Air traffic flow management is a critical component of air transport operations because at some point in time, often very frequently, one of more of the critical resources in the air transportation network has significantly reduced capacity, resulting in congestion and delay for airlines and other entities and individuals who use the network. Typically, these “bottlenecks” are noticed at a given airport or terminal area, but they also occur in en route airspace. The two-stage combinatorial optimization framework for air traffic flow management under constrained capacity that is presented in this thesis, represents a important step towards the full consideration of the combinatorial nature of air traffic flow management decision that is often ignored or dealt with via priority-based schemes. It also illustrates the similarities between two traffic flow management problems that heretofore were considered to be quite distinct. The runway systems at major airports are highly constrained resources. From the perspective of arrivals, unnecessary delays and emissions may occur during peak periods when one or more runways at an airport are in great demand while other runways at the same airport are operating under their capacity. The primary cause of this imbalance in runway utilization is that the traffic flow into and out of the terminal areas is asymmetric (as a result of airline scheduling practices), and arrivals are typically assigned to the runway nearest the fix through which they enter the terminal areas. From the perspective of departures, delays and emissions occur because arrivals take precedence over departures with regard to the utilization of runways (despite the absence of binding safety constraints), and because arrival trajectories often include level segments that ensure “procedural separation” from arriving traffic while planes are not allowed to climb unrestricted along the most direct path to their destination. Similar to the runway systems, the terminal radar approach control facilities (TRACON) boundary fixes are also constrained resources of the terminal airspace. Because some arrival traffic from different airports merges at an arrival fix, a queue for the terminal areas generally starts to form at the arrival fix, which are caused by delays due to heavy arriving traffic streams. The arrivals must then absorb these delays by path stretching and adjusting their speed, resulting in unplanned fuel consumption. However, these delays are often not distributed evenly. As a result, some arrival fixes experience severe delays while, similar to the runway systems, the other arrival fixes might experience no delays at all. The goal of this thesis is to develop a combined optimization approach for terminal airspace flow management that assigns a TRACON boundary fix and a runway to each flight while minimizing the required fuel burn and emissions. The approach lessens the severity of terminal capacity shortage caused by and imbalance of traffic demand by shunting flights from current positions to alternate runways. This is done by considering every possible path combination. To attempt to solve the congestion of the terminal airspace at both runways and arrival fixes, this research focuses on two sequential optimizations. The fix assignments are dealt with by considering, simultaneously, the capacity constraints of fixes and runways as well as the fuel consumption and emissions of each flight. The research also develops runway assignments with runway scheduling such that the total emissions produced in the terminal area and on the airport surface are minimized. The two-stage sequential framework is also extended to en route airspace. When en route airspace loses its capacity for any reason, e.g. severe weather condition, air traffic controllers and flight operators plan flight schedules together based on the given capacity limit, thereby maximizing en route throughput and minimizing flight operators' costs. However, the current methods have limitations due to the lacks of consideration of the combinatorial nature of air traffic flow management decision. One of the initial attempts to overcome these limitations is the Collaborative Trajectory Options Program (CTOP), which will be initiated soon by the Federal Aviation Administration (FAA). The developed two-stage combinatorial optimization framework fits this CTOP perfectly from the flight operator's perspective. The first stage is used to find an optimal slot allocation for flights under satisfying the ration by schedule (RBS) algorithm of the FAA. To solve the formulated first stage problem efficiently, two different solution methodologies, a heuristic algorithm and a modified branch and bound algorithm, are presented. Then, flights are assigned to the resulting optimized slots in the second stage so as to minimize the flight operator's costs.

