Tesi sul tema "Shelter location under uncertainty"

Cette thèse concerne le développement, l'extension et l'application d'une formulation stochastique des équations de la mécanique des fluides introduite par Mémin (2014). La vitesse petite échelle, non-résolue, est modélisée au moyen d'un champ aléatoire décorrélé en temps. Cela modifie l'expression de la dérivée particulaire et donc les équations de la mécanique des fluides. Les modèles qui en découlent sont dénommés modèles sous incertitude de position. La thèse s'articulent autour de l'étude successive de modèles réduits, de versions stochastiques du transport et de l'advection à temps long d'un champ de traceur par une vitesse mal résolue. La POD est une méthode de réduction de dimension, pour EDP, rendue possible par l'utilisation d'observations. L'EDP régissant l'évolution de la vitesse du fluide est remplacée par un nombre fini d'EDOs couplées. Grâce à la modélisation sous incertitude de position et à de nouveaux estimateurs statistiques, nous avons dérivé et simulé des versions réduites, déterministe et aléatoire, de l'équation de Navier-Stokes. Après avoir obtenu des versions aléatoires de plusieurs modèles océaniques, nous avons montré numériquement que ces modèles permettaient de mieux prendre en compte les petites échelles des écoulements, tout en donnant accès à des estimés de bonne qualité des erreurs du modèle. Ils permettent par ailleurs de mieux rendre compte des évènements extrêmes, des bifurcations ainsi que des phénomènes physiques réalistes absents de certains modèles déterministes équivalents. Nous avons expliqué, démontré et quantifié mathématiquement l'apparition de petites échelles de traceur, lors de l'advection par une vitesse mal résolu. Cette quantification permet de fixer proprement des paramètres de la méthode d'advection Lagrangienne, de mieux le comprendre le phénomène de mélange et d'aider au paramétrage des simulations grande échelle en mécanique des fluides
This thesis develops, analyzes and demonstrates several valuable applications of randomized fluid dynamics models referred to as under location uncertainty. The velocity is decomposed between large-scale components and random time-uncorrelated small-scale components. This assumption leads to a modification of the material derivative and hence of every fluid dynamics models. Through the thesis, the mixing induced by deterministic low-resolution flows is also investigated. We first applied that decomposition to reduced order models (ROM). The fluid velocity is expressed on a finite-dimensional basis and its evolution law is projected onto each of these modes. We derive two types of ROMs of Navier-Stokes equations. A deterministic LES-like model is able to stabilize ROMs and to better analyze the influence of the residual velocity on the resolved component. The random one additionally maintains the variability of stable modes and quantifies the model errors. We derive random versions of several geophysical models. We numerically study the transport under location uncertainty through a simplified one. A single realization of our model better retrieves the small-scale tracer structures than a deterministic simulation. Furthermore, a small ensemble of simulations accurately predicts and describes the extreme events, the bifurcations as well as the amplitude and the position of the ensemble errors. Another of our derived simplified model quantifies the frontolysis and the frontogenesis in the upper ocean. This thesis also studied the mixing of tracers generated by smooth fluid flows, after a finite time. We propose a simple model to describe the stretching as well as the spatial and spectral structures of advected tracers. With a toy flow but also with satellite images, we apply our model to locally and globally describe the mixing, specify the advection time and the filter width of the Lagrangian advection method, as well as the turbulent diffusivity in numerical simulations

