Orientador: Flávio Keidi Miyazawa / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-19T17:20:46Z (GMT). No. of bitstreams: 1 Silva_FabricioLuisSantosda_M.pdf: 657410 bytes, checksum: 65ac7a297f6547a9ac70dfa42604f1ce (MD5) Previous issue date: 2010 / Resumo: Neste trabalho lidamos com o problema de Empacotamento em Faixa Bidimensional considerando o caso em que os itens devem ser dispostos de forma a manter o empacotamento estável e satisfazer uma ordem de descarregamento imposta. Consideramos o caso em que a orientação dos itens é fixa. Definimos uma metodologia para analisar a estabilidade do empacotamento observando as condições de equilíbrio estático para corpos rígidos. Desenvolvemos heurísticas e formulamos um programa linear inteiro para o problema de Empacotamento em Faixa sujeito a tais restrições. A resolução da formulação inteira ocorre através de uma estratégia do tipo branch-and-cut. As restrições de estabilidade foram inseridas como planos de corte de maneira a remover empacotamentos que não são estáveis. Em nossos experimentos computacionais, vemos que o modelo proposto é adequado para lidar com instâncias de pequeno até médio porte, dentro de um tempo computacional razoável / Abstract: This paper investigates the Two-Dimensional Strip Packing Problem considering the case in which the items should be arranged to form a stable packing and satisfy an order of unloading, so that after unloading, the packing is still stable. We consider the case where the items are oriented and rotations are not allowed. We present a methodology to analyze the stability of the packing observing the conditions for static equilibrium of rigid bodies. We present heuristics and formulate an integer linear programming model for the Strip Packing problem considering such constraints. To solve the integer formulation, we develop a branch-and-cut approach. For each integer solution obtained during the branch-and-cut algorithm, corresponding to a non-stable packing, we insert a cutting plane for which this integer solution is not satisfied. In our computational experiments, we see that the proposed model is suitable to deal with small and mid-sized instances. Some optimal solutions were obtained after few hours of CPU processing / Mestrado / Mestre em Ciência da Computação

Traffic Engineering (TE) uses methods and models from a variety of mathematical fields, such as statistics and optimization, to improve the performance of telecommunication networks. In this thesis, we study TE problems dealing with networks that impose single-path routing. As the name infers, in this type of routing, the traffic flow of each "commodity" cannot be split in its path between its origin and destination. Given its cheap cost, single-path routing is widely used in today's data centers, where thousands of stored servers perform computations or host Internet services. One common case of single-path routing is the one enforced by the Spanning Tree Protocol (STP) in switched Ethernet networks. The STP requires the network to keep its activated links loop-free, while maintaining the other redundant links ready for back-up, in case of link failure. The Multiple Spanning Tree Protocol (MSTP) extends the STP by installing multiple virtual networks compliant with the STP, over a single physical topology. Therefore, the MSTP is greatly beneficial for network service providers, as it allows for a more efficient use of the existing resources.Network design problems dealing with the MSTP are generally highly combinatorial and very hard to solve. As such, TE literature mainly suggests heuristic methods, which can quickly produce reasonable designs. Notwithstanding, due to a scarce existence of lower bounds to the optimum values of such problems, there is little knowledge about the quality of the solutions provided by these heuristics.In this sense, we propose mathematical programming models and methods that can provide optimal designs for these networks, or at the very least, obtain valid lower bounds. Taking into mind the goal of avoiding congestion in the network, we focus on two problems that deal with the following load-balancing objectives: the minimization of the worst-case link utilization, and the minimization of flow costs given by piecewise linear functions that penalize heavily-loaded links. The study of both these problems yielded relevant by-products: the first is the study of a MSTP network design problem, where we minimize the total load, and the second is the study of a fundamental unsplittable multicommodity flow problem with piecewise linear costs.For all the considered problems, we provide studies of complexity, extensive polyhedral studies to compare the proposed formulations, and a wide array of computational experiments to evaluate the performance of the proposed models and methods. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Mixed-Integer Programming has been a vital tool for the chemical engineer in the recent decades and is employed extensively in process design and control. This dissertation presents some new Mixed-Integer Programming formulations developed for two well-studied problems, one with a central role in the area of Optimisation, the other of great interest to the chemical industry. These are the Travelling Salesman Problem and the problem of scheduling cleaning actions for heat exchanger networks subject to fouling. The Travelling Salesman Problem finds a plethora of applications in many scientific disciplines, Chemical Engineering included. None of the mathematical programming formulations proposed for solving the problem considers fewer than O(n^2) binary degrees of freedom. The first part of this dissertation introduces a novel mathematical description of the Travelling Salesman Problem that succeeds in reducing the binary degrees of freedom to O(nlog2(n)). Three Mixed-Integer Linear Programming formulations are developed and the computational performance of these is tested through computational studies. Sophisticated methods are now available for scheduling the cleaning actions for networks of heat exchangers subject to fouling. In the majority of these, only one form of cleaning is used, which restores the performance of the exchanger back to its clean level. A recent study revised the scheduling problem for the case where there are several cleaning methods available. The second part of this dissertation extends their approach, developed for individual units, to heat exchanger networks and explores the concept of selection of cleaning techniques further. Mixed-Integer Programming formulations are proposed for the scheduling task, for two fouling scenarios: (i) chemical reaction fouling and (ii) biological fouling. A series of results are presented for the implementation of the scheduling formulations to networks of different sizes.