In this thesis, we study three supply chain planning problems. The first two problems fall in the tactical planning level, while the third one falls in the strategic/tactical level. We present a direct application for the first two planning problems in the wind turbines industry. For the third problem, we show how it can be applied to supply chains in the food industry. Many countries and localities have the explicitly stated goal of increasing the fraction of their electrical power that is generated by wind turbines. This has led to a rapid growth in the manufacturing and installation of wind turbines. The globally installed capacity for the manufacturing of different components of the wind turbine is nearly fully utilized. Because of the large penalties for missing delivery deadlines for wind turbines, the effective planning of its supply chain has a significant impact on the profitability of the turbine manufacturers. Motivated by the planning challenges faced by one of the world’s largest manufacturers of wind turbines, we present a comprehensive tactical supply chain planning model for manufacturing of wind turbines in the first part of this thesis. The model is multi-period, multi-echelon, and multi-commodity. Furthermore, the model explicitly incorporates backorder penalties with a general cost structure, i.e., the cost structure does not have to be linear in function of the backorder delay. To the best of our knowledge, modeling-based supply chain planning has not been applied to wind turbines, nor has a model with all the above mentioned features been described in the literature. Based on real-world data, we present numerical results that show the significant impact of the capability to model backorder penalties with general cost structures on the overall cost of supply chains for wind turbines. With today’s rapidly changing global market place, it is essential to model uncertainty in supply chain planning. In the second part of this thesis, we develop a two-stage stochastic programming model for the comprehensive tactical planning of supply chains under supply uncertainty. In the first stage, procurement decisions are made while in the second stage, production, inventory, and delivery decisions are made. The considered supply uncertainty combines supplier random yields and stochastic lead times, and is thus the most general form of such uncertainty to date. We apply our model to the same wind turbines supply chain. We illustrate theoretical and numerical results that show the impact of supplier uncertainty/unreliability on the optimal procurement decisions. We also quantify the value of modeling uncertainty versus deterministic planning. Supplier selection with quantity discounts has been an active research problem in the operations research community. In this the last part of this thesis, we focus on a new quantity discounts scheme offered by suppliers in some industries. Suppliers are selected for a strategic planning period (e.g., 5 years). Fixed costs associated with suppliers’ selection are paid. Orders are placed monthly from any of the chosen suppliers, but the quantity discounts are based on the aggregated annual order quantities. We incorporate all this in a multi-period multi-product multi-echelon supply chain planning problem and develop a mixed integer programming (MIP) model for it. Leading commercial MIP solvers take 40 minutes on average to get any feasible solution for realistic instances of our model. With the aim of getting high-quality feasible solutions quickly, we develop an algorithm that constructs a good initial solution and three other iterative algorithms that improve this initial solution and are capable of getting very fast high quality primal solutions. Two of the latter three algorithms are based on MIP-based local search and the third algorithm incorporates a variable neighborhood Descent (VND) combining the first two. We present numerical results for a set of instances based on a real-world supply chain in the food industry and show the efficiency of our customized algorithms. The leading commercial solver CPLEX finds only a very few feasible solutions that have lower total costs than our initial solution within a three hours run time limit. All our iterative algorithms well outperform CPLEX. The VND algorithm has the best average performance. Its average relative gap to the best known feasible solution is within 1% in less than 40 minutes of computing time.

<p>Minimum cycle mean (MCM) is an important concept in directed graphs. From clock period optimization, timing analysis to layout optimization, minimum cycle mean algorithms have found widespread use in VLSI system design optimization. With transistor size scaling to 10nm and below, complexities and size of the systems have grown rapidly over the last decade. Scalability of the algorithms both in terms of their runtime and memory usage is therefore important. </p> <p><br></p> <p>Among the few classical MCM algorithms, the algorithm by Young, Tarjan, and Orlin (YTO), has been particularly popular. When implemented with a binary heap, the YTO algorithm has the best runtime performance although it has higher asymptotic time complexity than Karp's algorithm. However, as an efficient implementation of YTO relies on data redundancy, its memory usage is higher and could be a prohibitive factor in large size problems. On the other hand, a typical implementation of Karp's algorithm can also be memory hungry. An early termination technique from Hartmann and Orlin (HO) can be directly applied to Karp's algorithm to improve its runtime performance and memory usage. Although not as efficient as YTO in runtime, HO algorithm has much less memory usage than YTO. We propose several improvements to HO algorithm. The proposed algorithm has comparable runtime performance to YTO for circuit graphs and dense random graphs while being better than HO algorithm in memory usage. </p> <p><br></p> <p>Minimum balancing of a directed graph