offshore campuses, universities perform key education and training functions in regional economies worldwide. Few studies have acknowledged universities’ expanded role in knowledge and skill formation as both local providers and transnational managers of education and training. Not enough is known about the embedding of transnational universities in local skill formation and varying levels of embeddedness, as well as about the role of hosting states therein and consequences for local economies. This paper addresses this gap in the context of the city-state of Singapore, exploring how skill development at foreign universities has been locally embedded, and why this embeddedness of offshore campuses in local skill formation has changed over time. Empirical evidence is drawn from semi-structured interviews with managers of foreign university subsidiaries. It is found that the Singapore state has changed its role in engaging with foreign universities, from a first phase of importing ‘global’ knowledge in teaching and training to a second phase of strengthening ‘local’ knowledge and skill formation. With being distinctively more embedded than older offshore campuses, recently established subsidiaries perform specifically ‘local’ functions in Singapore’s progressing knowledge-based transformation project. The paper provides better understanding of varying/changing levels of offshore campus embeddedness and the interconnections between changing roles of the state, integration of foreign universities and regional development. A further contribution lies in presenting a conceptualisation of offshore campuses with high levels of embeddedness, helping shed light on the dynamics in local skill formation and in foreign actors’ functions for the regional economy more generally.
Transport-dominated systems are characterized by the propagation of waves and occur in many applications such as aerodynamics and chemical engineering. To predict the dynamics of such systems, ...mathematical models should ideally be fast to evaluate and at the same time sufficiently accurate. One possibility for deriving such models is to start with a complex and accurate full-order model (FOM) and use model order reduction (MOR) techniques to obtain a corresponding reduced-order model (ROM). Classical MOR methods are based on approximating the FOM state by a linear combination of ansatz functions or modes, but such approaches are often inadequate in the context of transport-dominated systems. This is one of the reasons why there has been an increasing research effort in the past years to develop MOR techniques which are based on nonlinear approximation ansatzes.As the field of nonlinear MOR is relatively new, there are still many open research questions to be addressed. These include for instance suitable choices for the approximation ansatz as well as appropriate ways for the construction of corresponding ROMs. Furthermore, nonlinear MOR approaches typically lead to ROMs whose evaluation scales with the dimension of the FOM and thus may be too expensive. In fact, similar issues may also occur in the context of linear MOR approaches and, therefore, one uses so-called hyperreduction techniques to obtain fast ROMs. However, classical hyperreduction methods suffer from similar difficulties as classical MOR schemes when being applied to transport-dominated systems. Another challenge is to develop nonlinear MOR techniques which preserve important system properties such as stability.In this thesis, we present a new nonlinear model reduction framework which is based on approximating the state of the FOM by a linear combination of transformed modes. The transformations may be, e.g., achieved by shift operators and are parametrized by so-called paths or shift amounts, which constitute a part of the ROM state. The resulting class of ansatzes is well-suited for obtaining low-dimensional and accurate approximations of transport-dominated systems. For the determination of the modes, we present an optimization approach based on given snapshot data of the FOM state. Furthermore, the construction of the ROM is carried out via a residual minimization approach and we also suggest a new hyperreduction framework to ensure that the ROM can be efficiently evaluated. In addition, we demonstrate how to preserve stability via an energy-based formulation using the framework of so-called port-Hamiltonian systems. Finally, we illustrate the new methodology by means of numerical experiments for some transport-dominated test cases.
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