## Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report)

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#### Year of publication

- 2007 (28) (remove)

#### Keywords

- numerical upscaling (4)
- Darcy’s law (2)
- effective heat conductivity (2)
- single phase flow (2)
- 3D (1)
- Asymptotic Expansion (1)
- Bayesian Model Averaging (1)
- Betriebsfestigkeit (1)
- Boolean polynomials (1)
- Bootstrap (1)

- 133
- New approaches to hub location problems in public transport planning (2007)
- In this paper, a new mixed integer mathematical programme is proposed for the application of Hub Location Problems (HLP) in public transport planning. This model is among the few existing ones for this application. Some classes of valid inequalities are proposed yielding a very tight model. To solve instances of this problem where existing standard solvers fail, two approaches are proposed. The first one is an exact accelerated Benders decomposition algorithm and the latter a greedy neighborhood search. The computational results substantiate the superiority of our solution approaches to existing standard MIP solvers like CPLEX, both in terms of computational time and problem instance size that can be solved. The greedy neighborhood search heuristic is shown to be extremely efficient.

- 132
- An efficient approach for upscaling properties of composite materials with high contrast of coefficients (2007)
- An efficient approach for calculating the effective heat conductivity for a class of industrial composite materials, such as metal foams, fibrous glass materials, and the like, is discussed. These materials, used in insulation or in advanced heat exchangers, are characterized by a low volume fraction of the highly conductive material (glass or metal) having a complex, network-like structure and by a large volume fraction of the insulator (air). We assume that the composite materials have constant macroscopic thermal conductivity tensors, which in principle can be obtained by standard up-scaling techniques, that use the concept of representative elementary volumes (REV), i.e. the effective heat conductivities of composite media can be computed by post-processing the solutions of some special cell problems for REVs. We propose, theoretically justify, and numerically study an efficient approach for calculating the effective conductivity for media for which the ratio of low and high conductivities satisfies 1. In this case one essentially only needs to solve the heat equation in the region occupied by the highly conductive media. For a class of problems we show, that under certain conditions on the microscale geometry, the proposed approach produces an upscaled conductivity that is O() close to the exact upscaled permeability. A number of numerical experiments are presented in order to illustrate the accuracy and the limitations of the proposed method. Applicability of the presented approach to upscaling other similar problems, e.g. flow in fractured porous media, is also discussed.

- 131
- Bringing robustness to patient flow management through optimized patient transports in hospitals (2007)
- Intra-hospital transports are often required for diagnostic or therapeutic reasons. Depending on the hospital layout, transportation between nursing wards and service units is either provided by ambulances or by trained personnel who accompany patients on foot. In many large German hospitals, the patient transport service is poorly managed and lacks workflow coordination. This contributes to higher hospital costs (e.g. when a patient is not delivered to the operating room on time) and to patient inconvenience due to longer waiting times. We have designed a computer-based planning system - Opti-TRANS c - that supports all phases of the transportation flow, ranging from travel booking, dispatching transport requests to monitoring and reporting trips in real-time. The methodology developed to solve the underlying optimization problem - a dynamic dial-a-ride problem with hospital-specific constraints - draws on fast heuristic methods to ensure the efficient and timely provision of transports. We illustrate the strong impact of Opti-TRANS c on the daily performance of the patient transportation service of a large German hospital. The major benefits obtained with the new tool include streamlined transportation processes and workflow, significant savings and improved patient satisfaction. Moreover, the new planning system has contributed to increase awareness among hospital staff about the importance of implementing efficient logistics practices.

- 130
- Facility Location and Supply Chain Management – A comprehensive review (2007)
- Facility location decisions play a critical role in the strategic design of supply chain networks. In this paper, an extensive literature review of facility location models in the context of supply chain management is given. Following a brief review of core models in facility location, we identify basic features that such models must capture to support decision-making involved in strategic supply chain planning. In particular, the integration of location decisions with other decisions relevant to the design of a supply chain network is discussed. Furthermore, aspects related to the structure of the supply chain network, including those specific to reverse logistics, are also addressed. Significant contributions to the current state-of-the-art are surveyed taking into account numerous factors. Supply chain performance measures and optimization techniques are also reviewed. Applications of facility location models to supply chain network design ranging across various industries are discussed. Finally, a list of issues requiring further research are highlighted.

