In this paper, we minimize the holding cost of the safety stock in the supply chain subject to linear constraints on the service times between the nodes of the network. In the problem, the objective function is concave as we assume the demand to be bounded by a concave function. The optimal solutions of the problem belong to the set of extreme points of the polyhedron, specified by the constraints of the problem. We first characterize the extreme points for the two-layer networks and then provide bounds to use in a branch and bound algorithm. / Singapore-MIT Alliance (SMA)

The scientific domain of this thesis is optimization under uncertainty for discrete event stochastic systems. In particular, this thesis focuses on the practical implementation of the Dynamic Programming (DP) methodology to discrete event stochastic systems. Unfortunately DP in its crude form suffers from three severe computational obstacles that make its imple-mentation to such systems an impossible task. This thesis addresses these obstacles by developing and executing practical Approximate Dynamic Programming (ADP) techniques. Specifically, for the purposes of this thesis we developed the following ADP techniques. The first one is inspired from the Reinforcement Learning (RL) literature and is termed as Real Time Approximate Dynamic Programming (RTADP). The RTADP algorithm is meant for active learning while operating the stochastic system. The basic idea is that the agent while constantly interacts with the uncertain environment accumulates experience, which enables him to react more optimal in future similar situations. While the second one is an off-line ADP procedure These ADP techniques are demonstrated on a variety of discrete event stochastic systems such as: i) a three stage queuing manufacturing network with recycle, ii) a supply chain of the light aromatics of a typical refinery, iii) several stochastic shortest path instances with a single starting and terminal state and iv) a general project portfolio management problem. Moreover, this work addresses, in a systematic way, the issue of multistage risk within the DP framework by exploring the usage of intra-period and inter-period risk sensitive utility functions. In this thesis we propose a special structure for an intra-period utility and compare the derived policies in several multistage instances.

Pagrindinis šio darbo tikslas yra sukurti daugiapakopių procesų būsenų modelį, kuriuo būtų galima modeliuoti įvairių galimų bet kokios sistemos trikdžių scenarijus ir atlikti demonstracinius skaičiavimus. Atsiradus sutrikimui ar pažeidimams sutrikdomas kitų sistemoje dalyvaujančių pakopų darbas ir turime tam tikras pasekmes, kurios iššaukia problemas, liečiančias aplinkui funkcionuojančius sektorius. Todėl yra labai svarbu nustatyti daugiapakopių procesų būsenų modelio galimų būsenų scenarijus, išanalizuoti jų tikėtinumą bei dažnumą ir įvertinti. Daugiausiai dėmesio skiriama perėjimo tikimybių iš vienos pakopos būsenų į kitos pakopos būsenas matricų modeliavimui ir skaičiavimo algoritmo kūrimui. Tada atliekame stebėjimą kaip elgiasi trikdžių pasirodymo tikimybės per 100 perėjimų. Tam naudojami Markovo grandinės bei procesai ir tikimybiniai skirstiniai. / The main purpose of this research is to develop multi-stage process states model that could simulate a possible range of any system failures and demonstrational calculations. In the event of disruption or irregularities affects the other systems involved in stage work and we have certain consequences, which triggered concerns about the functioning around the sector. It is very important to establish a multi-stage process states model, the possible states of scenarios, analyze their probability and the frequency and to assess it. Focuses on the transition probabilities between states in the next tier level status matrix modeling and computing algorithm. Then perform the behavior tracking script and the likelihood of interference, the likelihood of the appearance of over 100 transitions. For this purpose, Markov chains and processes, and probabilistic distributions are used.

