O ambiente produtivo denominado job shop representa empresas manufatureiras com características como: alta variedade de produtos, volume baixo de produção e uma fábrica dividida em áreas funcionais. O problema abordado neste trabalho trata da determinação do programa de produção (scheduling) de cada lote de produtos no ambiente job shop, com a premissa de que cada produto a ser elaborado surge através de um pedido realizado pelo cliente com especificações e particularidades próprias. O objetivo do trabalho é apresentar e examinar de forma detalhada as formulações matemáticas do tipo linear inteira mista (PLIM), encontradas na literatura para o ambiente que consideram a função objetivo do makespan. Além disso, se estabelece uma nova formulação matemática que auxilia a simulação do ambiente. Todas as formulações foram comparadas através de suas dimensões e testes computacionais. Adicionalmente são apresentadas três diferentes estratégias de resolução que permitem a exploração de soluções obtidas através de diferentes metodologias. A primeira estratégia estabelece para cada instância uma solução inicial que promove uma redução do número de combinações a serem avaliadas pelo software, a segunda estratégia combina duas formulações tornando uma formulação unificada, e a terceira estratégia, estabelece um processo que utiliza duas formulações de forma consecutiva compondo um procedimento sistemático. Experimentos computacionais indicam que a formulação com melhor desempenho para o problema de job shop é a formulação de Manne (1960) por obter o melhor limitante superior (upper bound). A formulação proposta apresenta o melhor limitante inferior (lower bound). Todas as formulações melhoram seus resultados através do uso das estratégias propostas. / The operational job shop environment, represents manufacturing companies with high product variety, low volume production and an organization divided into functional areas. The problem addressed in this work determines the production schedule of each batch production, with the premise that each product results from a request made by the client with specifications and its own particularities. The main objective here is to present and to examine in detail the mathematical integer - linear program formulations (MILP) from the literature for the job shop classic environment, which considers the makespan objective. Furthermore, a new mathematical formulation is provided to help with the simulation of the environment. All the formulations were compared by mathematical dimensions and computational tests. In addition, three different strategies are presented to promote the exploration of solutions obtained from new methodologies. The first strategy defines an initial solution for each problem and promotes a reduction of the combination number to be evaluated by the software. The second strategy considers the combination of two mathematical formulations under one objective function. The third strategy establishes a procedure in which two mathematical formulations are used consecutively, creating a systematic procedure. Computational experiments demonstrate that the best formulation for the job shop problem is the Manne (1960) formulation, since it obtains the best upper bound. The proposal formulation obtains the best lower bound. All of the formulations improve their results through the use of the proposed strategies.

Este texto trata de um dos temas fundamentais no planejamento de produção, o problema de dimensionamento de lotes de um único item. Uma descrição sucinta e informal do problema segue abaixo. Considere um intervalo de tempo dividido em períodos e que a cada período de tempo está associada a demanda de um item. Dados os custos e as eventuais restrições na produção e no armazenamento, determine os períodos em que se produzirá e em que quantidade para que as demandas sejam atendidas com o menor custo possível, respeitando as restrições impostas. Apresentamos aqui resultados sobre a estrutura ótima do problema, sobre complexidade e algoritmos para os casos básicos do problema / This text studies one of the core subjects in production planning, the single-item lot-sizing problem. A brief and informal description of this problem follows below. Considering a time interval split into time periods and that there is a demand of an item associated with each time period. Given production and holding costs and possibly production and holding restrictions, determine in which periods the production must occur and in which quantity, in order to attend the demands with a minimum cost, without violate any restriction. Here, it will be shown some results about the optimal structure of the problem, about the complexity and algorithms for the simpler cases

abstract: Fraud is defined as the utilization of deception for illegal gain by hiding the true nature of the activity. While organizations lose around $3.7 trillion in revenue due to financial crimes and fraud worldwide, they can affect all levels of society significantly. In this dissertation, I focus on credit card fraud in online transactions. Every online transaction comes with a fraud risk and it is the merchant's liability to detect and stop fraudulent transactions. Merchants utilize various mechanisms to prevent and manage fraud such as automated fraud detection systems and manual transaction reviews by expert fraud analysts. Many proposed solutions mostly focus on fraud detection accuracy and ignore financial considerations. Also, the highly effective manual review process is overlooked. First, I propose Profit Optimizing Neural Risk Manager (PONRM), a selective classifier that (a) constitutes optimal collaboration between machine learning models and human expertise under industrial constraints, (b) is cost and profit sensitive. I suggest directions on how to characterize fraudulent behavior and assess the risk of a transaction. I show that my framework outperforms cost-sensitive and cost-insensitive baselines on three real-world merchant datasets. While PONRM is able to work with many supervised learners and obtain convincing results, utilizing probability outputs directly from the trained model itself can pose problems, especially in deep learning as softmax output is not a true uncertainty measure. This phenomenon, and the wide and rapid adoption of deep learning by practitioners brought unintended consequences in many situations such as in the infamous case of Google Photos' racist image recognition algorithm; thus, necessitated the utilization of the quantified uncertainty for each prediction. There have been recent efforts towards quantifying uncertainty in conventional deep learning methods (e.g., dropout as Bayesian approximation); however, their optimal use in decision making is often overlooked and understudied. Thus, I present a mixed-integer programming framework for selective classification called MIPSC, that investigates and combines model uncertainty and predictive mean to identify optimal classification and rejection regions. I also extend this framework to cost-sensitive settings (MIPCSC) and focus on the critical real-world problem, online fraud management and show that my approach outperforms industry standard methods significantly for online fraud management in real-world settings. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2019

