The focus of this dissertation is solution strategies for stochastic mixed-integer programs with special structures. Motivation for the methods comes from the relatively sparse number of algorithms for solving stochastic mixed-integer programs. Two stage models with finite support are assumed throughout. The first contribution introduces the nodal decision framework under private information restrictions. Each node in the framework has control of an optimization model which may include stochastic parameters, and the nodes must coordinate toward a single objective in which a single optimal or close-to-optimal solution is desired. However, because of competitive issues, confidentiality requirements, incompatible database issues, or other complicating factors, no global view of the system is possible. An iterative methodology called the nodal decomposition-coordination algorithm (NDC) is formally developed in which each entity in the cooperation forms its own nodal deterministic or stochastic program. Lagrangian relaxation and subgradient optimization techniques are used to facilitate negotiation between the nodal decisions in the system without any one entity gaining access to the private information from other nodes. A computational study on NDC using supply chain inventory coordination problem instances demonstrates that the new methodology can obtain good solution values without violating private information restrictions. The results also show that the stochastic solutions outperform the corresponding expected value solutions. The next contribution presents a new algorithm called scenario Fenchel decomposition (SFD) for solving two-stage stochastic mixed 0-1 integer programs with special structure based on scenario decomposition of the problem and Fenchel cutting planes. The algorithm combines progressive hedging to restore nonanticipativity of the first-stage solution, and generates Fenchel cutting planes for the LP relaxations of the subproblems to recover integer solutions. A computational study SFD using instances with multiple knapsack constraint structure is given. Multiple knapsack constrained problems are chosen due to the advantages they provide when generating Fenchel cutting planes. The computational results are promising, and show that SFD is able to find optimal solutions for some problem instances in a short amount of time, and that overall, SFD outperforms the brute force method of solving the DEP.

This dissertation discusses two independent topics. The first part of the dissertation relates three theories of international economics (comparative advantage, competitive advantage, and competitiveness), and formulates the thesis that incorporating them in the form of readily available individual competitiveness indicators in OR/MS models offers promise to enhance decision-support for the strategic planning of global supply chains in general, and for locating facilities in particular. The objectives of this research were to relate each of these theories and to describe their interrelationships; to describe measures provided by two well-known annual competitiveness reports; and to illustrate application of the theories as a means of supporting the thesis of the research, and justifying the research questions we pose for future research. While this research discusses topics relative to the broader background of global supply chain design, it illustrates applications associated with facility location, a component of the global supply chain design. In the last chapter of the first part of the dissertation, we provide a vision to foster future research that will enhance the profitability of international enterprises under NAFTA. The second part of the dissertation deals with the DSCR model with capacity expansion and contraction. The strategic dynamic supply chain reconfiguration (DSCR) problem is to prescribe the location and capacity of each facility, select links used for transportation, and plan material flows through the supply chain, including production, inventory, backorder, and outsourcing levels. The objective is to minimize total cost. The configuration must be dynamically redesigned over time to accommodate changing trends in demand and/or costs by opening facilities, expanding and/or contracting their capacities, and closing facilities. The problem involves a multi-period, multi-product, multi-echelon supply chain. Research objectives are alternative formulations of DSCR and tests that identify the computational characteristics of each model to determine if one offers superior solvability in comparison with the others. To achieve the first objective, we present an initial MIP model, a refined model that relates decision variables according to a convenient structure, and branch and price (B&P) schemes for the refined model. We found that the network-based formulation offered superior solvability compared to the traditional formulation.

In this thesis modelling and solution methods for portfolio optimisation are presented. The investigations reported in this thesis extend the Markowitz mean-variance model to the domain of quadratic mixed integer programming (QMIP) models which are 'NP-hard' discrete optimisation problems. In addition to the modelling extensions a number of challenging aspects of solution algorithms are considered. The relative performances of sparse simplex (SSX) as well as the interior point method (IPM) are studied in detail. In particular, the roles of 'warmstart' and dual simplex are highlighted as applied to the construction of the efficient frontier which requires processing a family of problems; that is, the portfolio planning model stated in a parametric form. The method of solving QMIP models using the branch and bound algorithm is first developed; this is followed up by heuristics which improve the performance of the (discrete) solution algorithm. Some properties of the efficient frontier with discrete constraints are considered and a method of computing the discrete efficient frontier (DEF) efficiently is proposed. The computational investigation considers the efficiency and effectiveness in respect of the scale up properties of the proposed algorithm. The extensions of the real world models and the proposed solution algorithms make contribution as new knowledge.

