Models and algorithms for hard optimization problems

This thesis is devoted to exact solution methods for NP-hard integer programming models. We consider two of these problems, the cutting stock problem and the vehicle routing problem. Both problems have been studied for several decades by researchers and practitioners of the Operations Research eld. Their interest and contribution to real-world applications in business, industry and several kinds of organizations are irrefutable. Our solution approaches are always exact. We contribute with new lower bounds, families of valid inequalities, integer programming models and exact algorithms for the problems we explore. More precisely, we address two variants of each of the referred problems. In what concerns cutting stock problems, we analyze the one-dimensional pattern minimization problem and the two-dimensional cutting stock problem with the guillotine constraint. The one-dimensional pattern minimization problem is a cutting and packing problem that becomes relevant in situations where changing from one pattern to another involves, for example, a cost for setting up the cutting machine. It is the problem of minimizing the number of di erent patterns of a given cutting stock solution. For this problem, we contribute with new lower bounds. The two-dimensional cutting stock problem with the guillotine constraint and two stages is also addressed. We propose a pseudo-polynomial network ow model, along with some reduction criteria to reduce its symmetry. We strengthen the model with a new family of cutting planes and propose a new lower bound. For this variant, we also consider some variations of the problem.Regarding vehicle routing problems, we address the vehicle routing problem with time windows and multiple use of vehicles and the location routing problem, with capacitated vehicles and depots and multiple use of vehicles. The rst of these problems considers the well know case of vehicle routing with time windows with the additional consideration that vehicles can be assigned to several routes within the same planning period. The second variant considers the combination of the rst problem, without time windows, with a location problem. This means that the depots to be used must be selected from a set of available ones. For both of these variants, we propose a network ow model whose nodes of the underlying graph correspond to time instants of the planning period and whose arcs correspond to vehicle routes. We reduce their symmetry by deriving several reduction criteria. For the vehicle routing problem with time windows and multiple use of vehicles, we propose an iterative algorithm to solve the problem exactly. Our proposed procedures are tested and compared with other methods from the literature. All the computational results produced by the series of experiments are presented and discussed.Esta tese e dedicada a métodos de resolução exata para problemas de programação inteira NP-difíceis. São considerados dois desses problemas, nomeadamente o problema de corte e empacotamento e o problema de encaminhamento de veículos. Ambos os problemas têm vindo a ser abordados por investigadores e profissionais da área da Investigação Operacional há já várias décadas. O seu interesse e contribuição para aplicações reais do mundo dos negócios e industria, assim como para inúmeros outros tipos de organizações são, hoje em dia, inegáveis. A nossa abordagem para a resolução dos problemas descritos e exata. Contribuímos com novos limites inferiores, novas famílias de desigualdades validas, novos modelos de programação inteira e algoritmos de resolução exata para os problemas que nos propomos explorar. Em particular, abordamos duas variantes de cada um dos referidos problemas. Em relação ao problema de corte e empacotamento, analisamos o problema de minimização de padrões a uma dimensão e o problema de corte e empacotamento a duas dimensões, com restrição de guilhotina. O problema de minimização de padrões a uma dimensão e pertinente em situações em que a mudança de padrão envolve, por exemplo, custos de reconfiguração nas máquinas de corte. E o problema de minimização do numero de padrões diferentes de uma dada solução de um problema de corte. Para este problema contribuímos com novos limites inferiores. O problema de corte e empacotamento a duas dimensões com restrição de guilhotina e dois estágios e também abordado. Propomos um modelo pseudopolinomial de rede de fluxos, assim como critérios de redução que eliminam parte da sua simetria. Reforçamos o modelo com uma nova família de planos de corte e propomos novos limites inferiores. Para esta variante, consideramos também outras variações do problema original. No que se refere ao problema de encaminhamento de veículos, abordamos um problema de encaminhamento de veículos com janelas temporais e múltiplas viagens, e também um problema de localização e encaminhamento de veículos com capacidades nos veículos e depósitos e múltiplo uso dos veículos. O primeiro destes problemas considera o conhecido caso de encaminhamento de veículos com janelas temporais, com a consideração adicional de que os veículos podem ser alocados a v arias rotas no decurso do mesmo período de planeamento. A segunda variante considera a combinação do primeiro problema, embora sem janelas temporais, com um problema de localização. Isto significa que os depósitos a usar são selecionados de um conjunto de localizações disponíveis. Para ambas as variantes, propomos um modelo pseudo-polinomial de rede de fluxos cujos nodos do grafo correspondente representam instantes de tempo do período de planeamento, e cujos arcos representam rotas. Derivamos critérios de redução com o intuito de reduzir a simetria. Para o problema com janelas temporais e múltiplas viagens, propomos um algoritmo iterativo que o resolve de forma exata. Os procedimentos propostos são testados e comparados com outros métodos da literatura. Todos os resultados obtidos pelas experiencias computacionais são apresentados e discutidos