In this dissertation, we focus on the uncertainty quantification problems where the goal is to sample the porous media properties given integrated responses. We first introduce a reduced order model using the level set method to characterize the channelized features of permeability fields. The sampling process is completed under Bayesian framework. We hence study the regularity of posterior distributions with respect to the prior measures. The stochastic flow equations that contain both spatial and random components must be resolved in order to sample the porous media properties. Some type of upscaling or multiscale technique is needed when solving the flow and transport through heterogeneous porous media. We propose ensemble-level multiscale finite element method and ensemble-level preconditioner technique for solving the stochastic flow equations, when the permeability fields have certain topology features. These methods can be used to accelerate the forward computations in the sampling processes. Additionally, we develop analysis-of-variance-based mixed multiscale finite element method as well as a novel adaptive version. These methods are used to study the forward uncertainty propagation of input random fields. The computational cost is saved since the high dimensional problem is decomposed into lower dimensional problems. We also work on developing efficient advanced Markov Chain Monte Carlo methods. Algorithms are proposed based on the multi-stage Markov Chain Monte Carlo and Stochastic Approximation Monte Carlo methods. The new methods have the ability to search the whole sample space for optimizations. Analysis and detailed numerical results are presented for applications of all the above methods.

Solar cells constitute the most direct way of converting solar energy to electricity, and thin-film solar-cell technologies have lately been growing in importance, allowing the fabrication of less expensive modules that nonetheless have good power-conversion efficiencies. This thesis focuses on solar cells based on Cu(In,Ga)Se2, which is the thin-film technology that has shown the highest conversion efficiency to date, reaching 20.3 % on the laboratory scale. Solar modules still have some way to go to become entirely competitive with existing energy technologies, and there are two possible paths to this goal: Firstly, reducing their manufacturing costs, for instance by minimizing the material usage per module and/or by increasing the throughput of a given factory; and secondly, increasing the power output per module in other words, the module efficiency. The subject matters of this thesis are related to those two approaches. The first issue investigated is the possibility for reducing the thickness of the Cu(In,Ga)Se2 layer and compensating for lost absorption by using a ZrN back reflector. ZrN layers are fabricated by reactive sputtering and I present a method for tuning the sputtering parameters so as to obtain a back reflector with good optical, electrical and mechanical properties. The reflector layer cannot be used directly in CIGS devices, but relatively good devices can be achieved with a precursor providing a homogeneous supply of Na, the addition of a very thin sacrificial Mo layer that allows the formation of a film of MoSe2 passivating the back contact, and optionally a Ga gradient that further keeps electrons away from the back contact. The second field of study concerns the three-stage CIGS coevaporation process, which is widely used in research labs around the world and has yielded small-area cells with highest efficiencies, but has not yet made it to large scale production. My focus lies on the development and the effect of gradients in the [Ga]/[In+Ga] ratio. On the one hand, I investigate 'intrinsic' gradients (ones that form autonomously during the evaporation), and present a formation model based on the differing diffusivity of Ga and In atoms in CIGS and on the development along the quasi-binary tie line between (In,Ga)2Se3 and Cu2Se. On the other hand, I determine how the process should be designed in order to preserve 'extrinsic' gradients due to interdiffusion. Lastly, I examine the electrical effects of Ga-enhancement at the back and at the front of the absorber and of In-enhancement at the front. Over a wide range, In-rich top layers prove to have no or a weakly beneficial effect, while Ga-rich top regions pose a high risk to have a devastating effect on device performance.

Multi-stage programming is a valuable technique for improving the performance of computer programs through run-time optimization. Current implementations of multi-stage programming do not support run-time type introspection, which is a significant feature of modern object-oriented platforms such as Java and C#. This is unfortunate because many programs that use type introspection in these languages could be improved with multi-staging programming. The aim of this research is to investigate the interaction between multi-stage programming and object-oriented type introspection. This is done by the invention of a new programming language that is a multi-stage extension to C#. The language is capable of expressing traditional multi-stage programs as well as a new style of multi-stage programs that incorporate type introspection, most notably polytypic algorithms such as object serialization. A compiler for the language is implemented and freely available. The language is significant because it is the first object-oriented, multi-stage language; the first attempt to combine type introspection with multi-stage programming; and the first exploration of polytypic programming in a multi-stage context.

