For cost and reliability efficiency, optimal design and operation of pressurized water distribution networks is highly important. However, optimizing such networks is still a challenge since it requires an appropriate determination of: (1) dimension of pipe / pump / tank - decision variables (2) cost / network reliability - objective functions and (3) limits or restrictions within which the network must operate - a given set of constraints. The costs mentioned here consist in general of capital, construction, and operation costs. The reliability of a network mainly refers to the intrinsic capability of providing water with adequate volume and a certain pressure to consumers under normal and extreme conditions. These contradicting objective functions are functions of network configuration regarding component sizes and network layout. Because considerable uncertainties finally render the overall task to a highly complex problem, most recent approaches mainly focus only on finding a trade-off between minimizing cost and maximizing network reliability. To overcome these limitations, a novel model system that simultaneously considers network configuration, its operation and the relevant uncertainties is proposed in this study. For solving this multi-objective design problem, a simulation-based optimization approach has been developed and applied. The approach couples a hydraulic model (Epanet) with the covariance matrix adaptation evolution strategy (CMA-ES) and can be operated in two different modes. These modes are (1) simulation–based Single-objective optimization and (2) simulation-based multi-objective optimization. Single-objective optimization yields the single best solution with respect to cost or network reliability, whereas multi-objective optimization produces a set of non-dominated solutions called Pareto optimal solutions which are trade-offs between cost and reliability. In addition, to prevent a seriously under-designed network, demand uncertainties was also taken into account through a so called “robustness probability” of the network. This consideration may become useful for a more reliable water distribution network. In order to verify the performance of the proposed approach, it was systematically tested on a number of different benchmark water distribution networks ranging from simple to complex. These benchmark networks are either gravity-fed or pumped networks which need to be optimally designed to supply urban or irrigation water demand under specific constraints. The results show that the new approach is able: • to solve optimization problems of pressurized water distribution network design and operation regarding cost and network reliability; • to directly determine the pumping discharge and head, thus allowing to select pumps more adequately; • to simulate time series of tank water level; • to eliminate redundant pipes and pumps to generate an optimal network layout; • to respond well to complex networks other than only to simple networks; • to perform with multiple demand loading; • to produce reliable Pareto optimal solutions regarding multi-objective optimization. In conclusion, the new technique can be successfully applied for optimization problems in pressurized water distribution network design and operation. The new approach has been demonstrated to be a powerful tool for optimal network design not only for irrigation but also for an urban water supply.

Individual decision-making and the generation of medical demand are crucial subjects in healthcare economics. The following scientific discussion can be classified into these threads. The demand for health care services is typically connected to characteristic imperfections reflecting a bias between an objective and a subjective assessment of a specific demand situation or externally caused frictions. For that reason, the realized demand is not necessarily connected to an efficient allocation of resources. Hence, it is a crucial objective to analyze individual decision-making related on the one hand to specific treatment alternatives and on the other hand to the specified decision framework. This framework is characterized by both the attributes of the individual as well as by the external conditions in which the decision takes place. Theirby, the analysis focuses specifically on potential sources of demand inefficiency and their effectiveness. The following discussion broach the issue of two significant objectives within health economics: 1. Trade in medical care and patient migration, 2. Patient autonomy and education. Both fields find their analytical basis in a micro-economic discussion of individual decision behavior. The first field analyzes the decision between medical provision at home or abroad. This subject is specifically related to a potential efficiency gain due to the existence of cross-border price and quality gradients, usually a source of gains in trade. In the focus of the analysis is the impact of the specific characteristics of these gradients as determinants of cross-border medical demand. The second field discusses the investment decision in measures of patient education and prevention in a framework of a common consultation and self-care as imperfect treatment alternatives due to imperfect competences of self-diagnosis and medical self-supply. This subject is related to the commonly acknowledged positive correlation between health and education. Education is able to improve the quality of health production and, therefore, has a specific impact with respect to increasing autonomous behavior of the individual in issues of health production. The specific environment of these decisions significantly influences the mechanism of decision-making and the final outcome; this must be assessed according to the effect on the allocative efficiency of medical demand. The role of price and quality gradients between alternatives, the differentiation of illnesses, as well as subjective factors, are crucial to the results. Moreover, the individual's ability to appraise his or her own health stock and demand decisions is itself risky. Therefore, the form of the insurance coverage is another important element when analyzing individual decisions. The following discussion will clarify the decision-making mechanisms and their impact on efficient resource allocation. Since the focus is on demand behavior, the interaction with, and therefore the behavior of, the supply side is not explicitly formulated.

