Managing Rentals with Usage-Based Loss

Motivated by new and innovative rental business models, this paper develops a novel discrete-time model of a rental operation with random loss of inventory due to customer use. The inventory level is chosen before the start of a finite rental season, and customers not immediately served are lost. Our analysis framework uses stochastic comparisons of sample paths to derive structural results that hold under good generality for demands, rental durations, and rental unit lifetimes. Considering different \recirculation" rules | i.e., which rental unit to choose to meet each demand | we prove the concavity of the expected profit function and identify the optimal recirculation rule. A numerical study clarifies when considering rental unit loss and recirculation rules matters most for the inventory decision: Accounting for rental unit loss can increase the expected profit by 7% for a single season and becomes even more important as the time horizon lengthens. We also observe that the optimal inventory level in response to increasing loss probability is non-monotonic. Finally, we show that choosing the optimal recirculation rule over another simple policy allows more rental units to be profitably added, and the profit-maximizing service level increases by up to 6 percentage points.

Machine learning and data decompositions for complex networked dynamical systems

Thesis (Ph.D.)--University of Washington, 2016-08

Exact Solution of Bayes and Minimax Change-Detection Problems

The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations. Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.

Causal structure of the entanglement renormalization ansatz

We show that the multiscale entanglement renormalization ansatz (MERA) can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat space-like boundary, where the volume of a spacetime region corresponds to the number of variational parameters it contains. This result clarifies the nature of the ansatz, and suggests a generalization to quantum field theory. It also constitutes an independent justification of the connection between MERA and hyperbolic geometry which was proposed as a concrete implementation of the AdS-CFT correspondence.

Analyzing change in medication use - statistical approaches

The objective of this study was to gain an understanding of the effects of population heterogeneity, missing data, and causal relationships on parameter estimates from statistical models when analyzing change in medication use. From a public health perspective, two timely topics were addressed: the use and effects of statins in populations in primary prevention of cardiovascular disease and polypharmacy in older population. Growth mixture models were applied to characterize the accumulation of cardiovascular and diabetes medications among apparently healthy population of statin initiators. The causal effect of statin adherence on the incidence of acute cardiovascular events was estimated using marginal structural models in comparison with discrete-time hazards models. The impact of missing data on the growth estimates of evolution of polypharmacy was examined comparing statistical models under different assumptions for missing data mechanism. The data came from Finnish administrative registers and from the population-based Geriatric Multidisciplinary Strategy for the Good Care of the Elderly study conducted in Kuopio, Finland, during 2004–07. Five distinct patterns of accumulating medications emerged among the population of apparently healthy statin initiators during two years after statin initiation. Proper accounting for time-varying dependencies between adherence to statins and confounders using marginal structural models produced comparable estimation results with those from a discrete-time hazards model. Missing data mechanism was shown to be a key component when estimating the evolution of polypharmacy among older persons. In conclusion, population heterogeneity, missing data and causal relationships are important aspects in longitudinal studies that associate with the study question and should be critically assessed when performing statistical analyses. Analyses should be supplemented with sensitivity analyses towards model assumptions.

Method of numerical correction of errors occasioned by delay of records during the monitoring of environmental variables of interest for animal production

As condições de ambiente térmico e aéreo, no interior de instalações para animais, alteram-se durante o dia, devido à influência do ambiente externo. Para que análises estatísticas e geoestatísticas sejam representativas, uma grande quantidade de pontos distribuídos espacialmente na área da instalação deve ser monitorada. Este trabalho propõe que a variação no tempo das variáveis ambientais de interesse para a produção animal, monitoradas no interior de instalações para animais, pode ser modelada com precisão a partir de registros discretos no tempo. O objetivo deste trabalho foi desenvolver um método numérico para corrigir as variações temporais dessas variáveis ambientais, transformando os dados para que tais observações independam do tempo gasto durante a aferição. O método proposto aproximou os valores registrados com retardos de tempo aos esperados no exato momento de interesse, caso os dados fossem medidos simultaneamente neste momento em todos os pontos distribuídos espacialmente. O modelo de correção numérica para variáveis ambientais foi validado para o parâmetro ambiental temperatura do ar, sendo que os valores corrigidos pelo método não diferiram pelo teste Tukey, a 5% de probabilidade dos valores reais registrados por meio de dataloggers.

Optimal sequence of landfills in solid waste management

Given that landfills are depletable and replaceable resources, the right approach, when dealing with landfill management, is that of designing an optimal sequence of landfills rather than designing every single landfill separately. In this paper we use Optimal Control models, with mixed elements of both continuous and discrete time problems, to determine an optimal sequence of landfills, as regarding their capacity and lifetime. The resulting optimization problems involve splitting a time horizon of planning into several subintervals, the length of which has to be decided. In each of the subintervals some costs, the amount of which depends on the value of the decision variables, have to be borne. The obtained results may be applied to other economic problems such as private and public investments, consumption decisions on durable goods, etc.