is an application of the minimum cycle mean algorithm. Minimum balance algorithms have been used to optimally distribute slack for mitigating process variation induced timing violation issues in clock network. In a conventional minimum balance algorithm, the principal subroutine is that of finding MCM in a graph. In particular, the minimum balance algorithm iteratively finds the minimum cycle mean and the corresponding minimum-mean cycle, and uses the mean and cycle to update the graph by changing edge weights and reducing the graph size. The iterations terminate when the updated graph is a single node. Studies have shown that the bottleneck of the iterative process is the graph update operation as previous approaches involved updating the entire graph. We propose an improvement to the minimum balance algorithm by performing fewer changes to the edge weights in each iteration, resulting in better efficiency.</p> <p><br></p> <p>We also apply the minimum cycle mean algorithm in latency insensitive system design. Timing violations can occur in high performance communication links in system-on-chips (SoCs) in the late stages of the physical design process. To address the issues, latency insensitive systems (LISs) employ pipelining in the communication channels through insertion of the relay stations. Although the functionality of a LIS is robust with respect to the communication latencies, such insertion can degrade system throughput performance. Earlier studies have shown that the proper sizing of buffer queues after relay station insertion could eliminate such performance loss. However, solving the problem of maximum performance buffer queue sizing requires use of mixed integer linear programming (MILP) of which runtime is not scalable. We formulate the problem as a parameterized graph optimization problem where for every communication channel there is a parameterized edge with buffer counts as the edge weight. We then use minimum cycle mean algorithm to determine from which edges buffers can be removed safely without creating negative cycles. This is done iteratively in the similar style as the minimum balance algorithm. Experimental results suggest that the proposed approach is scalable. Moreover, quality of the solution is observed to be as good as that of the MILP based approach.</p><p><br></p>

Diese Arbeit leistet Beiträge zu zwei Gebieten der mathematischen Programmierung: stochastische Optimierung und gemischt-ganzzahlige nichtlineare Optimierung (MINLP). Im ersten Teil erweitern wir quantitative Stetigkeitsresultate für zweistufige stochastische gemischt-ganzzahlige lineare Programme auf Situationen in denen Unsicherheit gleichzeitig in den Kosten und der rechten Seite auftritt, geben eine ausführliche Übersicht zu Dekompositionsverfahren für zwei- und mehrstufige stochastische lineare und gemischt-ganzzahlig lineare Programme, und diskutieren Erweiterungen und Kombinationen des Nested Benders Dekompositionsverfahrens und des Nested Column Generationsverfahrens für mehrstufige stochastische lineare Programme die es erlauben die Vorteile sogenannter rekombinierender Szenariobäume auszunutzen. Als eine Anwendung dieses Verfahrens betrachten wir die optimale Zeit- und Investitionsplanung für ein regionales Energiesystem unter Einbeziehung von Windenergie und Energiespeichern. Im zweiten Teil geben wir eine ausführliche Übersicht zum Stand der Technik bzgl. Algorithmen und Lösern für MINLPs und zeigen dass einige dieser Algorithmen innerhalb des constraint integer programming Softwaresystems SCIP angewendet werden können. Letzteres erlaubt uns die Verwendung schon existierender Technologien für gemischt-ganzzahlige linear Programme und constraint Programme für den linearen und diskreten Teil des Problems. Folglich konzentrieren wir uns hauptsächlich auf die Behandlung der konvexen und nichtkonvexen nichtlinearen Nebenbedingungen mittels Variablenschrankenpropagierung, äußerer Approximation und Reformulierung. In einer ausführlichen numerischen Studie untersuchen wir die Leistung unseres Ansatzes anhand von Anwendungen aus der Tagebauplanung und des Aufbaus eines Wasserverteilungssystems und mittels verschiedener Vergleichstests. Die Ergebnisse zeigen, dass SCIP ein konkurrenzfähiger Löser für MINLPs geworden ist. / This thesis contributes to two topics in mathematical programming: stochastic optimization and mixed-integer nonlinear programming (MINLP). In the first part, we extend quantitative continuity results for two-stage stochastic mixed-integer linear programs to include situations with simultaneous uncertainty in costs and right-hand side, give an extended review on decomposition algorithm for two- and multistage stochastic linear and mixed-integer linear programs, and discuss extensions and combinations of the Nested Benders Decomposition and Nested Column Generation methods for multistage stochastic linear programs to exploit the advantages of so-called recombining scenario trees. As an application of the latter, we consider the optimal scheduling and investment planning for a regional energy system including wind power and energy storages. In the second part, we give a comprehensive overview about the state-of-the-art in algorithms and solver technology for MINLPs and show that some of these algorithm can be applied within the constraint integer programming framework SCIP. The availability of the latter allows us to utilize the power of already existing mixed integer linear and constraint programming technologies to handle the linear and discrete parts of the problem. Thus, we focus mainly on the domain propagation, outer-approximation, and reformulation techniques to handle convex and nonconvex nonlinear constraints. In an extensive computational study, we investigate the performance of our approach on applications from open pit mine production scheduling and water distribution network design and on various benchmarks sets. The results show that SCIP has become a competitive solver for MINLPs.