Abstract The purpose of this thesis is to investigate the economics of biodiversity maintenance in boreal forests. From the many tasks available in forest management to improve biodiversity maintenance, the focus is on the lengthening of forest rotation and strict protection, i.e., protected areas. Accordingly, the analysis basis on two different models named forest rotation model and site selection model. Moreover, both socially optimal and cost-effective conservation are considered. The data consists of 32 old-growth stands from northern Finland. The four studies of this dissertation provide evidence of the non-negligible economic consequences of taking biodiversity services into account along with timber production in the forest management. Study I shows that theoretically the optimal management of initial stands involves three alternatives: immediate clear cutting, delayed harvesting, and protection. Moreover, the numerical analysis reveals that taking into account the biodiversity services along with timber production results in considerably longer optimal rotation than in pure timber production management. Delayed harvesting is the most common option for socially optimal management of old-growth forests. However, the integrated approach results also in strict protection of some stands. Study II compares alternative approaches, named integrated, ecological and penny pincher selection, for selecting forest reserves. It suggests the integrated selection leads to 9–19% higher conservation cost-efficiency than the other selections. The integrated selection takes into account both the economic value and ecological features of the stands as the other selections focus only on one of these aspects. It seems also that the xeric forest type may be under-represented in the current old-growth forest preservation network in the studied region. Study III analyses the performance of alternative biodiversity indicators used in the selection of protected areas. It shows that the use of indicators likely results in a loss of species and, therefore, a complete species inventory is necessary if the goal is to maintain all species in the landscape. However, the use of indicators seems to be an economically more efficient practice than to execute a large species survey for habitat protection. Study IV examines the relative merits of alternative biodiversity conservation targets for forestry, which give different weights to species according to their conservation status and assumed population persistence. Also, socially optimal conservation is solved as a benchmark by maximizing the benefits from timber production and biodiversity services. According the results it is optimal to protect 16 out of 32 stands. Alternative conservation goals give different characters in terms of benefit-cost tradeoffs. More specifically goals relying on complementarity between protected stands result in great marginal costs at a high conservation level.

A key challenge for manufacturing companies is to store parts in an efficient way atthe lowest cost possible. As the demand of differentiated products increases, togetherwith the fact that old products are not phased out at the same pace, the need of usingstorage space as dynamically as possible becomes vital.Scania’s engine assembly manufactures engines for various automotive vehicles andmarine & industry applications. The variation in engine range in Scania’s offeringleads to the need of holding a vast, and increasing, assortment of parts in the produc-tion. As a consequence, this puts more pressure on the logistics and furnishing withinthe engine assembly.This master thesis aims to facilitate the process of assigning parts’ storage locationsin the most profitable manner through an optimization model, the Location Model, inExcel VBA. Together with the model, suggestions of work methods are presented.By implementing the Location Model at Scania’s engine assembly, 4,98 % of all keptparts are recommended location changes, while resulting in cost savings, for the chosen30-day period. These location changes result in a cost saving of 6,73 % of the totallogistic costs for the same time period.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Integer programming (IP) has been and continues to be widely used by industries to minimize cost and effectively manage resources. Faster computers and innovative IP techniques have enabled the solution to many large-scale IPs. However, IPs are NP-hard and many IPs require exponential time to solve. Lifting is one of the most widely used techniques that helps to reduce computational time and is widely applied in today's commercial IP software. Lifting was first introduced by Gomory for bounded integer programs and a theoretical and computationally intractible technique to simultaneously lift sets of variables was introduced by Zemel in 1978. This thesis presents a new algorithm called the Maximal Simultaneous Lifting Algorithm (MSLA), to simultaneously uplift sets of binary integer variables into a cover inequality. These lifted inequalities result in strong inequalities that are facet defining under fairly moderate assumptions. A computational study shows that this algorithm can find numerous strong inequalities for random Knapsack (KP) instances. The pre-processing time observed for these instances is less than 1/50th of a second, which is negligible. These simultaneously lifted inequalities are easy to find and incorporating these cuts to KP instances reduced the solution time by an average of 41%. Therefore, implementing MSLA should be highly beneficial for large real-world problems.