In April 2008, the Ontario government announced its top two healthcare priorities for the next 4 years, one of which is reducing wait time in emergency rooms. To study the wait time in emergency rooms or any other departments in a hospital, one must investigate resource planning, scheduling, and utilization within the hospital. This thesis provides hospitals with a set of simulation and optimization tools to help identify areas of improvement, particularly when there are a number of alternatives under consideration. A simulation tool (a Monte Carlo simulation model) estimates patient demand for beds in a hospital during a typical week. Two optimization tools (an integer programming mathematical model and a heuristics model) demonstrate opportunities for smoothing the patient demand for beds by adjusting the operating room schedule.

In April 2008, the Ontario government announced its top two healthcare priorities for the next 4 years, one of which is reducing wait time in emergency rooms. To study the wait time in emergency rooms or any other departments in a hospital, one must investigate resource planning, scheduling, and utilization within the hospital. This thesis provides hospitals with a set of simulation and optimization tools to help identify areas of improvement, particularly when there are a number of alternatives under consideration. A simulation tool (a Monte Carlo simulation model) estimates patient demand for beds in a hospital during a typical week. Two optimization tools (an integer programming mathematical model and a heuristics model) demonstrate opportunities for smoothing the patient demand for beds by adjusting the operating room schedule.

abstract: This research by studies the computational performance of four different mixed integer programming (MIP) formulations for single machine scheduling problems with varying complexity. These formulations are based on (1) start and completion time variables, (2) time index variables, (3) linear ordering variables and (4) assignment and positional date variables. The objective functions that are studied in this paper are total weighted completion time, maximum lateness, number of tardy jobs and total weighted tardiness. Based on the computational results, discussion and recommendations are made on which MIP formulation might work best for these problems. The performances of these formulations very much depend on the objective function, number of jobs and the sum of the processing times of all the jobs. Two sets of inequalities are presented that can be used to improve the performance of the formulation with assignment and positional date variables. Further, this research is extend to single machine bicriteria scheduling problems in which jobs belong to either of two different disjoint sets, each set having its own performance measure. These problems have been referred to as interfering job sets in the scheduling literature and also been called multi-agent scheduling where each agent's objective function is to be minimized. In the first single machine interfering problem (P1), the criteria of minimizing total completion time and number of tardy jobs for the two sets of jobs is studied. A Forward SPT-EDD heuristic is presented that attempts to generate set of non-dominated solutions. The complexity of this specific problem is NP-hard. The computational efficiency of the heuristic is compared against the pseudo-polynomial algorithm proposed by Ng et al. [2006]. In the second single machine interfering job sets problem (P2), the criteria of minimizing total weighted completion time and maximum lateness is studied. This is an established NP-hard problem for which a Forward WSPT-EDD heuristic is presented that attempts to generate set of supported points and the solution quality is compared with MIP formulations. For both of these problems, all jobs are available at time zero and the jobs are not allowed to be preempted. / Dissertation/Thesis / Ph.D. Industrial Engineering 2012