Assignment (MSc) -- University of Stellenbosch, 2004. / ENGLISH ABSTRACT: In an integrated crop-livestock production farm, the profitability and sustainability of farm production is dependent on the crop rotation strategy applied. Crop rotations have historically been applied to maintain long-term profitability and sustainabiliry of farming production by exploiting the jointly beneficial interrelationships existing among different crop types and the animal production activity. Monocrop (specifically wheat) growers in the Swartland area of the Western Cape are struggling to maintain long-term profitability and sustainability of the crop production, challenging them to rethink about the introduction crop rotation in the production planning. By making proper assumptions, this paper develops a mixed integer linear programming model to suggest a decision planning for the farm planning problem faced by an integratedcrop- livestock production farmer. The mathematical model developed includes crop production, dairy production and wool sheep production activities, which permitted the consideration of five crop types within a crop rotation system. By assuming that a farmer uses a cycle of at most three years, the crop rotation model was incorporated in the composite mixed integer linear farm planning model. In order to demonstrate the application of the mathematical farm planning model formulated, a case study is presented. Relevant data from the Koeberg area of the Swartland region of the Western Cape was applied. For each planning period, the model assumed that the farm has the option of selecting from any of 15 cropping strategies. A land which is not allocated to any of the 15 crop rotation strategies due to risky production situation is left as grass land for roughage purposes of the animal production. Results of the mathematical model indicated that farm profit is dependent on the cropping strategy selected. Additionally, animal production level was also dependent on the crop strategy appl ied. Furthermore, study results suggest that the profit generated from the integrated crop-livestock farm production by adopting crop rotation was superior to profit generated 1'1'0111 the farm activities which are based on monocrop wheat strategy. Empirical results also indicated that the complex interrelationship involved in a mixed crop-livestock farm operation play a major role in determining optimal farm plans. This complex interrelationships favour the introduction of crop rotation in the crop production activities of the farm under investigation. Crop production risk is the major risk component of risk the farmer faces in the farm production. In this study, risk is incorporated in the mixed integer programrnmg farm planning model as a deviation from the expected values of an activity of returns. Model solution with risk indicated that crop rotation strategy and animal production level is sensitive to risk levels considered. The Results also showed that the incorporation of risk in the model greatly affects the level of acreage allocation, crop rotation and animal production level of the farm. Finally, to improve the profitability and sustainability of the farm activity, the study results suggest that the introduction of crop rotation which consist cereals, oil crops and leguminous forages is of paramount importance. Furthermore, the inclusion of forage crops such as medics in the integrated crop livestock production is beneficial for sustained profitability from year to year. / AFRIKAANSE OPSOMMING: Wisselbou is baie belangrik om volhoubare winsgewindheid te verseker in 'n geintegreerde lewendehawe I gewasverbouing boerdery in die Swartland gebied van Wes-Kaap. "n Monokultuur van veral koring produksie het ernstige problerne vir produsente veroorsaak. In hierdie studie word 'n gemengde heeltallige liniere prograrnmerings-model gebruik om te help met besluitneming in sulke boerderye.Die wiskundige model beskou die produksie van kontant- en voer-gewasse (5 verskillende soorte) asook suiwel- en wol/vleis-produksie (beeste en skape) .Daar word aanvaar dat die boer "n siklus van hoogstens 3 jaar in die wisselbou rotasie model gebruik .. 'n Gevallestudie word gedoen met behulp van toepaslike data van 'n plaas in die Koeberg gebied. Die model aanvaar dat die produsent 'n keuse het uit 16 wisselbou strategic .Resultate toon dat winsgewindheid afhanklik is van die strategie gekies en dat wisselbou beter resultate lewer as in die geval van "n monokultuur.Dit wys ook dat die wisselwerking tussen diereproduksie en gewasproduksie baie belangrik is in die keuse van 'n optimale strategie. Die risiko in gewasverbouing is die belangrikste risiko factor vir die produsent.In hierdie studie word risiko ook ingesluit in die gemengde heeltallige model, naamlik as 'n afwyking van die verwagte opbrengs-waardes .Die model toon duidelik dat gewasproduksie en lewendehawe-produksie baie sensitief is ten opsigte van die gekose risiko vlak. Die studie toon ook dat 'n wisselbou program wat die produksie van graan (veral koring) .oliesade asook voere insluit belangrik is vir volhoubare winsgewindheid Die insluiting van klawers (bv "medics") is veral belangrik hier.

