Solution of minimum spanning forest problems with reliability constraints

We propose the reliability constrained k-rooted minimum spanning forest, a relevant optimization problem whose aim is to find a k-rooted minimum cost forest that connects given customers to a number of supply vertices, in such a way that a minimum required reliability on each path between a customer and a supply vertex is satisfied and the cost is a minimum. The reliability of an edge is the probability that no failure occurs on that edge, whereas the reliability of a path is the product of the reliabilities of the edges in such path. The problem has relevant applications in the design of networks, in fields such as telecommunications, electricity and transports. For its solution, we propose a mixed integer linear programming model, and an adaptive large neighborhood search metaheuristic which invokes several shaking and local search operators. Extensive computational tests prove that the metaheuristic can provide good quality solutions in very short computing times

Spatial Optimization Methods And System For Redistricting Problems

Redistricting is the process of dividing space into districts or zones while optimizing a set of spatial criteria under certain constraints. Example applications of redistricting include political redistricting, school redistricting, business service planning, and city management, among many others. Redistricting is a mission-critical component in operating governments and businesses alike. In research fields, redistricting (or region building) are also widely used, such as climate zoning, traffic zone analysis, and complex network analysis. However, as a combinatorial optimization problem, redistricting optimization remains one of the most difficult research challenges. There are currently few automated redistricting methods that have the optimization capability to produce solutions that meet practical needs. The absence of effective and efficient computational approaches for redistricting makes it extremely time-consuming and difficult for an individual person to consider multiple criteria/constraints and manually create solutions using a trial-and-error approach. To address both the scientific and practical challenges in solving real-world redistricting problems, this research advances the methodology and application of redistricting by developing a new computational spatial optimization method and a system platform that can address a wide range of redistricting problems, in an automated and computation-assisted manner. The research has three main contributions. First, an efficient and effective spatial optimization method is developed for redistricting. The new method is based on a spatially constrained and Tabu-based heuristics, which can optimize multiple criteria under multiple constraints to construct high-quality optimization solutions. The new approach is evaluated with real-world redistricting applications and compared with existing methods. Evaluation results show that the new optimization algorithm is more efficient (being able to allow real-time user interaction), more flexible (considering multiple user-expressed criteria and constraints), and more powerful (in terms of optimization quality) than existing methods. As such, it has the potential to enable general users to perform complex redistricting tasks. Second, a redistricting system, iRedistrict, is developed based on the newly developed spatial optimization method to provide user-friendly visual interface for defining redistricting problems, incorporating domain knowledge, configuring optimization criteria and methodology parameters, and ultimately meeting the needs of real-world applications for tackling complex redistricting tasks. It is particularly useful for users of different skill levels, including researchers, practitioners, and the general public, and thus enables public participation in challenging redistricting tasks that are of immense public interest. Performance evaluations with real-world case studies are carried out. Further computational strategies are developed and implemented to handle large datasets. Third, the newly developed spatial optimization method is extended to solve a different spatial optimization problem, i.e., spatial community structure detection in complex networks, which is to partition networks to discover spatial communities by optimizing an objective function. Moreover, a series of new evaluations are carried out with synthetic datasets. This set of evaluations is different from the previous evaluations with case studies in that, the optimal solution is known with synthetic data and therefore it is possible to evaluate (1) whether the optimization method can discover the true pattern (global optima), and (2) how different data characteristics may affect the performance of the method. Evaluation results reveal that existing non-spatial methods are not robust in detecting spatial community structure, which may produce dramatically different outcomes for the same data with different characteristics, such as different spatial aggregations, sampling rates, or noise levels. The new optimization method with spatial constraints is significantly more stable and consistent. In addition to evaluations with synthetic datasets, a case study is also carried out to detect urban community structure with human movements, to demonstrate the application and effectiveness of the approach

Operational research IO 2021—analytics for a better world. XXI Congress of APDIO, Figueira da Foz, Portugal, November 7–8, 2021

This book provides the current status of research on the application of OR methods to solve emerging and relevant operations management problems. Each chapter is a selected contribution of the IO2021 - XXI Congress of APDIO, the Portuguese Association of Operational Research, held in Figueira da Foz from 7 to 8 November 2021. Under the theme of analytics for a better world, the book presents interesting results and applications of OR cutting-edge methods and techniques to various real-world problems. Of particular importance are works applying nonlinear, multi-objective optimization, hybrid heuristics, multicriteria decision analysis, data envelopment analysis, simulation, clustering techniques and decision support systems, in different areas such as supply chain management, production planning and scheduling, logistics, energy, telecommunications, finance and health. All chapters were carefully reviewed by the members of the scientific program committee.info:eu-repo/semantics/publishedVersio

Recent Mathematical Approaches to Service Territory Design

Many companies and institutions operate a field service workforce to provide services at their customers\u27 sites. Examples include the sales force of consumer goods manufacturers, the field service technicians of engineering companies, and the nurses of home-health care providers. To obtain clearly defined areas of responsibility, the geographical region under study is in many cases subdivided into service territories, each of which is served by a single field worker or a team of field workers. The design of service territories is subject to various planning criteria. The most common ones are geographical compactness, contiguity, and balance in terms of workload or income potential, but there can be several additional criteria and requirements depending on the specific application. In this thesis, we deal with the development of mathematical models and methods for service territory design problems. Our focus is on planning requirements that are relevant for practice, but have received little attention in the existing literature on territory design so far. We address the question how these requirements can be incorporated into mathematical models and mathematical programming based solution methods. We first present requirements that restrict the feasible assignments of customers to field workers and provide components for their integration into mathematical models. We further consider the requirement that customers must be served multiple times during a given planning horizon. We introduce the resulting problem, which we call the multi-period service territory design problem (MPSTDP). It has not yet been studied in the literature. The emphasis is put on the scheduling task of the MPSTDP, which deals with the assignment of service visits to the days of the planning horizon. We formally define this task and devise a heuristic solution method. Our heuristic produces high-quality solutions and clearly outperforms the existing software product of our industry partner. Moreover, we present the first specially-tailored exact solution method for this task: a branch-and-price algorithm that incorporates specialized acceleration techniques, such as a fast pricing heuristic and symmetry reduction techniques. Ultimately, we study the design of territories for parcel delivery companies. We address the tactical design of the territories and their daily adjustment in order to cope with demand fluctuations. The problem involves determining the number of territories and assigning heterogeneous resources to the territories, a combination not yet addressed in literature. We propose different models as well as a heuristic solution approach, and we perform an extensive case study on real-world problem data