Master of Science / Department of Industrial and Manufacturing Systems Engineering / Todd W. Easton / Integer programming is an important discipline in operation research that positively impacts society. Unfortunately, no algorithm currently exists to solve IP's in polynomial time. Researchers are constantly developing new techniques, such as cutting planes, to help solve IPs faster. For example, DeLissa discovered the existence of equality cuts limited to zero and one coefficients for the multiple knapsack equality problem (MKEP). An equality cut is an improper cut because every feasible point satisfies the equality. However, such a cut always reduces the dimension of the linear relaxation space by at least one. This thesis introduces lifted equality cuts, which can have coefficients greater than or equal to two. Two main theorems provide the conditions for the existence of lifted equalities. These theorems provide the foundation for The Algorithm of Lifted Equality Cuts (ALEC), which finds lifted equality cuts in quadratic time. The computational study verifies the benefit of lifted equality cuts in random MKEP instances. ALEC generated millions of lifted equality cuts and reduced the solution time by an average of 15%. To the best of the author's knowledge, ALEC is the first algorithm that has found over 30.7 million cuts on a single problem, while reducing the solving time by 18%.

Cette thèse s’intéresse aux problèmes d’emploi du temps d’universités. Ces problèmes sont rencontrés chaque année par les utilisateurs. Nous proposons des bornes inférieures, des méthodes heuristiques et des modèles de programmation mixte en nombres entiers et de programmation par contraintes. Nous traitons le problème d’emploi du temps d’examens et celui d’affectation des étudiants. Nous proposons de nouvelles méthodes et formulations et les comparons aux approches existantes. Nous proposons, pour le problème d’emploi du temps d’examens, une amélioration d’un modèle mathématique en nombres entiers qui permettra d’obtenir des solutions optimales. Ensuite, des bornes inférieures, une formulation plus compacte des contraintes et un modèle de programmation par contraintes sont proposés. Pour le problème d’emploi du temps d’examens à l’Université de Technologie de Compiègne, nous proposons une approche mémétique. Enfin, nous présentons un modèle mathématique pour le problème d’affectation des étudiants et nous étudions sa performance sur un ensemble d’instances réelles. / This thesis investigates university timetabling problems. These problems occur across universities and are faced each year by the practitioners. We propose new lower bounds, heuristic approaches, mixed integer and constraint programming models to solve them. We address the exam timetabling and the student scheduling problem. We investigate new methods and formulations and compare them to the existing approaches. For exam timetabling, we propose an improvement to an existing mixed integer programming model that makes it possible to obtain optimal solutions. Next, lower bounds, a more compact reformulation for constraints and a constraint programming model are proposed. For the exam timetabling problem at Université de Technologie de Compiègne, we designed a memetic approach. Finally, we present a new formulation for the student scheduling problem and investigate its performance on a set of real-world instances.

The thesis describes a way of searching the best bill of fare for certain patient in hospital. The target is to set up and then to solve an optimization model. Criterion of performance is to minimize spending on selected foodstuff. The first part describes a theory of optimization models, the second is about nutrition and the third aims to solve a model and to interpret the results.

Crew scheduling is very important, especially in continuous operating environments running 24 hours a day, 7 days a week, more so if the demand for staff is varying over each hour of the day. This thesis focuses on staff optimization in a fast food chain where special conditions for scheduling like flexible starting-times and shift lengths or heterogeneous crew are present. Two new models based on a mixed integer programming approach were designed, dealing with data from a particular restaurant with the aim of improving schedules and saving time spent on the creation of those schedules. At the end of the thesis the empiric schedules and results obtained are compared and the computational efficiency of both models is discussed.