Die vorliegende Ausgabe konzentriert sich auf die Auswahl einer sinnvollen Analysemethode auf Basis des Realoptionsansatzes zur Analyse der Auswirkungen des demografischen Wandels auf die Siedlungsentwässerung. In der Literatur finden unterschiedliche Bewertungstechniken und verschiedene Bewertungsansätze der Realoptionstheorie Anwendung. Die in dieser Arbeit entwickelte Analysemethode kombiniert den qualitativen und den quantitativen Bewertungsansatz miteinander und plädiert für die Bewertungstechnik des Binomialmodells. Es wird eine Methode in fünf Arbeitsschritten vorgestellt, in der Kriterienüberprüfungen hinsichtlich des Vorhandenseins von Unsicherheit und Flexibilität vorgesehen sind. Zur empirischen Anwendung der Analysemethode bietet sich als Untersuchungsgebiet die Abwasserinfrastruktur des Plattenbaugebietes Weißwasser-Süd an, da dort vielfältige Probleme infolge des demografischen Wandels auftreten. Die Analyse zeigt, dass die Kriterien zur Anwendung der entwickelten Methode, Unsicherheit und Flexibilität, hinsichtlich mehrerer Einflussfaktoren und Anpassungsmaßnahmen erfüllt sind und somit die Anwendung des Realoptionsansatzes gerechtfertigt ist. Die Anwendung der Analysemethode auf das Untersuchungsgebiet in Weißwasser offenbart für das Versorgungsunternehmen vielfältige Handlungsmöglichkeiten zum Umgang mit bestehenden Problemen und zur Anpassung an beeinflussende unsichere Faktoren. Weiterhin können mit Hilfe der Analyse die Vor- und Nachteile der ausgewählten Methode aufgezeigt werden, was für weitere Untersuchungen des Themengebietes hilfreich sein kann.