A cause du réchauffement climatique, le nombre et l’intensité des feux de forêts augmentent autour du globe. Dansce contexte, la construction de refuges contre le feu est une solution de plus en plus envisagée. Le problème consisteessentiellement à localiser p refuges de sorte à minimiser la distance maximale qui sépare un usager du plus procherefuge accessible en cas de feux. Le territoire considéré est divisé en zones et est modélisé comme un graphe auxarêtes pondérées. Un départ de feux sur une seule zone (c’est-à-dire sur un sommet). La principale conséquence d’unfeu est que les chemins d’évacuation sont modifiés de deux manières. Premièrement, un chemin d’évacuation ne peutpas traverser le sommet en feu. Deuxièmement, le fait qu’une personne proche de l’incendie puisse avoir un choix limitéde direction d’évacuation, ou être sous stress, est modélisé à l’aide d’une stratégie d’évacuation nouvellement définie.Cette stratégie d’évacuation induit des distances d’évacuation particulières qui rendent notre modèle spécifique. Selon letype de données considéré et l’objectif recherché, nous proposons deux problèmes avec ce modèle: le Robust p-CenterUnder Pressure et le Probabilistic p-Center Under Pressure. Nous prouvons que ces deux problèmes sont NP-difficilessur des classes de graphes pertinentes pour notre contexte. Nous proposons également des résultats d’approximationet d’inapproximation. Finalement, nous développons des algorithmes polynomiaux sur des classes de graphes simples,et nous développons des algorithmes mathématiques basés sur la programmation linéaire
The location of shelters in different areas threatened by wildfires is one of the possible ways to reduce fatalities in acontext of an increasing number of catastrophic and severe forest fires. The problem is basically to locate p sheltersminimizing the maximum distance people will have to cover to reach the closest accessible shelter in case of fire. Thelandscape is divided in zones and is modeled as an edge-weighted graph with vertices corresponding to zones andedges corresponding to direct connections between two adjacent zones. Each scenario corresponds to a fire outbreak ona single zone (i.e., on a vertex) with the main consequence of modifying evacuation paths in two ways. First, an evacuationpath cannot pass through the vertex on fire. Second, the fact that someone close to the fire may have limited choice, ormay not take rational decisions, when selecting a direction to escape is modeled using a new kind of evacuation strategy.This evacuation strategy, called Under Pressure, induces particular evacuation distances which render our model specific.We propose two problems with this model: the Robust p-Center Under Pressure problem and the Probabilistic p-CenterUnder Pressure problem. First we prove hardness results for both problems on relevant classes of graphs for our context.In addition, we propose polynomial exact algorithms on simple classes of graphs and we develop mathematical algorithmsbased on integer linear programming

Effective aeromedical evacuation of casualties is one of the most important problems in military medical systems because high-priority casualties will not survive without timely medical care. The decision making process for aeromedical evacuation consists of the following components: (1) identifying which aeromedical evacuation asset (see figure 1) to dispatch to the casualty, (2) locating aeromedical evacuation assets strategically in anticipation of incoming demand, and (3) deciding which medical treatment facility to transport the casualty. These decisions are further complicated because prioritization of casualties is based on severity of injury while aeromedical evacuation assets and medical treatment facilities operate with varying capabilities. In this dissertation, discrete optimization models are developed to examine dispatch, delivery, and location logistics for the effective aeromedical evacuation of casualties in military medical systems.

The rapid environmental changes, high levels of uncertainty and difficulty in understanding these situations, make recession a uniquely challenging time for SMEs, particularly with respect to their strategic decision-making. This is especially true for retail SMEs: at the end of the supply chain, they are dependent on consumer buying power. Strategic decision-making in retail SMEs, notably location and expansion decisions, are under-researched, though there is evidence that such decisions are subjective, more an art than a science. These two elements, strategic decision making in SMEs and the context of recession are the focus and contribution of this thesis: the aim of the research was to compile a theoretical framework to portray the emergence of retail location strategies in recession. The research is underpinned by the theoretical domains of strategic location decision-making under the umbrella of complexity theory. The research comprises two case studies of SME electrical retailers in Greece. Pre-recession, these retailers had established track records of aggressive locational expansion and so the impact of the turbulence that accompanied the Greek recession made them ideal exemplar cases for this study. The data collection comprised observation, informal conversations, key informant interviews and focus groups. A thematic analysis approach was taken to the coding, organisation and reporting of the results. The results demonstrate how strategy development is supported by emerging organisational structures, including informal and opportunistic networks that facilitate the diffusion of tacit and explicit knowledge. These networks provide a friendly and supportive environment in which decision-makers are supported in their development of project-specific schemes. Thus this research contributes to understanding the locational decision process, successful locational strategy and strategic development in periods of instability and confusion.