本文提出一個新的混合整數線性規劃模型建立投資組合。這個模型所採用的風險函數為最大損失的絕對值，而不是一般常用的損失變異數。在給定的報酬水準下，模型尋找在觀測期間中最小的最大損失的投資組合，即為大中取小的原則。模型也同時考慮實務上常遇見之情況，如：交易成本、最小交易單位、固定交易費用比率、資產總類數等限制。因此，模型內需使用整數變數及二元變數，導致模型的計算求解過程變得比不含整數變數及二元變數的模型困難許多。我們以固定整數變數的啟發式演算法增進求解的效率，並以台灣股票市場的資料做為實證計算的對象。 / A new mixed integer linear program (MILP) for selecting portfolio based on historical return is proposed. This model uses the downside risk rather than the variance as a risk measure. The portfolio is chosen that minimizes the maximum downside risk over all past observation periods to reach a given return level. That is a mini-max principle. The model incorporates the practical characteristics such as transaction costs, minimum transaction units, fixed proportional transaction rates, and cardinality constraint. For this reason a set of integer variables and binary variables are introduced. The introduction, however, increases the computational complexity in model solution. Due to the difficulty of the MILP problem, a heuristic algorithm has been developed for the solution. The computational results are presented by applying the model to the Taiwan stock market.

投資者面對到期日相同的一序列不同履約價格的選擇權時，應如何建立最佳的組合交易策略，這個問題雖已有許多標準的交易公式可依循，但這些標準的交易策略無法全面涵蓋複雜多變的組合策略。本論文提出整數線性規劃模型用來建立選擇權的最佳交易策略。模型針對到期日相同的買權、賣權如何買賣的組合，建立最佳交易策略。若我們預期在到期日時，標的股價將會落在某一範圍內，則我們可修改原來的規劃模型配合此項預期，以尋求最佳的交易策略。最後，我們以Ericsson的選擇權為例，驗証本模型的效能。 / The problem of how to construct the optimal combination trading strategy for investors when they face a series of options of different exercise prices on the same maturity date can be solved by many standard trading rules. Yet these standard trading rules cannot completely cover the complex and highly changeable combination strategy. This thesis proposes an integer linear programming (ILP) model to construct the optimal trading strategy for option portfolio selection. This model focuses on constructing the optimal strategy for an option portfolio of call- and put-options on the same maturity date. Given the investor's belief of the stock price, we also provide an extended ILP model to include this belief. Finally, an empirical study will be presented by using the ILP model applied to the Ericsson's call and put options.