Submitted by Marcelo Ferreira (clikmarcelo@yahoo.com.br) on 2018-09-05T04:31:34Z No. of bitstreams: 1 Tese de Marcelo Ferreira - Doutorado em Matemática.pdf: 2503649 bytes, checksum: 7e5babb359afbdff94f0d88f504985c5 (MD5) / Rejected by Elza Mitiko Sato null (elzasato@ibilce.unesp.br), reason: Solicitamos que realize correções na submissão seguindo as orientações abaixo: Problema 01) A paginação deve ser sequencial, iniciando a contagem na folha de rosto e mostrando o número a partir da introdução, a ficha catalográfica ficará após a folha de rosto e não deverá ser contada, você iniciou a contagem na página que contém a lista de figuras. A correção deve ser feita também no sumário. OBS:-Estou encaminhando via e-mail o template/modelo das páginas pré-textuais para que você possa fazer as correções, sugerimos que siga este modelo pois ele contempla as normas da ABNT Lembramos que o arquivo depositado no repositório deve ser igual ao impresso, o rigor com o padrão da Universidade se deve ao fato de que o seu trabalho passará a ser visível mundialmente. Agradecemos a compreensão. on 2018-09-05T13:47:24Z (GMT) / Submitted by Marcelo Ferreira (clikmarcelo@yahoo.com.br) on 2018-09-05T17:21:36Z No. of bitstreams: 1 Tese Marcelo Ferreira.pdf: 2501829 bytes, checksum: 90e5dbff7459a9f26f354110d615fe46 (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2018-09-05T18:50:17Z (GMT) No. of bitstreams: 1 ferreira_m_dr_sjrp.pdf: 2463292 bytes, checksum: c3ef62f0a5f3a7e55c2010f641a09d3c (MD5) / Made available in DSpace on 2018-09-05T18:50:17Z (GMT). No. of bitstreams: 1 ferreira_m_dr_sjrp.pdf: 2463292 bytes, checksum: c3ef62f0a5f3a7e55c2010f641a09d3c (MD5) Previous issue date: 2018-07-31 / Nessa tese abordamos dois problemas reais identificados no processo produtivo de indústrias de embalagens de papelão ondulado, que denotaremos por Problema de Minimização de Trocas de Gramaturas e Rolos Corrugadores (PMTGRC) e Problema da Alocação de Bobinas no Corrugador (PABC). Ambos os problemas ocorrem no corrugador, máquina multiestágio que produz as chapas de papelão ondulado. O PMTGRC surge da necessidade de minimizar trocas de gramaturas e rolos corrugadores durante o processo de produção dos boletins, uma vez que cada boletim traz as gramaturas específicas das camadas da chapa, além do tipo de onda empregada no(s) miolos(s). O sequenciamento dos boletins impacta na quantidade de mudanças de gramaturas nos porta-bobinas e se haverátrocaderoloscorrugadoresparadoisboletinssubsequentes. Astrocasdegramaturas impactam em custos de transporte de bobinas e as trocas de rolos corrugadores impactam em perda de produtividade. Para o PMTGRC propomos quatro modelos inéditos de programação inteira capazes de integrar essas duas considerações. O PABC integra várias considerações relacionadas à alocação das bobinas no corrugador, como por exemplo, a minimização das sobras não aproveitáveis e das quantidades de consumos parciais, fatores que influenciam diretamente nos custos de produção. Um modelo linear inteiro misto inédito é proposto, determinando quais bobinas serão utilizadas em cada porta-bobinas. Além disso, propomos uma estratégia de sequenciamento das bobinas em cada porta-bobina, evitando paragens no corrugador. Uma série de testes computacionais utilizando instâncias geradas com base em dados reais foram realizados. Os resultados indicam que os modelos foram eficientes em tratar os problemas propostos. / In this thesis we approached two real problems identified over the productive process of corrugated cardboard industries, which we will denote as the Minimization of Converting Weights and Corrugators Problem (MCWCP) and the Corrugators Coil Allocation Problem (CCAP). Both of these problems happen in the corrugators, a multistage machine which produces corrugated cardboard. The MCWCP appears from the necessity to minimize changes of weight and corrugator rolls during the production process of the bulletins, since each one brings the specific layers’s weight of the sheets, besides the kind of wave put in the middle. The sequence of bulletins impact in the number of weight changes in the coil holders and if there will be corrugating rollers’s exchange for two following bulletins. The gramature’s exchanges impact in the costs of transportation and the corrugating rollers exchange causes lost in the productivity. We propose four whole programming models capable of integrating both considerations. The CCAP integrates many considerations related to the coils’s allocation on the corrugators, for example, the minimization of the non-usable leftovers and the amount of partial consumption, factors which influence directly on the production’s costs. A whole new mist linear model is proposed, determined which coil on the corrugators are going to be used in each coil holder. Besides this, we propose a sequel strategy for the coils in each coil holder, avoiding stops on the corrugators. A series of computation tests using instances created based on real data were made. The results indicate that the models were efficient in solving the problems.

abstract: Traditional deterministic reserve requirements rely on ad-hoc, rule of thumb methods to determine adequate reserve in order to ensure a reliable unit commitment. Since congestion and uncertainties exist in the system, both the quantity and the location of reserves are essential to ensure system reliability and market efficiency. The modeling of operating reserves in the existing deterministic reserve requirements acquire the operating reserves on a zonal basis and do not fully capture the impact of congestion. The purpose of a reserve zone is to ensure that operating reserves are spread across the network. Operating reserves are shared inside each reserve zone, but intra-zonal congestion may block the deliverability of operating reserves within a zone. Thus, improving reserve policies such as reserve zones may improve the location and deliverability of reserve. As more non-dispatchable renewable resources are integrated into the grid, it will become increasingly difficult to predict the transfer capabilities and the network congestion. At the same time, renewable resources require operators to acquire more operating reserves. With existing deterministic reserve requirements unable to ensure optimal reserve locations, the importance of reserve location and reserve deliverability will increase. While stochastic programming can be used to determine reserve by explicitly modelling uncertainties, there are still scalability as well as pricing issues. Therefore, new methods to improve existing deterministic reserve requirements are desired. One key barrier of improving existing deterministic reserve requirements is its potential market impacts. A metric, quality of service, is proposed in this thesis to evaluate the price signal and market impacts of proposed hourly reserve zones. Three main goals of this thesis are: 1) to develop a theoretical and mathematical model to better locate reserve while maintaining the deterministic unit commitment and economic dispatch structure, especially with the consideration of renewables, 2) to develop a market settlement scheme of proposed dynamic reserve policies such that the market efficiency is improved, 3) to evaluate the market impacts and price signal of the proposed dynamic reserve policies. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2015

