The evolution and deployment of fifth-generation (5G) and beyond (B5G) infrastructure will require a tremendous effort to specify the design, standards, and manufacturing. 5G is vital to modern technological evolution, including industry 4.0, automotive, entertainment, and health care. The ambitious and challenging 5G project is classified into three categories, which provide an essential supporting platform for applications associated with: Enhanced mobile broadband (eMBB) Ultra-reliable low-latency communication (URLLC) Massive machine-type communication (mMTC) The demand for URLLC grows, particularly for applications like autonomous guided vehicles (AGVs), unmanned aerial vehicles (UAVs), and factory automation, and has a strict requirement of low latency of 1 ms and high reliability of 99.999%. To meet the needs of communication-sensitive and computation-intensive applications with different quality-of-service (QoS) requirements, this evolution focuses on ultra-dense edge networks with multi-access edge computing (MEC) facilities. MEC emerges as a solution, placing resourceful servers closer to users. However, the dynamic nature of processing and interaction patterns necessitates effective network control, which is challenging due to stringent requirements on both communication and computation. In this context, we introduce a novel approach to optimally manage task offloading, considering the intricacies of heterogeneous computing and communication services. Unlike existing methods, our methodology incorporates the number of admitted service migrations and QoS upper and lower bounds as binding constraints. The comprehensive model encompasses agent positions, MEC servers, QoS requirements, edge network communication, and server computing capabilities. Formulated as a mixed-integer linear program (MILP), it provides an optimal schedule for service migrations and bandwidth allocation, addressing the challenges posed by computation-intensive and communication-sensitive applications. Moreover, tailoring to an indoor robotics environment, we explore optimization-based approaches seeking an optimal system-level architecture while considering QoS guarantees. Optimization tools, e.g., ARCHEX, prove their ability to capture cyber-physical systems (CPS) requirements and generate correct-by-construction architectural solutions. We propose an extension in ARCHEX by incorporating dynamic properties, i.e., robot trajectories, time dimension, application-specific QoS constraints, and finally, integrating the optimization tool with a discrete-event network simulator (OMNeT++). This extension automates the generation of configuration files and facilitates result analysis, ensuring a comprehensive evaluation. This part of the work focuses on the dynamism of robots, server-to-service mapping, and the integration of automated simulation. The proposed extension is validated by optimizing and analyzing various indoor robotics scenarios, emphasizing critical performance parameters such as overall throughput and end-to-end delay (E2E). This integrated approach addresses the complex interplay of computation and communication resources, providing a solution for dynamic mobility, traffic, and application patterns in edge server environments.

通常已建立的指數基金，經過一段時間後其追蹤指數的效能已經無法滿足初期建購時的要求，此時管理者便面臨指數基金投資組合的調整問題。本論文融合建構指數基金的方法及最小化交易成本的概念，提出一個新的混合整數線性規劃模型以調整指數基金投資組合。模型亦考慮實務中交易成本、最小交易單位及批量、固定交易費用比率、以及資產總類數等限制。因此，模型包含整數變數及二元變數，求解也較為困難許多。本論文以啟發式演算法增進求解的效率，並以台灣50指數的相關資料做為實證研究的對象。 / The efficiency of index-tracking in index fund, which has been built, has usually been incapable to meet the needs after a period of time. In this moment, the managers have to face with the problems of the adjusting for index fund portfolio. In this paper, we integrate the methods of constructing index fund and the concepts of minimum transaction cost with it, and propose a new mixed integer linear program model to adjust the index fund portfolio. Moreover, the model also considers some limitations, such as the transaction costs, minimum transaction units and lots, fixed proportional transaction rates, and cardinality constraint in practical operating. For this reason, a set of integer variables and binary variables are introduced. However, they increase 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 50 index.