A organização da justiça eleitoral brasileira : um método de redistribuição das zonas eleitorais de Santa Catarina

Orientador : Prof. Dr. Cassius Tadeu ScarpinAnexo cd-romDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia de Produção. Defesa: Curitiba, 12/03/2015Inclui referênciasResumo: A criação e a abrangências das Zonas Eleitorais no Brasil se deu principalmente, até o presente momento, segundo um único critério, a saber, o número de eleitores. Fatores como o número de processos tramitando, o número de municípios atendidos e outros não foram levados em consideração, causando distorções no volume de trabalho de cada Zona Eleitoral. Surge então, neste contexto, a oportunidade de aplicação dos conceitos e métodos de Pesquisa Operacional no sentido de estudar o problema em tela e reorganizar os recursos humanos e materiais já existentes para equalizar o volume de trabalho das zonas eleitorais, trazendo reflexo direto no melhor atendimento à população e ao uso mais eficiente dos recursos públicos, fato que é um anseio e uma necessidade crescente em nosso país. Utilizou-se uma modelagem multi-objetivo para realizar a designação de aproximadamente 3900 pontos (os locais de votação de Santa Catarina) a um intervalo de 76 a 131 Zonas Eleitorais, gerando a simulação de 56 cenários disponíveis para análises. Palavras chave: Setor público, otimização, Justiça Eleitoral, p-mediana, algoritmo genético.Abstract: The creation and the frontiers of Electoral Districts in Brazil, until now, followed the application of only one criteria, the number of electors. The number of judicial processes, the number of municipalities and other factors were not considered before, causing distortions on the work load distribution of each electoral district. This scenario brings the opportunity to the direct application of Operational Research Methods to study the problem and reorganize human and materials resources, to balance the work load, in order to provide a best service to the citizens and more efficient use to the public funds, which is an aspiration and need in Brazil. The work is a multi-objective modeling to designate 3912 points (the voting sites in the state of Santa Catarina, Brazil) to an interval from 76 to 131 electoral districts. This task generated 56 scenarios available to analisys. Key-words: public service, optimization, genetic algorith

New Applications of the Nearest-Neighbor Chain Algorithm

The nearest-neighbor chain algorithm was proposed in the eighties as a way to speed up certain hierarchical clustering algorithms. In the first part of the dissertation, we show that its application is not limited to clustering. We apply it to a variety of geometric and combinatorial problems. In each case, we show that the nearest-neighbor chain algorithm finds the same solution as a preexistent greedy algorithm, but often with an improved runtime. We obtain speedups over greedy algorithms for Euclidean TSP, Steiner TSP in planar graphs, straight skeletons, a geometric coverage problem, and three stable matching models. In the second part, we study the stable-matching Voronoi diagram, a type of plane partition which combines properties of stable matchings and Voronoi diagrams. We propose political redistricting as an application. We also show that it is impossible to compute this diagram in an algebraic model of computation, and give three algorithmic approaches to overcome this obstacle. One of them is based on the nearest-neighbor chain algorithm, linking the two parts together

Three essays in public economics

This dissertation consists of three essays exploring how individuals, groups, and firms respond to public policy changes. The first two chapters focus on labor supply and demand responses to tax and unemployment insurance reforms, while the third explores the effects of reconfiguring political boundaries on ethnic identity and social stability. The first essay (with Simon Trenkle) studies the speed with which workers increase their earnings following a tax break. We do so in Germany, where a large discontinuity in the tax schedule induces sharp bunching in the earnings distribution at the expected cutoff. We analyze earnings responses following two separate reforms that increase this cutoff. While some workers adjust instantly post-reform, others take several years to increase their earnings. Adjustment behavior is strongly correlated within firms. We posit that idiosyncratic differences in labor demand across firms drive cross-firm heterogeneity in adjustment rates, and find support for this channel in the data. The second essay (with Johannes Schmieder, Simon Trenkle, and Han Ye) studies older workers' responses to unemployment insurance (UI) extensions in Germany. Extending UI benefits can affect labor supply along two margins: it can lengthen the unemployment duration of an individual on UI - the intensive margin - and it can alter the inflows into UI - the extensive margin. We document extensive margin responses in the form of bunching in UI entries at precisely the age that ensures workers can transition into retirement immediately following UI expiration. Consequently, we show that standard, intensive margin estimates of the non-employment effect of UI are downward biased. The third essay (with Samuel Bazzi) analyzes the effects of political boundaries on ethnic divisions and conflict. In the early 2000s, Indonesia created hundreds of new local governments, thereby redrawing subnational boundaries and altering each districts' ethnic composition. We argue that such changes in political boundaries can fundamentally reshape ethnic divisions. Exploiting quasi-experimental variation in the timing of redistricting, we show that redistricting along group lines increases social stability, but that these gains are undone and even reversed in newly polarized districts. Our findings show that ethnic divisions are not fixed and instead depend on political boundaries