abstract: Revenue management is at the core of airline operations today; proprietary algorithms and heuristics are used to determine prices and availability of tickets on an almost-continuous basis. While initial developments in revenue management were motivated by industry practice, later developments overcoming fundamental omissions from earlier models show significant improvement, despite their focus on relatively esoteric aspects of the problem, and have limited potential for practical use due to computational requirements. This dissertation attempts to address various modeling and computational issues, introducing realistic choice-based demand revenue management models. In particular, this work introduces two optimization formulations alongside a choice-based demand modeling framework, improving on the methods that choice-based revenue management literature has created to date, by providing sensible models for airline implementation. The first model offers an alternative formulation to the traditional choice-based revenue management problem presented in the literature, and provides substantial gains in expected revenue while limiting the problem’s computational complexity. Making assumptions on passenger demand, the Choice-based Mixed Integer Program (CMIP) provides a significantly more compact formulation when compared to other choice-based revenue management models, and consistently outperforms previous models. Despite the prevalence of choice-based revenue management models in literature, the assumptions made on purchasing behavior inhibit researchers to create models that properly reflect passenger sensitivities to various ticket attributes, such as price, number of stops, and flexibility options. This dissertation introduces a general framework for airline choice-based demand modeling that takes into account various ticket attributes in addition to price, providing a framework for revenue management models to relate airline companies’ product design strategies to the practice of revenue management through decisions on ticket availability and price. Finally, this dissertation introduces a mixed integer non-linear programming formulation for airline revenue management that accommodates the possibility of simultaneously setting prices and availabilities on a network. Traditional revenue management models primarily focus on availability, only, forcing secondary models to optimize prices. The Price-dynamic Choice-based Mixed Integer Program (PCMIP) eliminates this two-step process, aligning passenger purchase behavior with revenue management policies, and is shown to outperform previously developed models, providing a new frontier of research in airline revenue management. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2016

A presente pesquisa aborda um problema de roteirização e programação de veículos incorporando uma nova restrição operacional: a requisição simultânea de múltiplos veículos para atendimento da demanda. Trata-se de uma característica encontrada em operações de apoio à exploração de petróleo \"offshore\", em que mais de uma embarcação é requerida para executar tarefas de reboque e lançamento de linhas de ancoragem. Esta imposição, somada às restrições de janela de tempo, precedência entre tarefas, autonomia das embarcações e atendimento integral da demanda, configuram este problema. A programação é orientada pela minimização dos custos variáveis da operação e dos custos associados ao nível de serviço no atendimento. Este problema é uma variação do problema clássico de roteirização e programação de veículos com janela de tempo, de classe NP-Difícil. Nesta pesquisa, propõe-se modelar e resolver o problema em escala real por meio do algoritmo \"branch and cut\" acoplado às heurísticas de busca em vizinhança \"local branching\" e \"variable neighborhood search\". Para gerar as soluções iniciais será empregado o método \"feasibility pump\" e uma heurística construtiva. / This research focuses a fleet scheduling problem with new operational constraints: each task requiring multiple types of vehicles simultaneously. This kind of operation occurs in offshore exploitation and production sites, when more than one vessel is needed to accomplish the tugging and mooring of oil platforms. Other constraints are maintained such as time windows, precedence between tasks, route duration and the demand attendance. The solution schedules are cost oriented, which encompasses the routing variable costs and the customer service costs. This is a variation of the classical fleet routing and scheduling, which is an NP-Hard problem. This research aims to solve the real scale problem through a combined use of branch and cut strategy with local search algorithms such as local branching and variable neighborhood search. An efficient heuristic rule will be used in order to generate initial solutions using the feasibility pump method.