Modern traffic signal control systems have not changed significantly in the past 40-50 years. The most widely applied traffic signal control systems are still time-of-day, coordinated-actuated system, since many existing advanced adaptive signal control systems are too complicated and fathomless for most of people. Recent advances in communications standards and technologies provide the basis for significant improvements in traffic signal control capabilities. In the United States, the IntelliDriveSM program (originally called Vehicle Infrastructure Integration - VII) has identified 5.9GHz Digital Short Range Communications (DSRC) as the primary communications mode for vehicle-to-vehicle (v2v) and vehicle-to-infrastructure (v2i) safety based applications, denoted as v2x. The ability for vehicles and the infrastructure to communication information is a significant advance over the current system capability of point presence and passage detection that is used in traffic control systems. Given enriched data from IntelliDriveSM, the problem of traffic control can be solved in an innovative data-driven and mathematical way to produce robust and optimal outputs.In this doctoral research, three different problems within a v2x environment- "enhanced pseudo-lane-level vehicle positioning", "robust coordinated-actuated multiple priority control", and "multimodal platoon-based arterial traffic signal control", are addressed with statistical techniques and mathematical programming.First, a pseudo-lane-level GPS positioning system is proposed based on an IntelliDriveSM v2x environment. GPS errors can be categorized into common-mode errors and noncommon-mode errors, where common-mode errors can be mitigated by differential GPS (DGPS) but noncommon-mode cannot. Common-mode GPS errors are cancelled using differential corrections broadcast from the road-side equipment (RSE). With v2i communication, a high fidelity roadway layout map (called MAP in the SAE J2735 standard) and satellite pseudo-range corrections are broadcast by the RSE. To enhance and correct lane level positioning of a vehicle, a statistical process control approach is used to detect significant vehicle driving events such as turning at an intersection or lane-changing. Whenever a turn event is detected, a mathematical program is solved to estimate and update the GPS noncommon-mode errors. Overall the GPS errors are reduced by corrections to both common-mode and noncommon-mode errors.Second, an analytical mathematical model, a mixed-integer linear program (MILP), is developed to provide robust real-time multiple priority control, assuming penetration of IntelliDriveSM is limited to emergency vehicles and transit vehicles. This is believed to be the first mathematical formulation which accommodates advanced features of modern traffic controllers, such as green extension and vehicle actuations, to provide flexibility in implementation of optimal signal plans. Signal coordination between adjacent signals is addressed by virtual coordination requests which behave significantly different than the current coordination control in a coordinated-actuated controller. The proposed new coordination method can handle both priority and coordination together to reduce and balance delays for buses and automobiles with real-time optimized solutions.The robust multiple priority control problem was simplified as a polynomial cut problem with some reasonable assumptions and applied on a real-world intersection at Southern Ave. & 67 Ave. in Phoenix, AZ on February 22, 2010 and March 10, 2010. The roadside equipment (RSE) was installed in the traffic signal control cabinet and connected with a live traffic signal controller via Ethernet. With the support of Maricopa County's Regional Emergency Action Coordinating (REACT) team, three REACT vehicles were equipped with onboard equipments (OBE). Different priority scenarios were tested including concurrent requests, conflicting requests, and mixed requests. The experiments showed that the traffic controller was able to perform desirably under each scenario.Finally, a unified platoon-based mathematical formulation called PAMSCOD is presented to perform online arterial (network) traffic signal control while considering multiple travel modes in the IntelliDriveSM environment with high market penetration, including passenger vehicles. First, a hierarchical platoon recognition algorithm is proposed to identify platoons in real-time. This algorithm can output the number of platoons approaching each intersection. Second, a mixed-integer linear program (MILP) is solved to determine the future optimal signal plans based on the real-time platoon data (and the platoon request for service) and current traffic controller status. Deviating from the traditional common network cycle length, PAMSCOD aims to provide multi-modal dynamical progression (MDP) on the arterial based on the real-time platoon information. The integer feasible solution region is enhanced in order to reduce the solution times by assuming a first-come, first-serve discipline for the platoon requests on the same approach. Microscopic online simulation in VISSIM shows that PAMSCOD can easily handle two traffic modes including buses and automobiles jointly and significantly reduce delays for both modes, compared with SYNCHRO optimized plans.