Terrorism threatens both international peace and security and is a national concern. It is believed that terrorist organizations rely heavily on a few key leaders and that destroying such an organization's leadership is essential to reducing its influence. Martonosi et al. (2011) argues that increasing the amount of communication through a key leader increases the likelihood of detection. If we model a covert organization as a social network where edges represent communication between members, we want to determine the subset of members to remove that maximizes the amount of communication through the key leader. A mixed-integer linear program representing this problem is presented as well as a decomposition for this optimization problem. As these approaches prove impractical for larger graphs, often running out of memory, the last section focuses on structural characteristics of vertices and subsets that increase communication. Future work should develop these structural properties as well as heuristics for solving this problem.

Network design problems have been prevalent and popular in the operations research community for decades, because of their practical and theoretical significance. Due to the relentless progression of technology and the creative development of intelligent, efficient algorithms, today we are able to efficiently solve or give excellent heuristic solutions to many network design problem instances. The purpose of this work is to thoroughly examine and tackle two classes of highly complex network design problems which find themselves at the cutting edge of modern research. First we examine the stochastic incremental network design problem. This problem differs from traditional network design problems through the addition of both temporal and stochastic elements. We present a modeling framework for this class of problems, conduct a thorough theoretical analysis of the solution structure, and give insights into solution methods. Next we introduce the robust network design problem with decision-dependent uncertainties. Traditional stochastic optimization approaches shy away from randomness which is directly influenced by a user's decisions, due to the computational challenges that arise. We present a two-stage stochastic programming framework, noting that the complexity of this class of problems is derived from a highly nonlinear term in the first-stage objective function. This term is due to the decision-dependent nature of the uncertainty. We perform a rigorous computational study in which we implement various solution algorithms which are both exact and heuristic, as well as both well-studied and original. For each of the two classes of problems examined in our work, we give suggestions for future study and offer insights into effective ways of tackling these problems in practice.

Improving performance of wind turbines through effective control strategies to reduce the power generation cost is highly desired by the wind industry. The majority of the literature on performance of wind turbines has focused on models derived from principles versed in physics. Physics-based models are usually complex and not accurate due to the fact that wind turbines involve mechanical, electrical, and software components. These components interact with each other and are subjected to variable loads introduced by the wind as well as the rotating elements of the wind turbine. Recent advances in data acquisition systems allow collection of large volumes of wind energy data. Although the prime purpose of data collection is monitoring conditions of wind turbines, the collected data offers a golden opportunity to address most challenging issues of wind turbine systems. In this dissertation, data mining is applied to construct accurate models based on the turbine collected data. To solve the data-driven models, evolutionary computation algorithms are applied. As data-driven based models are non-parametric, the evolutionary computation approach makes an ideal solution tool. Optimizing wind turbines with different objectives is studied to accomplish different research goals. Two research directions of wind turbines performance are pursued, optimizing a wind turbine performance and optimizing a wind farm performance. The goal of single wind turbine optimization is to improve wind turbine efficiency and its life-cycle. The performance optimization of a wind farm is to minimize the total cost of operating a wind farm based on the computed turbine scheduling strategies. The methodology presented in the dissertation is applicable to processes besides wind industry.