Die deterministische Modellierung des Niederschlags-Abfluss(N-A)-Prozesses mit flächendifferenzierten, prozessbasierten Modellen ist von zahlreichen Unsicherheiten beeinflusst. Diese Unsicherheiten resultieren hauptsächlich aus den genutzten Daten, die Messfehlern unterliegen sowie für eine flächendifferenzierte Modellierung entsprechend aufbereitet werden müssen, und der Abstraktion der natürlichen Prozesse im Modell selbst. Da N-A-Modelle in der hydrologischen Praxis vielfältig eingesetzt werden, sind Zuverlässigkeitsaussagen im Hinblick auf eine spezielle Anwendung nötig, um das Vertrauen in die Modellergebnisse zu festigen. Die neu entwickelte Strategie zur Analyse und Simulation der Unsicherheiten eines flächendifferenzierten, prozessbasierten N-A-Modells ermöglicht eine umfassende, globale und komponentenbasierte Unsicherheitsbestimmung. Am Beispiel des mesoskaligen Einzugsgebiets der Schwarzen Pockau/Pegel Zöblitz im mittleren Erzgebirge wird der Einfluss maßgebender Unsicherheiten im N-A-Prozess sowie deren Kombination zu einer Gesamt-Unsicherheit auf den Gebietsabfluss aufgezeigt. Zunächst werden die maßgebenden Unsicherheiten separat quantifiziert, wobei die folgenden Methoden eingesetzt werden: (i) Monte-Carlo Simulationen mit flächendifferenzierten stochastischen Bodenparametern zur Analyse des Einflusses unsicherer Bodeninformationen, (ii) Bayes’sche Inferenz und Markov-Ketten-Monte-Carlo Simulationen, die eine Unsicherheitsbestimmung der konzeptionellen Modellparameter der Abflussbildung und -konzentration ermöglichen und (iii) Monte-Carlo Simulationen mit stochastisch generierten Niederschlagsfeldern, die die raum-zeitliche Variabilität interpolierter Niederschlagsdaten beschreiben. Die Kombination der Unsicherheiten zu einer hydrologischen Unsicherheit und einer Gesamt-Unsicherheit erfolgt ebenfalls mit Monte-Carlo Methoden. Dieses Vorgehen ermöglicht die Korrelationen der Zufallsvariablen zu erfassen und die mehrdimensionale Abhängigkeitsstruktur innerhalb der Zufallsvariablen empirisch zu beschreiben. Die Ergebnisse zeigen für das Untersuchungsgebiet eine Dominanz der Unsicherheit aus der raum-zeitlichen Niederschlagsverteilung im Gebietsabfluss gefolgt von den Unsicherheiten aus den Bodeninformationen und den konzeptionellen Modellparametern. Diese Dominanz schlägt sich auch in der Gesamt-Unsicherheit nieder. Die aus Messdaten abgeleiteten Unsicherheiten weisen eine Heteroskedastizität auf, die durch den Prozessablauf geprägt ist. Weiterhin sind Indizien für eine Abhängigkeit der Unsicherheit von der Niederschlagsintensität sowie strukturelle Defizite des N-A-Modells sichtbar. Die neu entwickelte Strategie ist prinzipiell auf andere Gebiete und Modelle übertragbar. / Modelling rainfall-runoff (R-R) processes using deterministic, spatial distributed, process-based models is affected by numerous uncertainties. One major source of these uncertainties origins from measurement errors together with the errors occurring in the process of data processing. Inadequate representation of the governing processes in the model with respect to a given application is another source of uncertainty. Considering that R-R models are commonly used in the hydrologic practise a quantification of the uncertainties is essential for a realistic interpretation of the model results. The presented new framework allows for a comprehensive, total as well as component-based estimation of the uncertainties of model results from spatial distributed, process-based R-R modelling. The capabilities of the new framework to estimate the influence of the main sources of uncertainties as well as their combination to a total uncertainty is shown and analysed at the mesoscale catchment of the Schwarze Pockau of the Ore Mountains. The approach employs the following methods to quantify the uncertainties: (i) Monte Carlo simulations using spatial distributed stochastic soil parameters allow for the analysis of the impact of uncertain soil data (ii) Bayesian inference und Markov Chain Monte Carlo simulations, yield an estimate of the uncertainty of the conceptual model parameters governing the runoff formation and - concentration processes. (iii) Monte Carlo simulations using stochastically generated rainfall patterns describing the spatiotemporal variability of interpolated rainfall data. Monte Carlo methods are also employed to combine the single sources of uncertainties to a hydrologic uncertainty and a total uncertainty. This approach accounts for the correlations between the random variables as well as an empirical description of their multidimensional dependence structure. The example application shows a dominance of the uncertainty resulting from the spatio-temporal rainfall distribution followed by the uncertainties from the soil data and the conceptual model parameters with respect to runoff. This dominance is also reflected in the total uncertainty. The uncertainties derived from the data show a heteroscedasticity which is dominated by the process. Furthermore, the degree of uncertainty seems to depend on the rainfall intensity. The analysis of the uncertainties also indicates structural deficits of the R-R model. The developed framework can principally be transferred to other catchments as well as to other R-R models.

Zugl.: Aachen, Techn. Hochsch., Diss., 2008.

Zugl.: Leipzig, Universiẗat, Diss., 2008.

Zugleich: Diss. Hagen, 1997. / Literaturverz.