Approved for public release; distribution is unlimited / To ensure sufficient capacity to handle unexpected demands for electric power, decision makers often over-estimate expeditionary power requirements. Therefore, we often use limited resources inefficiently by purchasing more generators and investing in more renewable energy sources than needed to run power systems on the battlefield. Improvement of the efficiency of expeditionary power units requires better managing of load requirements on the power grids and, where possible, shifting those loads to a more economical time of day. We analyze the performance of a previously developed optimization model for scheduling time-shiftable electrical loads in an expeditionary power grids model in two experiments. One experiment uses model data similar to the original baseline data, in which expected demand and expected renewable production remain constant throughout the day. The second experiment introduces unscheduled demand and realistic fluctuations in the power production and the demand distributions data that more closely reflect actual data. Our major findings show energy grid power production composition affects which uncertain factor(s) influence fuel con-sumption, and uncertainty in the energy grid system does not always increase fuel consumption by a large amount. We also discover that the generators running the most do not always have the best load factor on the grid, even when optimally scheduled. / Lieutenant Commander, United States Navy

Plusieurs problématiques de gestion d’opérations peuvent être formalisées avec un problème d’optimisation discret. Ces modèles d’optimisation sont traditionnellement développés sous l’hypothèse que les données d’entrée sont déterministes, non impactées par des changements inattendus ou des incertitudes. Au cours des dernières années, le besoin en modèles performants, incluant des outils efficaces et permettant de réagir de manière optimale aux imprévus (perturbations), n’a cessé de croitre. En phase d’exécution d’un système, plusieurs événements imprévus (incertitudes) peuvent le perturber et le faire dévier de son parcours original voire rendre son exécution impossible. Il est vrai que ces incertitudes peuvent être considérées de manière proactive par le biais d’une optimisation stochastique ou des modèles d'optimisation robustes. Mais même avec des solutions robustes, des événements inattendus peuvent encore se produire nécessitant de revoir le plan robuste en cours d’exécution. Dans cette thèse, l’objectif est de prendre en compte ces incertitudes de manière réactive dans les modèles. Ainsi, une nouvelle méthodologie générique est proposée pour les problèmes d'optimisation de réparation / récupération. En considérant les solutions réparées / récupérées fournies par cette méthodologie appliquée à un plan initial en cours de mise en oeuvre, un décideur peut vouloir minimiser les coûts d'exploitation, mais aussi limiter les changements par rapport au plan initial. Le problème de réparation / récupération est formulé comme un problème d'optimisation multiobjectif, qui minimise des fonctions spécifiques relatives à divers critères de réparation (pilotés par les choix du décideur). / A wide variety of operations management problems can be formulated and solved as discrete optimization problems. Traditionally, these models have been mostly developed and used under the assumption that the input data are known in advance, not subject to unexpected changes, nor impacted by uncertainty. In recent years, the need for improved models providing efficient tools for quickly and optimally reacting to the occurrence of unexpected events (disruptions) has become a more and more important issue. In the execution phase, various unanticipated events will disrupt the system and make the plan deviate from its intended course and even make it infeasible.Uncertainty can be taken into account in a proactive way with stochastic optimization or robust optimization models. However, even with robust solutions, unexpected events can still occur requiring to reconsider the robust plan under execution. In this thesis, we are interested to cope with uncertainty in a reactive way. We propose a new generic methodology for repair/recovery optimization problems. When considering repair/recovery solutions for the initial plan under implementation, the decision-maker may want to minimize operating costs, but also limit the changes with respect to the initial plan. We formulate the repair/recovery problem as a multiobjective optimization problem minimizing specified functions for various repair criteria.