In today’s extremely competitive marketplace, firms are facing the need to meet or exceed increasing customer expectations while cutting costs to stay competitive in a global market. To develop competitive advantage in this business climate, companies must make informed decisions regarding their supply chain. In recent years, supply chain networks have received increasing attention among companies. The decision makers confront the network design problem in different situations. In order to make decisions, especially in strategic supply chain management, decision makers must have a holistic view of all the components. Supply chain network design, particular facility location problems, is one of the most complex strategic decision problems in supply chain management The aim of this dissertation is to make an inquiry about the facility location problems and related issues in supply chain and logistics management, and the use of modelling approaches to solve these problems. The methodology is to construct a review protocol by forming a review panel, and developing a detailed search strategy with clear inclusion and exclusion criteria. In addition, the measurement for evaluating the quality of studies is presented with a strategy for extracting data and synthesising the methodologies. The search results show the background of the facility location problems, the importance and the basic questions of these problems. The taxonomy of facility location problems with eighteen factors is presented. The basic static and deterministic problems in facility location including the covering, centre, median and fixed charge problems are discussed. Also, the extension of facility location problems comprises of location-allocation, multi-objective, hierarchical, hub, undesirable and competitive problems. In terms of uncertainty, dynamic, stochastic and robust facility location problems are presented. Finally, strengths and weaknesses of different modelling approaches are discussed; importantly, gaps from the review process are indentified. Recommendations of future research are described; and the facility location problem to be addressed by the proposed research is shown. In addition, contributions of the proposed facility location problem are illustrated.

The retail industry is considered to be a very competitive industry in the United States since there are so many players in the almost saturated retail markets that provide similar products and services at similar price levels to customers. Market selection has been identified as an important strategy to differentiate a retailer in this competitive market. Therefore in this thesis, we describe a conceptual framework to evaluate retailers investment opportunities in dynamic, competitive retail markets. The objective is to describe a conceptual investment analysis framework to address the strategic aspects of a retailer s investment opportunity as well as the dynamic uncertainty of a retail market in a single framework. This conceptual framework outlines a strategic view towards retail stores as flexible assets of a retail enterprise. This conceptual framework is general and can be adjusted and applied to investments options in other services. In addition, we develop an integrated investment analysis approach based on dynamic programming to explore retailers investment behaviors in dynamic markets. The objective is to determine retailers optimal investment thresholds in noncompetitive and competitive markets. We consider two retailers to illustrate our approach and use a simple game theory treatment to address competition in retail markets. We use our integrated investment analysis model based on a real options methodology to evaluate the apparent tendency for the small discount retailer invests earlier in a new developing market due to the competition effect from the large discount retailer. This early entry gives the small retail a first-mover advantage and delays the big retailer s entry into the competitive market. In addition, we conduct sensitivity analysis to characterize how significantly the values of our model parameters impact the retailers investment decisions. We also develop an integrated investment analysis approach based on contingent claims analysis to explore retailers investment behaviors in dynamic markets. The objective is to determine retailers optimal investment thresholds in noncompetitive and competitive markets. The equivalent risk neutral evaluation approach is presented in this thesis as an extended version of the contingent claims analysis approach, which facilitates the market-oriented valuation of the retailer s investment option in dynamic markets. Sensitivity analysis is conducted to study how retailers optimal investment thresholds change as the values of parameters in this equivalent risk neutral evaluation approach change. The relationship between the dynamic programming and the equivalent risk neutral evaluation approach is also summarized in this thesis to identify the similarities and the differences between these two investment analysis approaches. One of the most important objectives of this comparison is to determine in what market conditions the choice of investment analysis approach is critical and dramatically changes the retailer s optimal investment threshold. Finally, we empirically examine an important aspect of our theoretical work that the big retailer invests and opens a store relatively later in markets with a small retailer compared to markets without a small retailer. In addition, the big retailer opens a store at relatively higher retail market potential in markets with a small retailer compared to markets without a small retailer. In this thesis, we discuss some empirical evidence to support these theoretical results. We chose Wal-Mart and Dollar General as the big and small retailers, respectively, in our empirical study. Our empirical results do not validate the theory and just provide supporting evidence for our theoretical works.

