Made available in DSpace on 2016-08-10T10:40:20Z (GMT). No. of bitstreams: 1 JEANCARLO RIBEIRO.pdf: 683766 bytes, checksum: 28e6690b67012436dd91788ec7ff346b (MD5) Previous issue date: 2013-06-17 / The classroom assignment problem at universities consist in distributing classes scheduled for the appropriate rooms, respecting the requirements in each situation. The objective of this work is to apply the Hungarian algorithm and a computational system to solve the classroom assignment problem time by time. The tests were performed with real data from the PUC Goiás for a quantitative of 5116 classes into 313 classrooms. As a result, we solved the problem in approximately 12 minutes and the solution quality was compared with manual designation usually applied by the institution, which takes a month and a half. / O problema de designação de salas de aula em Universidades consiste em distribuir turmas programadas para as devidas salas, respeitando os requisitos estabelecidos em cada situação. O objetivo deste trabalho é a aplicação do algoritmo húngaro e de um sistema computacional para a resolução do problema de alocação horário por horário. Os testes foram realizados com dados reais da PUC Goiás para um quantitativo de 5116 turmas em 313 salas de aula. Como resultados, resolvemos o problema em aproximadamente 12 minutos e comparamos a qualidade da solução com a designação manual usualmente realizada pela Instituição, a qual leva um mês e meio.

Made available in DSpace on 2016-08-10T10:40:24Z (GMT). No. of bitstreams: 1 Davi Taveira Alencar Alarcao.pdf: 944757 bytes, checksum: 30d55936bd0acaff3d7ecf1816fe22f5 (MD5) Previous issue date: 2015-02-07 / The classroom assignment problem at universities consist in distributing classes scheduled for the appropriate rooms, respecting the requirements in each situation. The objective of this work is to improve the process of allocation of classroom PUC Goiás. The tests were performed with real data from the PUC Goiás for a quantitative of 5116 classes into 312 classrooms. As a result, we solved the problem in approximately 34 minutes and the solution quality was compared both with manual designation usually applied by the institution, which takes a month and a half, as with the results found in Ribeiro (2012). / O problema de designação de salas de aula em Universidades consiste em distribuir turmas programadas para as devidas salas, respeitando os requisitos estabelecidos em cada situação. O objetivo deste trabalho é o de melhorar o processo de alocação de salas de aula da PUC Goiás. Os testes foram realizados com dados reais da PUC Goiás para um quantitativo de 5116 turmas em 312 salas de aula. Como resultados, resolvemos o problema em aproximadamente 34 minutos e comparamos a qualidade da solução tanto com a designação manual usualmente realizada pela Instituição, a qual leva um mês e meio, quanto com os resultados encontrados em Ribeiro (2012).

The Birnbaum importance (BI) is a well-known measure that evaluates the relative contribution of components to system reliability. It has been successfully applied to tackling some reliability problems. This dissertation investigates two topics related to the BI in the reliability field: the patterns of component BIs and the BI-based heuristics and meta-heuristics for solving the component assignment problem (CAP).There exist certain patterns of component BIs (i.e., the relative order of the BI values to the individual components) for linear consecutive-k-out-of-n (Lin/Con/k/n) systems when all components have the same reliability p. This study summarizes and annotates the existing BI patterns for Lin/Con/k/n systems, proves new BI patterns conditioned on the value of p, disproves some patterns that were conjectured or claimed in the literature, and makes new conjectures based on comprehensive computational tests and analysis. More importantly, this study defines a concept of segment in Lin/Con/k/n systems for analyzing the BI patterns, and investigates the relationship between the BI and the common component reliability p and the relationship between the BI and the system size n. One can then use these relationships to further understand the proved, disproved, and conjectured BI patterns.The CAP is to find the optimal assignment of n available components to n positions in a system such that the system reliability is maximized. The ordering of component BIs has been successfully used to design heuristics for the CAP. This study proposes five new BI-based heuristics and discusses their corresponding properties. Based on comprehensive numerical experiments, a BI-based two-stage approach (BITA) is proposed for solving the CAP with each stage using different BI-based heuristics. The two-stage approach is much more efficient and capable to generate solutions of higher quality than the GAMS/CoinBonmin solver and a randomization method.This dissertation then presents a meta-heuristic, i.e., a BI-based genetic local search (BIGLS) algorithm, for the CAP in which a BI-based local search is embedded into the genetic algorithm. Comprehensive numerical experiments show the robustness and effectiveness of the BIGLS algorithm and especially its advantages over the BITA in terms of solution quality.