Queueuing system with failures and priorities

Queueing theory provides models, structural insights, problem solutions and algorithms to many application areas. Due to its practical applicability to production, manufacturing, home automation, communications technology, etc, more and more complex systems requires more elaborated models, tech- niques, algorithm, etc. need to be developed. Discrete-time models are very suitable in many situations and a feature that makes the analysis of discrete time systems technically more involved than its continuous time counterparts. In this paper we consider a discrete-time queueing system were failures in the server can occur as-well as priority messages. The possibility of failures of the server with general life time distribution is considered. We carry out an extensive study of the system by computing generating functions for the steady-state distribution of the number of messages in the queue and in the system. We also obtain generating functions for the stationary distribution of the busy period and sojourn times of a message in the server and in the system. Performance measures of the system are also provided.

On the duration of negative surplus

Doutoramento em Matemática

Feasibility study and flow scheduling optimization of a multi-product pipeline system

The first goal of this study is to analyse a real-world multiproduct onshore pipeline system in order to verify its hydraulic configuration and operational feasibility by constructing a simulation model step by step from its elementary building blocks that permits to copy the operation of the real system as precisely as possible. The second goal is to develop this simulation model into a user-friendly tool that one could use to find an “optimal” or “best” product batch schedule for a one year time period. Such a batch schedule could change dynamically as perturbations occur during operation that influence the behaviour of the entire system. The result of the simulation, the ‘best’ batch schedule is the one that minimizes the operational costs in the system. The costs involved in the simulation are inventory costs, interface costs, pumping costs, and penalty costs assigned to any unforeseen situations. The key factor to determine the performance of the simulation model is the way time is represented. In our model an event based discrete time representation is selected as most appropriate for our purposes. This means that the time horizon is divided into intervals of unequal lengths based on events that change the state of the system. These events are the arrival/departure of the tanker ships, the openings and closures of loading/unloading valves of storage tanks at both terminals, and the arrivals/departures of trains/trucks at the Delivery Terminal. In the feasibility study we analyse the system’s operational performance with different Head Terminal storage capacity configurations. For these alternative configurations we evaluated the effect of different tanker ship delay magnitudes on the number of critical events and product interfaces generated, on the duration of pipeline stoppages, the satisfaction of the product demand and on the operative costs. Based on the results and the bottlenecks identified, we propose modifications in the original setup.

Propagation modelling and resource allocation in mobile radio communications

Over the past years, ray tracing (RT) models popularity has been increasing. From the nineties, RT has been used for field prediction in environment such as indoor and urban environments. Nevertheless, with the advent of new technologies, the channel model has become decidedly more dynamic and to perform RT simulations at each discrete time instant become computationally expensive. In this thesis, a new dynamic ray tracing (DRT) approach is presented in which from a single ray tracing simulation at an initial time t0, through analytical formulas we are able to track the motion of the interaction points. The benefits that this approach bring are that Doppler frequencies and channel prediction can be derived at every time instant, without recurring to multiple RT runs and therefore shortening the computation time. DRT performance was studied on two case studies and the results shows the accuracy and the computational gain that derives from this approach. Another issue that has been addressed in this thesis is the licensed band exhaustion of some frequency bands. To deal with this problem, a novel unselfish spectrum leasing scheme in cognitive radio networks (CRNs) is proposed that offers an energy-efficient solution minimizing the environmental impact of the network. In addition, a network management architecture is introduced and resource allocation is proposed as a constrained sum energy efficiency maximization problem. System simulations demonstrate an increment in the energy efficiency of the primary users’ network compared with previously proposed algorithms.

Dynamics in discrete phase spaces and time interval operators

The von Neumann-Liouville time evolution equation is represented in a discrete quantum phase space. The mapped Liouville operator and the corresponding Wigner function are explicitly written for the problem of a magnetic moment interacting with a magnetic field and the precessing solution is found. The propagator is also discussed and a time interval operator, associated to a unitary operator which shifts the energy levels in the Zeeman spectrum, is introduced. This operator is associated to the particular dynamical process and is not the continuous parameter describing the time evolution. The pair of unitary operators which shifts the time and energy is shown to obey the Weyl-Schwinger algebra. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Artificial evolution on network structures : how time and space influence dynamics