In this thesis, we generalize a set of facility location models within a two-stage robust optimization framework by assuming each demand is only known to lie within a continuous and bounded uncertainty region. Our approach involves discretizing each uncertainty region into a set of finite scenarios, each of which represents a potential location where the demand may be realized. We show that the gap between the optimal values of the theorized continuous uncertainty problem and our discretized model can be bounded by a function of the granularity of the discretization. We then propose a solution technique based on row-and-column generation, and compare its performance with existing solution methods. Lastly, we apply our robust location models to the problem of ambulance positioning using cardiac arrest location data from the City of Toronto, and show that hedging against demand location uncertainty may help decrease EMS response times to cardiac arrest emergencies.

We study three problems on supply chain location and inventory under uncertainty. In Chapter 2, we study the inventory purchasing and allocation problem in a movie rental chain under demand uncertainty. We formulate this problem as a newsvendor-like problem with multiple rental opportunities. We study several demand and return forecasting models based on comparable films using iterative maximum likelihood estimation and Bayesian estimation via Markov chain Monte Carlo simulation. Test results on data from a large movie rental firm reveal systematic under-buying of movies purchased through revenue sharing contracts and over-buying of movies purchased through standard ones. For the movies considered, the model estimates an increase in the average profit per title for new movies by 15.5% and 2.5% for revenue sharing and standard titles, respectively. We discuss the implications of revenue sharing on the profitability of both the rental firm and the studio. In Chapter 3, we focus on the effect of travel time uncertainty on the location of facilities that provide service within a given coverage radius on the transportation network. Three models - expected covering, robust covering and expected p-robust covering - are studied; each appropriate for different types of facilities. Exact and approximate algorithms are developed. The models are used to analyze the location of fire stations in the city of Toronto. Using real traffic data we show that the current system design is quite far from optimality and provide recommendations for improving the performance. In Chapter 4, we continue our analysis in Chapter 3 to study the trade-off between adding new facilities versus relocating some existing facilities. We consider a multi-objective problem that aims at minimizing the number of facility relocations while maximizing expected and worst case network coverage. Exact and approximate algorithms are developed to solve three variations of the problem and find expected--worst case trade-off curves for any given number of relocations. The models are used to analyze the addition of four new fire stations to the city of Toronto. Our results suggest that the benefit of adding four new stations is achievable, at a lower cost, by relocating 4-5 stations.