We define an order cutoff for a retailer as a time in the day such that orders sent to the depot before this point will be delivered by tomorrow, and orders submitted after will be delivered by the day after tomorrow. The later a retailer’s cutoff, the sooner it receives its orders which helps it to maintain ideal inventory levels. Generally, not all retailers in a supply chain can have the latest cutoff since transportation takes a significant amount of time. This thesis tries to assign optimal order cutoffs to retailers. We call this an order cutoff assignment problem and we solve it using three different mathematical programming approaches. The approaches are exhaustive route generation and selection, a series of mixed integer programs, and branch-and-price. 60 sample problems were solved and results showed that branch-and-price is often the most effective method.

We define an order cutoff for a retailer as a time in the day such that orders sent to the depot before this point will be delivered by tomorrow, and orders submitted after will be delivered by the day after tomorrow. The later a retailer’s cutoff, the sooner it receives its orders which helps it to maintain ideal inventory levels. Generally, not all retailers in a supply chain can have the latest cutoff since transportation takes a significant amount of time. This thesis tries to assign optimal order cutoffs to retailers. We call this an order cutoff assignment problem and we solve it using three different mathematical programming approaches. The approaches are exhaustive route generation and selection, a series of mixed integer programs, and branch-and-price. 60 sample problems were solved and results showed that branch-and-price is often the most effective method.

Much research has been undertaken to gain insight into business alignment of IT. This alignment basically aims to improve a firm’s performance by an improved harmonization of the business function and the IT function within a firm. The thesis discusses previous approaches and constructs an overall framework, which a potential approach needs to fit in. Being in a highly regulated industry, for airports there is little space left to increase revenues. However, the retailing business has proven to be an area that may contribute towards higher income for airport operators. Consequently, airport management should focus on supporting this business segment. Nevertheless, it needs to be taken into account that smooth airport operations are a precondition for successful retailing business at an airport. Applying the concept of information intensity, the processes of gate allocation and airport retailing have been determined to appraise the potential that may be realized upon (improved) synchronization of the two. It has been found that the lever is largest in the planning phase (i.e. prior to operations), and thus support by means of information technology (for information distribution and improved planning) may help to enable an improved overall retail performance. In order to determine potential variables, which might influence the output, a process decomposition has been conducted along with the development of an appropriate information model. The derived research model has been tested in different scenarios. For this purpose an adequate gate allocation algorithm has been developed and implemented in a purposewritten piece of software. To calibrate the model, actual data (several hundred thousand data items from Frankfurt Airport) from two flight plan seasons has been used. Key findings: The results show that under the conditions described it seems feasible to increase retail sales in the magnitude of 9% to 21%. The most influential factors (besides the constraining rule set and a retail area’s specific performance) proved to be a flight’s minimum and maximum time at a gate as well as its buffer time at gate. However, as some of the preconditions may not be accepted by airport management or national regulators, the results may be taken as an indication for cost incurred, in case the suggested approach is not considered. The transferability to other airport business models and limitations of the research approach are discussed at the end along with suggestions for future areas of research.