Radio spectrum has become increasingly scarce due to the proliferation of new wireless communication services. This problem has been exacerbated by fixed bandwidth licensing policies that often lead to spectral underutilization. Cognitive radio networks (CRN) can address this issue using flexible spectrum management that permits unlicensed (secondary) users to access the licensed spectrum. Supporting real-time quality-of-service (QoS) in CRNs however, is very challenging, due to the random spectrum availability induced by the licensed (primary) user activity. This thesis considers the problem of real-time voice transmission in CRNs with an emphasis on secondary network ``friendliness''. Friendliness is measured by the secondary real-time voice capacity, defined as the number of connections that can be supported, subject to typical QoS constraints. The constant bit rate (CBR) air interface case is first assumed. An offline scheduler that maximizes friendliness is derived using an integer linear program (ILP) that can be solved using a minimum cost flow graph construction. Two online primary scheduling algorithms are then introduced. The first algorithm is based on shaping the primary spectral hole patterns subject to primary QoS constraints. The second applies real-time scheduling to both primary traffic and virtual secondary calls. The online scheduling algorithms are found to perform well compared to the friendliness upper bound. Extensive simulations of the primary friendly schedulers show the achievable secondary voice capacity for a variety of parameters compared to non-friendly primary scheduling. The thesis then considers the variable bit rate (VBR) air interface option for primary transmissions. Offline and online approaches are taken to generate a primary VBR traffic schedule that is friendly to secondary voice calls. The online VBR schedulers are found to perform well compared to the friendliness upper bound. Simulation results are presented that show the effect of the primary traffic load and primary network delay tolerance on the primary network friendliness level towards potential secondary voice traffic. Finally, secondary user friendliness is considered from an infrastructure deployment point of view. A cooperative framework is proposed, which allows the primary traffic to be relayed by helper nodes using decode-and-forward (DF) relaying. This approach decreases the primary traffic channel utilization, which, in turn, increases the capacity available to potential secondary users. A relay selection optimization problem is first formulated that minimizes the primary channel utilization. A greedy algorithm that assigns relay nodes to primary data flows is introduced and found to perform well compared to the optimum bound. Results are presented that show the primary network friendliness for different levels of primary channel utilization. / Dissertation / Doctor of Philosophy (PhD)

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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.

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.

O sequenciamento e a programação da produção trazem grandes benefícios financeiros às empresas se realizados de forma adequada. Atualmente, soluções generalizadas apresentam resultados aceitáveis, porém têm como consequência benefícios inferiores quando comparados a estudos específicos. O ramo da otimização de resultados possui dois tipos de soluções: as exatas para problemas de menores dimensões e não exatas, ou heurísticas, para problemas de médias e grandes dimensões. Este trabalho apresenta algoritmos exatos do tipo Branch & Bound e Modelos de Programação Linear Inteira Mista para solucionar quatro variações de problemas de scheduling: Fm|block|∑Cjm, Fm|block|∑Tj, Fm|block, Sijk|∑Cjm e Fm|block, Sijk|∑Tj. As abordagens utilizadas são inéditas na literatura e apresentaram resultados animadores para a maioria dos cenários. O limitante para o tempo total de fluxo obteve resposta ótima em 100% dos casos para problemas de até 20 tarefas e 4 máquinas em menos de uma hora. Para o tempo total de atraso, o limitante se mostrou mais eficiente quando os valores das due dates apresentam alta taxa de dispersão. Para os casos com setup, foram elaboradas três variações de limitantes para cada problema. O limitante com setup que apresentou o melhor desempenho foi o que obteve a melhor relação entre o seu valor numérico e seu custo computacional. Os modelos MILP solucionaram 100% dos problemas sem setup para até 20 tarefas e 4 máquinas e para os casos com setup, foram solucionados problemas de até 14 tarefas e 4 máquinas no tempo limite de uma hora. Os testes computacionais mostram a eficiência na redução do número de nós e, consequentemente, no tempo de execução. Portanto, o estudo realizado indica que, para problemas de pequeno porte e médio, os métodos em questão possuem grande potencial para aplicações práticas. / Job Sequence and Programming give benefits both financial and organizational to any company when performed properly. Nowadays, there is still a gap between theory and practice due to solutions that are short in specification. The analyzed problems differ in type and dimension thus modifying its complexity. The results optimization field is divided into two types of solution: the exact solution for minor problems and the non-exact solution for greater dimension problems. The present paper presents exact algorithms to solve the problems Fm|block|∑Cjm, Fm|block|∑Tj, Fm|block, Sijk|∑Cjm by the Branch & Bounds and Mixed Integer Linear Program models. The approaches are new and presented good results for most cases. Bounds for the no-setup total flow time scenario solved 100% of the 20 jobs and 4 machines cases. High dispersion range due dates contributed for the effectiveness of the no-setup total tardiness bound\'s effectiveness. Three different approaches were developed for the setup cases. The best approach aimed to optimize the value/effort factor for the B&B. The Mixed Integer Linear Program models solved 100% of the no-setup cases for 20 jobs and 4 machines. The MILPs setup cases solved optimally 14 jobs and 4 machines cases. Computational tests were executed and analyzed and they highlighted the node count reduction and, consequently, the execution time. The present study points out that the exact methods can be applied to small and medium scheduling problems in practice.