For cost and reliability efficiency, optimal design and operation of pressurized water distribution networks is highly important. However, optimizing such networks is still a challenge since it requires an appropriate determination of: (1) dimension of pipe / pump / tank - decision variables (2) cost / network reliability - objective functions and (3) limits or restrictions within which the network must operate - a given set of constraints. The costs mentioned here consist in general of capital, construction, and operation costs. The reliability of a network mainly refers to the intrinsic capability of providing water with adequate volume and a certain pressure to consumers under normal and extreme conditions. These contradicting objective functions are functions of network configuration regarding component sizes and network layout. Because considerable uncertainties finally render the overall task to a highly complex problem, most recent approaches mainly focus only on finding a trade-off between minimizing cost and maximizing network reliability. To overcome these limitations, a novel model system that simultaneously considers network configuration, its operation and the relevant uncertainties is proposed in this study. For solving this multi-objective design problem, a simulation-based optimization approach has been developed and applied. The approach couples a hydraulic model (Epanet) with the covariance matrix adaptation evolution strategy (CMA-ES) and can be operated in two different modes. These modes are (1) simulation–based Single-objective optimization and (2) simulation-based multi-objective optimization. Single-objective optimization yields the single best solution with respect to cost or network reliability, whereas multi-objective optimization produces a set of non-dominated solutions called Pareto optimal solutions which are trade-offs between cost and reliability. In addition, to prevent a seriously under-designed network, demand uncertainties was also taken into account through a so called “robustness probability” of the network. This consideration may become useful for a more reliable water distribution network. In order to verify the performance of the proposed approach, it was systematically tested on a number of different benchmark water distribution networks ranging from simple to complex. These benchmark networks are either gravity-fed or pumped networks which need to be optimally designed to supply urban or irrigation water demand under specific constraints. The results show that the new approach is able: • to solve optimization problems of pressurized water distribution network design and operation regarding cost and network reliability; • to directly determine the pumping discharge and head, thus allowing to select pumps more adequately; • to simulate time series of tank water level; • to eliminate redundant pipes and pumps to generate an optimal network layout; • to respond well to complex networks other than only to simple networks; • to perform with multiple demand loading; • to produce reliable Pareto optimal solutions regarding multi-objective optimization. In conclusion, the new technique can be successfully applied for optimization problems in pressurized water distribution network design and operation. The new approach has been demonstrated to be a powerful tool for optimal network design not only for irrigation but also for an urban water supply.

We examine the economic behavior of the regret-averse firm under price uncertainty. We show that the global and marginal effects of price uncertainty on production are both positive (negative) when regret aversion prevails if the random output price is positively (negatively) skewed. In this case, high (low) output prices are much more likely to be seen than low (high) output prices. To minimize regret, the firm is induced to raise (lower) its output optimal level. The skewness of the price distribution as such plays a pivotal role in determining the regret-averse firm\'s production decision.

Die vorliegende Ausgabe konzentriert sich auf die Auswahl einer sinnvollen Analysemethode auf Basis des Realoptionsansatzes zur Analyse der Auswirkungen des demografischen Wandels auf die Siedlungsentwässerung. In der Literatur finden unterschiedliche Bewertungstechniken und verschiedene Bewertungsansätze der Realoptionstheorie Anwendung. Die in dieser Arbeit entwickelte Analysemethode kombiniert den qualitativen und den quantitativen Bewertungsansatz miteinander und plädiert für die Bewertungstechnik des Binomialmodells. Es wird eine Methode in fünf Arbeitsschritten vorgestellt, in der Kriterienüberprüfungen hinsichtlich des Vorhandenseins von Unsicherheit und Flexibilität vorgesehen sind. Zur empirischen Anwendung der Analysemethode bietet sich als Untersuchungsgebiet die Abwasserinfrastruktur des Plattenbaugebietes Weißwasser-Süd an, da dort vielfältige Probleme infolge des demografischen Wandels auftreten. Die Analyse zeigt, dass die Kriterien zur Anwendung der entwickelten Methode, Unsicherheit und Flexibilität, hinsichtlich mehrerer Einflussfaktoren und Anpassungsmaßnahmen erfüllt sind und somit die Anwendung des Realoptionsansatzes gerechtfertigt ist. Die Anwendung der Analysemethode auf das Untersuchungsgebiet in Weißwasser offenbart für das Versorgungsunternehmen vielfältige Handlungsmöglichkeiten zum Umgang mit bestehenden Problemen und zur Anpassung an beeinflussende unsichere Faktoren. Weiterhin können mit Hilfe der Analyse die Vor- und Nachteile der ausgewählten Methode aufgezeigt werden, was für weitere Untersuchungen des Themengebietes hilfreich sein kann.