Tese de doutoramento em Gestão, no ramo de Ciência aplicada à Decisão, apresentada à Faculdade de Economia da Universidade de Coimbra
This thesis is devoted to mathematical modelling and solution techniques for dynamic facility location problems under uncertainty. The uncertainty regarding the evolution of important problems' parameters along the planning horizon, such as setup and assignment costs, as well as level or location of demand, is explicitly incorporated into the dynamic models through a finite and discrete set of possible scenarios. In the present work we first propose a two-stage stochastic model for the uncapacitated problem. The first decisions to be made are the strategic ones, where and when to locate the facilities throughout the planning horizon. The second-stage decisions refer to the assignment of the existing customers to the open facilities over the whole planning horizon under each possible scenario. As opposite to location decisions, that must be made here and now and should be valid for all possible future scenarios, assignment can be decided after the uncertainty has been resolved and thus can be adjusted in each time period to each possible scenario. The objective is to find a solution that minimizes the expected total cost over all possible scenarios. This model is then extended to other situations, recognizing that other features should be included in the mathematical model to be able to generate other possible solutions. A set of robust constraints is incorporated into that model, that in spite of restricting the set of admissible solutions, it offers more informed and robust solutions under uncertainty. A multi-objective problem wherein each scenario gives rise to an objective is then developed, and relations with other known problems are established as well. For this latter model, requirements about scenarios probabilities or risk profiles are dropped. Within this context, it is emphasized that the Decision Maker will have a better picture of the compromises that exist among the possible scenarios. In terms of models, we conclude with several extensions considering capacitated facilities. The possibility of unmet demand appears naturally in this class of problems, giving rise to other interesting and challenging questions. We propose and discuss both mono and multi-objective approaches. We proceed with the description of the solution techniques that have been developed to tackle the uncapacitated problems. First we present a primal-dual heuristic approach inspired on classical works and a branch&bound scheme integrating this same heuristic. Afterwards, a Lagrangean relaxation approach developed to tackle the problem with robust constraints is detailed. The calculation of non-dominated solutions for the multi-objective problem is discussed and illustrated. Finally, as the models and algorithms were tested over sets of randomly generated problems, the computational experiments and results obtained are provided including comparisons with general solvers. The results of this work aim to help Decision Makers in the difficult process of decision making when dealing with location problems under uncertainty, and thus should be interpreted as decision support tools.
Esta tese versa sobre modelação matemática e algoritmos de resolução de problemas de localização dinâmica em contextos de incerteza. A incerteza acerca de como importantes parâmetros dos problemas irão evoluir ao longo do tempo, tais como custos de instalação de serviços e de afetação, localização ou nível da procura, é explicitamente incorporada nos modelos dinâmicos através de um conjunto finito e discreto de cenários. Na presente dissertação, propomos em primeiro lugar um modelo estocástico de duas fases para o problema de localização sem restrições de capacidades. As primeiras decisões a serem tomadas são as estratégicas, onde e quando localizar os serviços ao longo do horizonte temporal. As decisões de segunda fase referem-se à afetação dos clientes com procura aos serviços abertos ao longo do horizonte temporal para todos os cenários possíveis. Ao contrário das decisões de localização, tomadas no presente e válidas para todos os futuros possíveis, as decisões de afetação podem ser tomadas após a realização da incerteza e ajustadas em cada período temporal a cada cenário. O objetivo do problema é encontrar uma solução que minimize o custo total esperado para todos os cenários possíveis. Este modelo é depois alargado a outras situações, reconhecendo-se que outras características devem ser incluídas no modelo de modo a gerar outras soluções para o problema. Um conjunto de restrições de robustez é incorporado no modelo que, apesar de restringir o conjunto de soluções admissíveis, oferece soluções mais informadas e robustas em situações de incerteza. Um problema multi-objetivo em que cada cenário origina um objetivo é depois apresentado, assim como relações com outros problemas conhecidos. Requisitos acerca das probabilidades associadas aos cenários ou acerca de perfis de risco são desnecessários. É ainda sublinhado que neste contexto o Agente de Decisão terá um melhor retrato dos compromissos existentes entre os possíveis cenários. Em termos de modelos, concluímos com várias extensões considerando serviços com capacidades limitadas. A possibilidade de procura insatisfeita surge naturalmente nesta classe de problemas, dando lugar a outras interessantes e desafiantes questões. Propomos e discutimos abordagens mono e multi-objetivo. Procedemos à descrição dos algoritmos construídos para resolução dos problemas sem restrições de capacidades. Apresentamos uma heurística primal-dual inspirada em abordagens clássicas e um algoritmo branch&bound que integra aquela heurística. Uma técnica usando relaxação Lagrangeana é depois detalhada para resolução do problema com as restrições de robustez. O cálculo de soluções não dominadas para o problema multi-objetivo é discutido e ilustrado com um exemplo. Finalmente, como tanto os modelos como os algoritmos foram testados com instâncias geradas aleatoriamente, as experiências e resultados computacionais são apresentados, incluindo comparações com general solvers. Os resultados deste trabalho pretendem ajudar os Agentes de Decisão no difícil processo de decisão perante problemas de localização em contexto de incerteza, e assim devem ser interpretados como ferramentas de apoio à decisão.