This dissertation explores workforce planning in manufacturing and healthcare systems. In manufacturing systems, the existing workforce planning models often lack fidelity with respect to the mechanism of learning. Learning refers to that employees’ productivity increases as they gain more experience. Workforce scheduling in the short term has a longer term impact on organizations’ capacity. The mathematical representations of learning are usually nonlinear. This nonlinearity complicates the planning models and provides opportunities to develop solution methodologies for realistically-sized instances. This research formulates the workforce planning problem as a mixed-integer nonlinear program (MINLP) and overcomes the limitations of cur- rent solution methods. Specifically, this research develops a reformulation technique that converts the MINLP to a mixed integer linear program (MILP) and proposes several techniques to speed up the solution time of solving the MILP. In organizations that use group work, workers learn not only by individual learning but also from knowledge transferred from team members. Managers face the decision of how to pair or team workers such that organizations benefit from this transfer of learning. Using a mathematical representation that incorporates both in- dividual learning and knowledge transfer between workers, this research considers the problem of grouping workers to teams and assigning teams to sets of jobs based on workers’ learning and knowledge transfer characteristics. This study builds a Mixed- integer nonlinear programs (MINP) for parallel systems with the objective of maximizing the system throughput and propose exact and heuristic solution approaches for solving the MINLP. In healthcare systems, we focus on managing medical technicians in medical laboratories, in particular, the phlebotomists. Phlebotomists draw specimens from patients based on doctors’ orders, which arrive randomly in a day. According to the literature, optimizing scheduling and routing in hospital laboratories has not been regarded as a necessity for laboratory management. This study is motivated by a real case at University of Iowa Hospital and Clinics, where there is a team of phlebotomists that cannot fulfill doctors requests in the morning shift. The goal of this research is routing these phlebotomists to patient units such that as many orders as possible are fulfilled during the shift. The problem is a team orienteering problem with stochastic rewards and service times. This research develops an a priori approach which applies a variable neighborhood search heuristic algorithm that improves the daily performance compared to the hospital practice.

We introduce and study a novel graph optimization problem to search for multiple cliques with the maximum overall weight, to which we denote as the Maximum Weighted Multiple Clique Problem (MWMCP). This problem arises in research involving network-based data mining, specifically, in bioinformatics where complex diseases, such as various types of cancer and diabetes, are conjectured to be triggered and influenced by a combination of genetic and environmental factors. To integrate potential effects from interplays among underlying candidate factors, we propose a new network-based framework to identify effective biomarkers by searching for "groups" of synergistic risk factors with high predictive power to disease outcome. An interaction network is constructed with vertex weight representing individual predictive power of candidate factors and edge weight representing pairwise synergistic interaction among factors. This network-based biomarker identification problem is then formulated as a MWMCP. To achieve near optimal solutions for large-scale networks, an analytical algorithm based on column generation method as well as a fast greedy heuristic have been derived. Also, to obtain its exact solutions, an advanced branch-price-and-cut algorithm is designed and solved after studying the properties of the problem. Our algorithms for MWMCP have been implemented and tested on random graphs and promising results have been obtained. They also are used to analyze two biomedical datasets: a Type 1 Diabetes (T1D) dataset from the Diabetes Prevention Trial-Type 1 (DPT-1) Study, and a breast cancer genomics dataset for metastasis prognosis. The results demonstrate that our network-based methods can identify important biomarkers with better prediction accuracy compared to the conventional feature selection that only considers individual effects.

In this thesis, we address problems from two topics of applied mathematics: linear integer programming and polyhedral computation. Linear integer programming concerns solving optimisation problems to maximise a linear cost function over the set of integer points in a polyhedron. Polyhedral computation is concerned with algorithms for computing different properties of convex polyhedra. First, we explore the theory and computation of Gröbner bases and Markov bases for linear integer programming. Second, we investigate and improve an algorithm from polyhedral computation that converts between different representations of cones and polyhedra. A Markov basis is a set of integer vectors such that we can move between any two feasible solutions of an integer program by adding or subtracting vectors in the Markov basis while never moving outside the set of feasible solutions. Markov bases are mainly used in algebraic statistics for sampling from a set of feasible solutions. The major contribution of this thesis is a fast algorithm for computing Markov bases, which we used to solve a previously intractable computational challenge. Gröbner basis methods are exact local search approaches for solving integer programs. We present a Gröbner basis approach that can use the structure of an integer program in order to solve it more efficiently. Gröbner basis methods are interesting mainly from a purely theoretical viewpoint, but they are also interesting because they may provide insight into why some classes of integer programs are difficult to solve using standard techniques and because someday they may be able to solve these difficult problems. Computing the properties of convex polyhedra is useful for solving problems within different areas of mathematics such as linear programming, integer programming, combinatorial optimisation, and computational geometry. We investigate and improve an algorithm for converting between a generator representation of a cone or polyhedron and a constraint representation of the cone or polyhedron and vice versa. This algorithm can be extended to compute circuits of matrices, which are used in computational biology for metabolic pathway analysis.

We propose an approach to address data uncertainty for discrete optimization problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. When both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty, we propose a robust integer programming problem of moderately larger size that allows to control the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation. When only the cost coefficients are subject to uncertainty and the problem is a 0 - 1 discrete optimization problem on n variables, then we solve the robust counterpart by solving n + 1 instances of the original problem. Thus, the robust counterpart of a polynomially solvable 0 -1 discrete optimization problem remains polynomially solvable. Moreover, we show that the robust counterpart of an NP-hard α-approximable 0 - 1 discrete optimization problem remains α-approximal. / Singapore-MIT Alliance (SMA)