In this thesis, we consider the k-edge connected L-hop-constrained network design problem. Given a weighted graph G=(N,E), a set D of pairs of terminal nodes, and two integers k,L > 1, it consists in finding in G the minimum cost subgraph containing at least k edge-disjoint paths of at most L edges between each pair in D. This problem is of great interest in today's telecommunication industry, where highly survivable networks need to be constructed. We first study the particular case where the set of demands D is reduced to a single pair {s,t}. We propose an integer programming formulation for the problem, which consists in the st-cut and trivial inequalities, along with the so-called L-st-path-cut inequalities. We show that these three classes of inequalities completely describe the associated polytope when k=2 and L=2 or 3, and give necessary and sufficient conditions for them to be facet-defining. We also consider the dominant of the associated polytope, and discuss how the previous inequalities can be separated in polynomial time. We then extend the complete and minimal description obtained above to any number k of required edge-disjoint L-st-paths, but when L=2 only. We devise a cutting plane algorithm to solve the problem, using the previous polynomial separations, and present some computational results. After that, we consider the case where there is more than one demand in D. We first show that the problem is strongly NP-hard, for all L fixed, even when all the demands in D have one root node in common. For k=2 and L=2,3, we give an integer programming formulation, based on the previous constraints written for all pairs {s,t} in D. We then proceed by giving several new classes of facet-defining inequalities, valid for the problem in general, but more adapted to the rooted case. We propose separation procedures for these inequalities, which are embedded within a Branch-and-Cut algorithm to solve the problem when L=2,3. Extensive computational results from it are given and analyzed for both random and real instances. Since those results appear less satisfactory in the case of arbitrary demands (non necessarily rooted), we present additional families of valid inequalites in that situation. Again, separation procedures are devised for them, and added to our previous Branch-and-Cut algorithm, in order to see the practical improvement granted by them. Finally, we study the problem for greater values of L. In particular, when L=4, we propose new families of constraints for the problem of finding a subgraph that contains at least two L-st-paths either node-disjoint, or edge-disjoint. Using these, we obtain an integer programming formulation in the space of the design variables for each case. ------------------------------------------------ Dans cette thèse, nous considérons le problème de conception de réseau k-arete connexe à chemins L-bornés. Etant donné un graphe pondéré G=(N,E), un ensemble D de paires de noeuds terminaux, et deux entiers k,L > 1, ce problème consiste à trouver, dans G, un sous-graphe de cout minimum tel que, entre chaque paire dans D, il existe au moins k chemins arete-disjoints de longueur au plus L. Ce problème est d'un grand intéret dans l'industrie des télécommunications, où des réseaux hautement fiables doivent etre construits. Nous étudions tout d'abord le cas particulier où l'ensemble des demandes D est réduit à une seule paire de noeuds. Nous proposons une formulation du problème sous forme de programme linéaire en nombres entiers, laquelle consiste en les inégalités triviales et de coupe, ainsi que les inégalités dites de L-chemin-coupe. Nous montrons que ces trois types d'inégalités décrivent complètement le polytope associé lorsque k=2 et L=2,3, et donnons des conditions nécessaires et suffisantes pour que celles-ci en définissent des facettes. Nous considérons également le dominant du polytope associé et discutons de la séparation polynomiale des trois classes précédentes. Nous étendons alors cette description complète et minimale à tout nombre k de chemins arete-disjoints de longueur au plus 2. De plus, nous proposons un algorithme de plans coupants utilisant les précédentes séparations polynomiales, et en présentons quelques résultats calculatoires, pour tout k>1 et L=2,3. Nous considérons ensuite le cas où plusieurs demandes se trouvent dans D. Nous montrons d'abord que le problème est fortement NP-dur, pour tout L fixé et ce, meme si les demandes sont toutes enracinées en un noeud. Pour k=2 et L=2,3, nous donnons une formulation du problème sous forme de programme linéaire en nombres entiers. Nous proposons également de nouvelles classes d'inégalités valides, pour lesquelles nous réalisons une étude faciale. Celles-ci sont alors séparées dans le cadre d'un algorithme de coupes et branchements pour résoudre des instances aléatoires et réelles du problème. Enfin, nous étudions le problème pour de plus grandes valeurs de L. En particulier, lorsque L=4, nous donnons de nouvelles familles de contraintes pour le problème consistant à déterminer un sous-graphe contenant entre deux noeuds fixés au moins deux chemins de longueur au plus 4, que ceux-ci doivent etre arete-disjoints ou noeud-disjoints. Grace à ces dernières, nous parvenons à donner une formulation naturelle du problème dans chacun de ces deux cas.