碩士
國立成功大學
工業與資訊管理學系碩博士班
101
Facility Location Allocation (FLA) problems involve many qualitative factors like environment, political and quantitative factors such as setup and transportation costs. In order to deal with this problem, decision makers can consider many different criteria using an approach called Multiple Criteria Decision Making (MCDM). According to different application methods for scholars, MCDM can be divided into Multiple Attribute Decision Making (MADM) and Multiple Objective Decision Making (MODM). In addition, when decision makers deal with qualitative criteria, subjective opinions often exist, and crisp value cannot express expert opinions completely. Thus, this study builds a model in a fuzzy environment that will handle the MCDM problem with fuzzy linguistic variables. The proposed model includes a preparation state, a first state and a second state. In the preparation state, experts identify criteria and alternatives and then divide the criteria into qualitative criteria and quantitative criteria. The purpose of the first state is to deal with the qualitative criteria. In this state, the experts give performance ratings to alternatives using linguistic variables and then apply Fuzzy MADM to obtain an assessment of each alternative. In the second state, we build a multi-objective model using fuzzy goal programming that takes into consideration the fuzzy relation and priorities among objectives, and then we determine the number and locations of facilities as well as the demand. We subsequently compare and analyze the results between two methodologies, suggesting that the model can be applied to solve the FLA problem and give suggestions to decision makers.

碩士
朝陽科技大學
建築及都市設計研究所
92
This thesis proposes a model for use in selecting the location for a park facility where an uncertainty population is taken as a factor. In other existing models, the uncertainty population factor is simplified by using a fixed value or a value based on existing but inaccurate data. These methods oversimplify the issue and do not reflect actual circumstances, thereby causing inaccurate decisions. The proposed model seeks to rectify this problem. Taiwan has already reached a certain level of development that the old models are no longer appropriate. The proposed model seeks to complement the current situation while taking into consideration the uncertainty population factor. In the research conducted for the creation of the proposed model, detailed reviews of existing location theories, Genetic Algorithm, Monte Carlo simulation and Simulation Optimization have been made. An application regression model is used to make a projection on the uncertainty population and consideration to the uncertainty distance of travel. The Monte Carlo simulation is used for risk estimation. Integrate P-median concept of location theory to build an urban neighborhood park location selection basic model under uncertainty factors. Finally, the use of Genetic Algorithm in RISKOptimizer effectively shortens the computation time that would generate the optimum results in the selection of a location for the park facility. A case study has been made using the proposed model in selecting a location for a park facility in the West district of Taichung City in Taiwan. The proposed model considered the uncertain population of the neighborhood in the future and was able to generate results that reflected the actual circumstance more than the existing models.

碩士
國立臺灣科技大學
工業管理系
107
A significant increase in urban population causes demand for daily needs to rise. To fulfill all the order request, logistic companies are required to be more responsive and flexible. To maximize their profit, each company will try to use its resources efficiently in distributing goods to customers. A conventional way is to dispatch more vehicles operating around the city center. Consequently, more logistic activities are expected to happen, which might be accompanied by the occurrence of freight transport issues, such as traffic congestion, excess emission, noise, and crashes. Enabling collaboration between logistic companies and setting up intermediate facilities (satellites) in the city can be considered as alternatives to overcome the problems above. Previous researches have claimed that the implementation of both strategies might help to reduce the volume of vehicles traveling around the urban area. Given the positive impacts, this study applies a collaborative strategy along with the use of intermediate facilities to solve logistical problems in the Special Region of Yogyakarta, as one of the most densely populated cities in Indonesia. However, in solving real-world problems, there are daily uncertainties that need to be considered, such as variability in demand. To capture demand variability, two-stage stochastic programming with recourse model is developed. This research proposes a mathematical programming model for collaborative two-echelon location routing problem under demand uncertainty and uses CPLEX to solve small instances. A simulated annealing algorithm is employed to solve bigger problems. To evaluate the performance of the collaborative strategy, a comparative study between collaborative and non-collaborative scenario is conducted. The result shows that a collaborative approach can reduce the total distribution cost along with the decrement in total traveled distances and the number of utilized resources. Moreover, several cost allocation mechanisms based on cooperative game theory are presented to give a better overview of collaborative logistics as well as provide more options to allocate the post-collaboration cost among companies involved.