Two-arm group sequential designs have been widely used for over forty years, especially for studies with mortality endpoints. The natural generalization of such designs to trials with multiple treatment arms and a common control (MAMS designs) has, however, been implemented rarely. While the statistical methodology for this extension is clear, the main limitation has been an efficient way to perform the computations. Past efforts were hampered by algorithms that were computationally explosive. With the increasing interest in adaptive designs, platform designs, and other innovative designs that involve multiple comparisons over multiple stages, the importance of MAMS designs is growing rapidly. This dissertation proposes a group sequential approach to design MAMS trial where the test statistic is the maximum of the cumulative score statistics for each pair-wise comparison, and is evaluated at each analysis time point with respect to efficacy and futility stopping boundaries while maintaining strong control of the family wise error rate (FWER). In this dissertation we start with a break-through algorithm that will enable us to compute MAMS boundaries rapidly. This algorithm will make MAMS design a practical reality. For designs with efficacy-only boundaries, the computational effort increases linearly with number of arms and number of stages. For designs with both efficacy and futility boundaries the computational effort doubles with successive increases in number of stages. Previous attempts to obtain MAMS boundaries were confined to smaller problems because their computational effort grew exponentially with number of arms and number of stages. We will next extend our proposed group sequential MAMS design to permit adaptive changes such as dropping treatment arms and increasing the sample size at each interim analysis time point. In order to control the FWER in the presence of these adaptations the early stopping boundaries must be re-computed by invoking the conditional error rate principle and the closed testing principle. This adaptive MAMS design is immensely useful in phase~2 and phase~3 settings. An alternative to the group sequential approach for MAMS design is the p-value combination approach. This approach has been in place for the last fifteen years.This alternative MAMS approach is based on combining independent p-values from the incremental data of each stage. Strong control of the FWER for this alternative approach is achieved by closed testing. We will compare the operating characteristics of the two approaches both analytically and empirically via simulation. In this dissertation we will demonstrate that the MAMS group sequential approach dominates the traditional p-value combination approach in terms of statistical power.

In this work the concept of multistage neural networks is going to be presented. The possibility of using this type of structure for pattern recognition would be discussed and examined with chosen problem from eld area. The results of experiment would be confront with other possible methods used for the problem.

This thesis is focused on experimental work in the domain of vacuum evaporation efficiency improvement. The first part introduces theory of liquids evaporation and its influencing factors, then multi-stage flash distillation technology. The next part of theory is an overview of other technologies used for desalination of sea water and introduction to the design of experiments. In the practical part are selected factors affecting efficiency of device and experiment plan is designed for them. When the experiment is done, optimal operating conditions of technology are designed on basis of analysis.

Space-time Adaptive Processing (STAP) is a two-dimensional filtering technique for antenna array with multiple spatial channels. The name "space-time" describes the coupling of these spatial channels with pulse-Doppler waveforms. Applications for STAP includes ground moving target indicator (GMTI) for airborne radar systems. Today, there are strong interests to develop STAP algorithms for operations in “sample starved” environments, where intense environmental interference can reduce STAP capacity to detect and track ground targets. Careful applications of STAP can effectively overcome these conditions by suppressing these interferences and maximize the signal to interference plus noise ratio (SINR). The Multi-stage Wiener filter (MWF) and principal component signal dependent (PC-SD) algorithm are two such methods that can suppress these interference through truncation of the signal subspace. This thesis makes contribution in several ways. First it details the importance of rank compression and sample compression for effective STAP operations in “sample starved” environments. Second, it shows how MWF and PC-SD could operate in this type of environment. Third it details how a “soft stop” technique like diagonal loading (DL) could improve STAP performance in target detection for MWF and PC-SD. Fourth, this thesis contrasts the performance of several existing “hard stop” techniques in rank compression and introduces a new one using a-priori knowledge.