Technology and Management for Sustainable Buildings and Infrastructures

A total of 30 articles have been published in this special issue, and it consists of 27 research papers, 2 technical notes, and 1 review paper. A total of 104 authors from 9 countries including Korea, Spain, Taiwan, USA, Finland, China, Slovenia, the Netherlands, and Germany participated in writing and submitting very excellent papers that were finally published after the review process had been conducted according to very strict standards. Among the published papers, 13 papers directly addressed words such as sustainable, life cycle assessment (LCA) and CO2, and 17 papers indirectly dealt with energy and CO2 reduction effects. Among the published papers, there are 6 papers dealing with construction technology, but a majority, 24 papers deal with management techniques. The authors of the published papers used various analysis techniques to obtain the suggested solutions for each topic. Listed by key techniques, various techniques such as Analytic Hierarchy Process (AHP), the Taguchi method, machine learning including Artificial Neural Networks (ANNs), Life Cycle Assessment (LCA), regression analysis, Strength–Weakness–Opportunity–Threat (SWOT), system dynamics, simulation and modeling, Building Information Model (BIM) with schedule, and graph and data analysis after experiments and observations are identified

Reformulation and decomposition of integer programs

In this survey we examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branch-and-bound based algorithm. First we cover in detail reformulations based on decomposition, such as Lagrangean relaxation, Dantzig-Wolfe column generation and the resulting branch-and-price algorithms. This is followed by an examination of Benders’ type algorithms based on projection. Finally we discuss in detail extended formulations involving additional variables that are based on problem structure. These can often be used to provide strengthened a priori formulations. Reformulations obtained by adding cutting planes in the original variables are not treated here.Integer program, Lagrangean relaxation, column generation, branch-and-price, extended formulation, Benders' algorithm

Throughput and Yield Improvement for a Continuous Discrete-Product Manufacturing System

A seam-welded steel pipe manufacturing process has mainly four distinct major design and/or operational problems dealing with buffer inventory, cutting tools, pipe sizing and inspection-rework facility. The general objective of this research is to optimally solve these four important problems to improve the throughput and yield of the system at a minimum cost. The first problem of this research finds the optimal buffer capacity of steel strip coils to minimize the maintenance and downtime related costs. The total cost function for this coil feeding system is formulated as a constrained non-linear programming (NLP) problem which is solved with a search algorithm. The second problem aims at finding the optimal tool magazine reload timing, magazine size and the order quantity for the cutting tools. This tool magazine system is formulated as a mixed-integer NLP problem which is solved for minimizing the total cost. The third problem deals with different type of manufacturing defects. The profit function of this problem forms a binary integer NLP problem which involves multiple integrals with several exponential and discrete functions. An exhaustive search method is employed to find the optimum strategy for dealing with the defects and pipe sizing. The fourth problem pertains to the number of servers and floor space allocations for the off-line inspection-rework facility. The total cost function forms an integer NLP structure, which is minimized with a customized search algorithm. In order to judge the impact of the above-mentioned problems, an overall equipment effectiveness (OEE) measure, coined as monetary loss based regression (MLBR) method, is also developed as the fifth problem to assess the performance of the entire manufacturing system. Finally, a numerical simulation of the entire process is conducted to illustrate the applications of the optimum parameters setting and to evaluate the overall effectiveness of the simulated system. The successful improvement of the simulated system supports this research to be implemented in a real manufacturing setup. Different pathways shown here for improving the throughput and yield of industrial systems reflect not only to the improvement of methodologies and techniques but also to the advancement of new technology and national economy

Dealing with Nonregular Shapes Packing

This paper addresses the irregular strip packing problem, a particular two-dimensional cutting and packing problem in which convex/nonconvex shapes (polygons) have to be packed onto a single rectangular object. We propose an approach that prescribes the integration of a metaheuristic engine (i.e., genetic algorithm) and a placement rule (i.e., greedy bottom-left). Moreover, a shrinking algorithm is encapsulated into the metaheuristic engine to improve good quality solutions. To accomplish this task, we propose a no-fit polygon based heuristic that shifts polygons closer to each other. Computational experiments performed on standard benchmark problems, as well as practical case studies developed in the ambit of a large textile industry, are also reported and discussed here in order to testify the potentialities of proposed approach

Waste Material Recycling in the Circular Economy

This book highlights current challenges and developments in waste material recycling in the framework of a circular economy. The increase in the standard of living has resulted in the large consumption of several materials, mainly polymers. Therefore the problem of waste recycling, specifically polymer recycling, in an environmentally friendly way is more urgent than ever. Nowadays, more specialized recycling methods are required to manage a wide variety of wastes. Over fourteen chapters in three sections, this book addresses such topics as chemical recycling techniques, recycling of polyethylene, denim production and recycling, valorization of waste materials, urban mining, the circular economy, and much more

Composite reinforced propellant tanks

Design studies involving weight and cost were carried out for several structural concepts applicable to space shuttle disposable tankage. An effective design, a honeycomb stabilized pressure vessel, was chosen. A test model was designed and fabricated