Abstract The main objective of this work is to show how the choice of the temporal dimension and of the spatial structure of the population influences an artificial evolutionary process. In the field of Artificial Evolution we can observe a common trend in synchronously evolv¬ing panmictic populations, i.e., populations in which any individual can be recombined with any other individual. Already in the '90s, the works of Spiessens and Manderick, Sarma and De Jong, and Gorges-Schleuter have pointed out that, if a population is struc¬tured according to a mono- or bi-dimensional regular lattice, the evolutionary process shows a different dynamic with respect to the panmictic case. In particular, Sarma and De Jong have studied the selection pressure (i.e., the diffusion of a best individual when the only selection operator is active) induced by a regular bi-dimensional structure of the population, proposing a logistic modeling of the selection pressure curves. This model supposes that the diffusion of a best individual in a population follows an exponential law. We show that such a model is inadequate to describe the process, since the growth speed must be quadratic or sub-quadratic in the case of a bi-dimensional regular lattice. New linear and sub-quadratic models are proposed for modeling the selection pressure curves in, respectively, mono- and bi-dimensional regu¬lar structures. These models are extended to describe the process when asynchronous evolutions are employed. Different dynamics of the populations imply different search strategies of the resulting algorithm, when the evolutionary process is used to solve optimisation problems. A benchmark of both discrete and continuous test problems is used to study the search characteristics of the different topologies and updates of the populations. In the last decade, the pioneering studies of Watts and Strogatz have shown that most real networks, both in the biological and sociological worlds as well as in man-made structures, have mathematical properties that set them apart from regular and random structures. In particular, they introduced the concepts of small-world graphs, and they showed that this new family of structures has interesting computing capabilities. Populations structured according to these new topologies are proposed, and their evolutionary dynamics are studied and modeled. We also propose asynchronous evolutions for these structures, and the resulting evolutionary behaviors are investigated. Many man-made networks have grown, and are still growing incrementally, and explanations have been proposed for their actual shape, such as Albert and Barabasi's preferential attachment growth rule. However, many actual networks seem to have undergone some kind of Darwinian variation and selection. Thus, how these networks might have come to be selected is an interesting yet unanswered question. In the last part of this work, we show how a simple evolutionary algorithm can enable the emrgence o these kinds of structures for two prototypical problems of the automata networks world, the majority classification and the synchronisation problems. Synopsis L'objectif principal de ce travail est de montrer l'influence du choix de la dimension temporelle et de la structure spatiale d'une population sur un processus évolutionnaire artificiel. Dans le domaine de l'Evolution Artificielle on peut observer une tendence à évoluer d'une façon synchrone des populations panmictiques, où chaque individu peut être récombiné avec tout autre individu dans la population. Déjà dans les année '90, Spiessens et Manderick, Sarma et De Jong, et Gorges-Schleuter ont observé que, si une population possède une structure régulière mono- ou bi-dimensionnelle, le processus évolutionnaire montre une dynamique différente de celle d'une population panmictique. En particulier, Sarma et De Jong ont étudié la pression de sélection (c-à-d la diffusion d'un individu optimal quand seul l'opérateur de sélection est actif) induite par une structure régulière bi-dimensionnelle de la population, proposant une modélisation logistique des courbes de pression de sélection. Ce modèle suppose que la diffusion d'un individu optimal suit une loi exponentielle. On montre que ce modèle est inadéquat pour décrire ce phénomène, étant donné que la vitesse de croissance doit obéir à une loi quadratique ou sous-quadratique dans le cas d'une structure régulière bi-dimensionnelle. De nouveaux modèles linéaires et sous-quadratique sont proposés pour des structures mono- et bi-dimensionnelles. Ces modèles sont étendus pour décrire des processus évolutionnaires asynchrones. Différentes dynamiques de la population impliquent strategies différentes de recherche de l'algorithme résultant lorsque le processus évolutionnaire est utilisé pour résoudre des problèmes d'optimisation. Un ensemble de problèmes discrets et continus est utilisé pour étudier les charactéristiques de recherche des différentes topologies et mises à jour des populations. Ces dernières années, les études de Watts et Strogatz ont montré que beaucoup de réseaux, aussi bien dans les mondes biologiques et sociologiques que dans les structures produites par l'homme, ont des propriétés mathématiques qui les séparent à la fois des structures régulières et des structures aléatoires. En particulier, ils ont introduit la notion de graphe sm,all-world et ont montré que cette nouvelle famille de structures possède des intéressantes propriétés dynamiques. Des populations ayant ces nouvelles topologies sont proposés, et leurs dynamiques évolutionnaires sont étudiées et modélisées. Pour des populations ayant ces structures, des méthodes d'évolution asynchrone sont proposées, et la dynamique résultante est étudiée. Beaucoup de réseaux produits par l'homme se sont formés d'une façon incrémentale, et des explications pour leur forme actuelle ont été proposées, comme le preferential attachment de Albert et Barabàsi. Toutefois, beaucoup de réseaux existants doivent être le produit d'un processus de variation et sélection darwiniennes. Ainsi, la façon dont ces structures ont pu être sélectionnées est une question intéressante restée sans réponse. Dans la dernière partie de ce travail, on montre comment un simple processus évolutif artificiel permet à ce type de topologies d'émerger dans le cas de deux problèmes prototypiques des réseaux d'automates, les tâches de densité et de synchronisation.

Quantum discrete phase space dynamics and its continuous limit

The main aspects of a discrete phase space formalism are presented and the discrete dynamical bracket, suitable for the description of time evolution in finite-dimensional spaces, is discussed. A set of operator bases is defined in such a way that the Weyl-Wigner formalism is shown to be obtained as a limiting case. In the same form, the Moyal bracket is shown to be the limiting case of the discrete dynamical bracket. The dynamics in quantum discrete phase spaces is shown not to be attained from discretization of the continuous case.

Symmetries and time evolution in discrete phase spaces: a soluble model calculation

Using the flexibility and constructive definition of the Schwinger bases, we developed different mapping procedures to enhance different aspects of the dynamics and of the symmetries of an extended version of the two-level Lipkin model. The classical limits of the dynamics are discussed in connection with the different mappings. Discrete Wigner functions are also calculated. © 1995.