在全球化的環境下推出新產品，企業除了面臨隨著產品生命週期改變的顧客需求以及成本上的不確定因素外，同時還必須考量全球營運帶來的種種挑戰。 許多供應鏈管理數量模式相關文獻針對全球運籌、新產品供應鏈等議題多有所探討，利用數量模式的計算以反應真實世界中的種種不確定性，讓管理者在供應鏈策略規劃時有所依據，但卻少有同時探討全球運籌以及新產品供應鏈的相關文獻。學者Butler, Ammons, and Sokol認為過去新產品供應鏈模式忽略了新產品將有可能無法存活下來的情形，因此發展一套新產品供應鏈模式，使新產品供應鏈能夠順利從上市成長到成熟階段，並利用此模式決定新設施、新機器購入的時機。 本研究延伸Butler等人之新產品供應鏈模式，考量更完整之全球運籌相關議題，透過混合整數線性規劃描述新產品發展時全球運籌配置問題，並利用情境為基礎的穩健最佳化以取得低風險的供應鏈配置，此外加入可靠度的影響，以彌補供應鏈規劃與實際操作的差距，並加入缺貨之懲罰成本，最後以範例資料進行計算與分析此數量模式，經由模式計算結果發現本研究規劃之結果，相較於原Butler等人之模式有較低的缺貨的發生可能性，且所求得之配置整體可靠度皆有所提升。 本研究所提出之規劃與分析方法可提供決策者在進行新產品全球佈局規劃時，能當作其新產品運籌配置之決策參考。 / When putting out new products under the environment of globalization, enterprise not only faces the uncertain factors in the demand of the customers and the costs that change with product life cycles, but considers all sorts of challenges which come with global operation. Many researches into supply chain quantitative model that probe into global logistics and the new product supply chain employ the quantitative model to reflect all sorts of uncertainty in the real world. They provide managers with the basis for the supply chain strategy and management. But few researches discuss about the global logistics and the new product supply chain simultaneously. Bulter, Ammons, and Sokol argue that the model of new product supply chain of the past neglects the condition which new products may not survive. Thus they developed a new product supply chain model to enable new products to launch the market and grow to maturity as well as decide when to purchase new supply chain facilities and equipments. This research which extends the new product supply chain model of Bulter et al. considers issues on global logistics from a more integrated view. First of all, it solves the global logistic settings problem in new product development by means of mixed-integer linear programming. Secondly, it uses the scenario-based robust optimization to lower the risk in the supply chain design. Then it adds the reliability calculation to make up for the gap between the plan and the real operation. At last it calculates and analyzes the quantitative model on the basis of the case data. This research establishes a methodology for decision makers to apply to plan and analyzing their new product supply chain when they make the global arrangement of new products.

Optical microcavities (OMs) are receiving increasing attention owing to their potential applications ranging from cavity quantum electrodynamics, optical detection to photonic devices. Recently, rolled-up structures have been demonstrated as OMs which have gained considerable attention owing to their excellent customizability. To fully exploit this customizability, asymmetric and topological rolled-up OMs are proposed and investigated in addition to conventional rolled-up OMs in this thesis. By doing so, novel phenomena and applications are demonstrated in OMs. The fabrication of conventional rolled-up OMs is presented in details. Then, dynamic mode tuning by a near-field probe is performed on a conventional rolled-up OM. Next, mode splitting in rolled-up OMs is investigated. The effect of single nanoparticles on mode splitting in a rolled-up OM is studied. Because of a non-synchronized oscillating shift for different azimuthal split modes induced by a single nanoparticle at different positions, the position of the nanoparticle can be determined on the rolled-up OM. Moreover, asymmetric rolled-up OMs are fabricated for the purpose of introducing coupling between spin and orbital angular momenta (SOC) of light into OMs. Elliptically polarized modes are observed due to the SOC of light. Modes with an elliptical polarization can also be modeled as coupling between the linearly polarized TE and TM mode in asymmetric rolled-up OMs. Furthermore, by adding a helical geometry to rolled-up structures, Berry phase of light is introduced into OMs. A -π Berry phase is generated for light in topological rolled-up OMs so that modes have a half-integer number of wavelengths. In order to obtain a deeper understanding for existing rolled-up OMs and to develop the new type of rolled-up OMs, complete theoretical models are also presented in this thesis.