The variety of principal minors of nxn symmetric matrices, denoted Zn, can be described naturally as a projection from the Lagrangian Grassmannian. Moreover, Zn is invariant under the action of a group G C GL(2n) isomorphic to (SL(2)xn) x Sn. One may use this symmetry to study the defining ideal of Zn as a G-module via a coupling of classical representation theory and geometry. The need for the equations in the defining ideal comes from applications in matrix theory, probability theory, spectral graph theory and statistical physics. I describe an irreducible G-module of degree 4 polynomials called the hyperdeterminantal module (which is constructed as the span of the G-orbit of Cayley's hyperdeterminant of format 2 x 2 x 2) and show that it that cuts out Zn set theoretically. This result solves the set-theoretic version of a conjecture of Holtz and Sturmfels and gives a collection of necessary and sufficient conditions for when it is possible for a given vector of length 2n to be the principal minors of a symmetric n x n matrix. In addition to solving the Holtz and Sturmfels conjecture, I study Zn as a prototypical G-variety. As a result, I exhibit the use of and further develop techniques from classical representation theory and geometry for studying G-varieties.

In this thesis, we consider the Multi Resource Agent Bottleneck Generalized Assignment Problem. We aim to minimize the maximum load over all agents. We study the Linear Programming (LP) relaxation of the problem. We use the optimal LP relaxation solutions in our Branch and Bound algorithm while defining lower and upper bounds and branching schemes. We find that our Branch and Bound algorithm returns optimal solutions to the problems with up to 60 jobs when the number of agents is 5, and up to 30 jobs when the number of agents is 10, in less than 20 minutes. To find approximate solutions, we define a tabu search algorithm and an &amp / #945 / approximation algorithm. Our computational results have revealed that these procedures can find high quality solutions to large sized instances very quickly.

In this document, we study the nonnegative least squares primal-dual method for solving linear programming problems. In particular, we investigate connections between this primal-dual method and the classical Hungarian method for the assignment problem. Firstly, we devise a fast procedure for computing the unrestricted least squares solution of a bipartite matching problem by exploiting the special structure of the incidence matrix of a bipartite graph. Moreover, we explain how to extract a solution for the cardinality matching problem from the nonnegative least squares solution. We also give an efficient procedure for solving the cardinality matching problem on general graphs using the nonnegative least squares approach. Next we look into some theoretical results concerning the minimization of p-norms, and separable differentiable convex functions, subject to linear constraints described by node-arc incidence matrices for graphs. Our main result is the reduction of the assignment problem to a single nonnegative least squares problem. This means that the primal-dual approach can be made to converge in one step for the assignment problem. This method does not reduce the primal-dual approach to one step for general linear programming problems, but it appears to give a good starting dual feasible point for the general problem.

The frequency assignment (FAP) consists in assigning the frequency on the radio links of a network which satisfiesthe electromagnetic interference among the links. Given the limited spectrum resources for each application, the fre-quency resources are often insufficient to deploy a wireless network without interference. In this case, the network isover-contrained and the problem is infeasible. Our objective is to identify an area with heavy interference.The work presented here concerns the detection for one of these areas with an algorithmic approach based onmodeling the problem by CSP. The problem of frequency assignment can be modeled as a constraint satisfactionproblem (CSP) which is represented by a triple: a set of variables (radio links), a set of constraints (electromagneticinterference) and a set of available frequencies.The interfered area in CSP can be considered a subset of irreducible feasible subset (IIS). An IIS is a infeasiblesubproblem with irreducible size, that is to say that all subsets of an IIS are feasible. The identification of an IIS ina CSP refers to two general interests. First, locating an IIS can easily prove the infeasibility of the problem. Becausethe size of IIS is assumed to be smaller compared to the entire problem, its infeasibility is relatively easier to prove.Second, we can locate the reason of infeasibility, in this case, the decision maker can provide the solutions to relax theconstraints inside IIS, which perhaps leads to a feasible solution to the problem.This work proposes algorithms to identify an IIS in the over-constrained CSP. These algorithms have tested on the well known benchmarks of the FAP and of the problem of graph k-coloring. The results show a significant improve-ment on instances of FAP compared to known methods.