- 129
- Computation of the permeability of porous materials from their microstructure by FFF-Stokes (2007)
- A fully automatic procedure is proposed to rapidly compute the permeability of porous materials from their binarized microstructure. The discretization is a simplified version of Peskin’s Immersed Boundary Method, where the forces are applied at the no-slip grid points. As needed for the computation of permeability, steady flows at zero Reynolds number are considered. Short run-times are achieved by eliminating the pressure and velocity variables using an Fast Fourier Transform-based and 4 Poisson problembased fast inversion approach on rectangular parallelepipeds with periodic boundary conditions. In reference to calling it a fast method using fictitious or artificial forces, the implementation is called FFF-Stokes. Large scale computations on 3d images are quickly and automatically performed to estimate the permeability of some sample materials. A matlab implementation is provided to allow readers to experience the automation and speed of the method for realistic three-dimensional models.

- 128
- On the role of modeling parameters in IMRT plan optimization (2007)
- Modeling and formulation of optimization problems in IMRT planning comprises the choice of various values such as function-specific parameters or constraint bounds. These values also affect the characteristics of the optimization problem and thus the form of the resulting optimal plans. This publication utilizes concepts of sensitivity analysis and elasticity in convex optimization to analyze the dependence of optimal plans on the modeling parameters. It also derives general rules of thumb how to choose and modify the parameters in order to obtain the desired IMRT plan. These rules are numerically validated for an exemplary IMRT planning problems.

- 127
- Pareto navigation – systematic multicriteria-based IMRT treatment plan determination (2007)
- Background and purpose Inherently, IMRT treatment planning involves compromising between different planning goals. Multi-criteria IMRT planning directly addresses this compromising and thus makes it more systematic. Usually, several plans are computed from which the planner selects the most promising following a certain procedure. Applying Pareto navigation for this selection step simultaneously increases the variety of planning options and eases the identification of the most promising plan. Material and methods Pareto navigation is an interactive multi-criteria optimization method that consists of the two navigation mechanisms “selection” and “restriction”. The former allows the formulation of wishes whereas the latter allows the exclusion of unwanted plans. They are realized as optimization problems on the so-called plan bundle – a set constructed from precomputed plans. They can be approximately reformulated so that their solution time is a small fraction of a second. Thus, the user can be provided with immediate feedback regarding his or her decisions.

- 126
- A novel non-linear approach to minimal area rectangular packing (2007)
- This paper disscuses the minimal area rectangular packing problem of how to pack a set of specified, non-overlapping rectangels into a rectangular container of minimal area. We investigate different mathematical programming approaches of this and introduce a novel approach based on non-linear optimization and the \\\"tunneling effect\\\" achieved by a relaxation of the non-overlapping constraints.

- 125
- Heterogeneous redundancy in software quality prediction using a hybrid Bayesian approach (2007)
- With the ever-increasing significance of software in our everyday lives, it is vital to afford reliable software quality estimates. Typically, quantitative software quality analyses rely on either statistical fault prediction methods (FPMs) or stochastic software reliability growth models (SRGMs). Adopting solely FPMs or SRGMs, though, may result in biased predictions that do not account for uncertainty in the distinct prediction methods; thus rendering the prediction less reliable. This paper identifies flaws of the individual prediction methods and suggests a hybrid prediction approach that combines FPMs and SRGMs. We adopt FPMs for initially estimating the expected number of failures for fi- nite failure SRGMs. Initial parameter estimates yield more accurate reliability predictions until sufficient failures are observed that enable stable parameter estimates in SRGMs. Being at the equilibrium level of FPM and SRGM pre- dictions we suggest combining the competing prediction methods with respect to the principle of heterogeneous redundancy. That is, we propose using the in- dividual methods separately and combining their predictions. In this paper we suggest Bayesian model averaging (BMA) for combining the different methods. The hybrid approach allows early reliability estimates and encourages higher confidence in software quality predictions.

- 124
- A Comparative Study of the Vasicek and the CIR Model of the Short Rate (2007)
- In this work, we analyze two important and simple models of short rates, namely Vasicek and CIR models. The models are described and then the sensitivity of the models with respect to changes in the parameters are studied. Finally, we give the results for the estimation of the model parameters by using two different ways.