In this dissertation, a finitely convergent disjunctive programming procedure, the Convex Hull Tree (CHT) algorithm, is proposed to obtain the convex hull of a general mixed–integer linear program with bounded integer variables. The CHT algorithm constructs a linear program that has the same optimal solution as the associated mixed-integer linear program. The standard notion of sequential cutting planes is then combined with ideasunderlying the CHT algorithm to help guide the choice of disjunctions to use within a new cutting plane method, the Cutting Plane Tree (CPT) algorithm. We show that the CPT algorithm converges to an integer optimal solution of the general mixed-integer linear program with bounded integer variables in finitely many steps. We also enhance the CPT algorithm with several techniques including a “round-of-cuts” approach and an iterative method for solving the cut generation linear program (CGLP). Two normalization constraints are discussed in detail for solving the CGLP. For moderately sized instances, our study shows that the CPT algorithm provides significant gap closures with a pure cutting plane method.

A payment is the most fundamental aspect of a trade that involves funds. In recent years, the development of new payment services has accelerated significantly as the world has moved further into the digital era. This transition has led to an increased demand of digital payment solutions that can handle trades across the world. As trades today can be agreed at any time wherever the payer and payee are located, the party that mediates payments must at any time to be available in order to mediate an agreed exchange. This requires the payment service provider to always have funds available in the required countries and currencies in order for trades to always be available. This thesis concerns how a payment service provider can reallocate capital in a cost efficient way in order for trades to always be available. Traditionally, the reallocation of capital is done in a rule-based manner, which discard the cost dimension and thereby only focus on the reallocation itself. This thesis concerns methods to optimally reallocate capital focusing on the cost of transferring capital within the network. Where the concerned methods has the potential of transferring capital in a far more cost efficient way. When mathematically formulating the reallocation decisions as an optimization problem, the cost function is formulated as a linear program with both Boolean and real constraints. This impose non-feasibility of locating the optimal solution using traditional methods for linear programs, why developed traditional and more advanced methods were used. The model was evaluated based on a large number of simulations in comparison with the performance of a rule-based reallocation system. The developed model provides a significant cost reduction compared to the rule-based approach and thereby outperforms the traditional reallocation system. Future work should focus on expanding the model by broadening the available transfer options, by increasing the considered uncertainty via a bayesian treatment and finally by considering all cost aspects of the network. / En betalning är den mest fundamentala aspekten av handel som involverar kapital. De senaste åren har utvecklingen av nya betalmedel ökat drastiskt då världen fortsatt att utvecklas genom digitaliseringen. Utvecklingen har lett till en ökad efterfrågan på digitala betalningslösningar som kan hantera handel över hela världen. Då handel idag kan ske när som helst oberoende av var betalaren och betalningsmottagaren befinner sig, måste systemet som genomför betalningen alltid vara tillgängligt för att kunna förmedla handel mellan olika parter. Detta kräver att betalningssystemet alltid måste ha medel tillgängligt i efterfrågade länder och valutor för att handeln ska kunna genomföras. Den här uppsatsen fokuserar på hur kapital kostnadseffektivt kan omallokeras i ett betalsystem för att säkerställa att handel alltid är tillgängligt. Traditionellt har omallokeringen av kapital gjorts på ett regelbaserat sätt, vilket inte tagit hänsyn till kostnadsdimensionen och därigenom enbart fokuserat på själva omallokeringen. Den här uppsatsen använder metoder för att optimalt omallokera kapital baserat på kostnaderna för omallokeringen. Därigenom skapas en möjlighet att flytta kapital på ett avsevärt mer kostnadseffektivt sätt. När omallokeringsbesluten formuleras matematiskt som ett optimeringsproblem är kostnadsfunktionen formulerad som ett linjärt program med både Booleska och reella begränsningar av variablerna. Detta gör att traditionella lösningsmetoder för linjära program inte är användningsbara för att finna den optimala lösningen, varför vidareutveckling av tradtionella metoder tillsammans med mer avancerade metoder använts. Modellen utvärderades baserat på ett stort antal simuleringar som jämförde dess prestanda med det regelbaserade systemet. Den utvecklade modellen presterar en signfikant kostnadsreduktion i jämförelse med det regelbaserade systemet och överträffar därigenom det traditionellt använda systemet. Framtida arbete bör fokusera på att expandera modellen genom att utöka de potentiella överföringsmöjligheterna, att ta ökad hänsyn till osäkerhet genom en bayesiansk hantering, samt slutligen att integrera samtliga kostnadsaspekter i nätverket.

Submitted by Luciano Pereira Varanis (luciano_varanis@yahoo.com) on 2015-06-29T19:17:42Z No. of bitstreams: 1 Dissertação _Luciano_Varanis - Completo.pdf: 1367224 bytes, checksum: 848c44e67420ced7c19a6d2d1ab98f61 (MD5) / Approved for entry into archive by Janete de Oliveira Feitosa (janete.feitosa@fgv.br) on 2015-07-22T20:07:23Z (GMT) No. of bitstreams: 1 Dissertação _Luciano_Varanis - Completo.pdf: 1367224 bytes, checksum: 848c44e67420ced7c19a6d2d1ab98f61 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2015-07-24T17:56:00Z (GMT) No. of bitstreams: 1 Dissertação _Luciano_Varanis - Completo.pdf: 1367224 bytes, checksum: 848c44e67420ced7c19a6d2d1ab98f61 (MD5) / Made available in DSpace on 2015-07-24T17:56:24Z (GMT). No. of bitstreams: 1 Dissertação _Luciano_Varanis - Completo.pdf: 1367224 bytes, checksum: 848c44e67420ced7c19a6d2d1ab98f61 (MD5) Previous issue date: 2014-12-18 / In this dissertation we discuss models and solution methods of stochastic programs to solve ALM problmes for pension funds. We will provide the model from Drijver et al. based on Multistage Mixed-integer Stochastic Programming. A case study based on simulation for an ALM problem will be presented / Nesta dissertação discutiremos modelos e métodos de soluções de programação estocástica para resolver problemas de ALM em fundos de pensão. Apresentaremos o modelo de (Drijver et al.), baseado na programação estocástica multiestágios inteira-mista. Um estudo de caso para um problema de ALM será apresentado usando simulação de cenários.

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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

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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.