Todo início de período letivo, gestores de instituições de ensino se deparam com um típico problema: montar as grades horárias das turmas, segundo as demandas de aulas de suas disciplinas e considerando as restrições de disponibilidade horária de todos os envolvidos. Conhecido na literatura como School Timetabling Problem (STP), este típico problema de otimização combinatória é reconhecidamente complexo por conta do seu elevado número de variáveis e restrições. Devido à dependência das regras do sistema educacional de cada país, o STP pode ter inúmeras variantes, cada uma com o seu próprio conjunto de particularidades. Este trabalho se propõe a oferecer um modelo para o STP considerando o sistema educacional brasileiro, visando alocar não apenas professores, mas também determinando que disciplina cada professor deve ministrar e alocando os locais de aula. O modelo proposto, baseado na meta-heurística simulated annealing, foi concebido para que cada instituição de ensino usuária tenha liberdade para definir a penalidade de cada tipo possível de inconformidade ou restrição, de modo que o algoritmo empregado possa encontrar uma solução com o menor custo possível. / Every beginning of term, educational institution managers face a typical problem: planning the classes' timetable, according to their lesson demands for each subject, considering, furthermore, the schedule constrains of all actors. Known as school timetabling problem (STP), this typical combinatorial optimization problem is remarkably complex due to the high number of variables and constraints. Owing to the rules of each country's educational system, STP can have uncountable variants, each one with their own set of features. This dissertation searches to offer a model to STP considering the Brazilian Educational System, focusing on allocating not only the teachers but also determining which subject each teacher should teach and allocating classrooms, laboratories and the like. The propesed model, based on the metaheuristic simulated annealing, was conceived so that each educational institution using this model has the freedom to define which penalty will be applied to each possible kind of noncomformity and constraint, in order for the applied algorithm to find a solution at the lowest cost as possible.

A geração de quadros de horários escolares é um problema clássico de otimização que tem sido largamente estudado devido a sua importâncias prática e teórica. O problema consiste em alocar um conjunto de aulas entre professor-turma em períodos de tempo pré-determinados, satisfazendo diferentes tipos de requisitos. Devido a natureza combinatória do problema, a resolução de instâncias médias e grandes torna-se uma tarefa desafiadora. Quando recursos são escassos, mesmo uma solução factível pode ser difícil de ser encontrada. Várias técnicas tem sido propostas na literatura científica para resolver o problema de geração de quadros de horários escolares, no entanto, métodos robustos ainda não existem. Visto que o uso de métodos exatos, como por exemplo, técnicas de programação matemática, não podem ser utilizados na prática, para resolver instâncias grandes da realidade, meta-heurísticas e meta-heurísticas híbridas são usadas com frequência como abordagens de resolução. Nesta pequisa, são desenvolvidas técnicas que combinam programação matemática e heurísticas, denominadas mateheurísticas, para resolver de maneira eficiente e robusta algumas variações de problemas de geração de quadros de horários escolares. Embora neste trabalho sejam abordados problemas encontrados no contexto de instituições brasileiras, os métodos propostos também podem ser aplicados em problemas similares oriundo de outros países. / The school timetabling is a classic optimization problem that has been extensively studied due to its practical and theoretical importance. It consists in scheduling a set of class-teacher meetings in a prefixed period of time, satisfying requirements of different types. Given the combinatorial nature of this problem, solving medium and large instances of timetabling to optimality is a challenging task. When resources are tight, it is often difficult to find even a feasible solution. Several techniques have been developed in the scientific literature to tackle the high school timetabling problem, however, robust solvers do not exist yet. Since the use of exact methods, such as mathematical programming techniques, is considered impracticable to solve large real world instances, metaheuristics and hybrid metaheuristics are the most used solution approaches. In this research we develop techniques that combine mathematical programming and heuristics, so-called matheuristics, to solve efficiently and in a robust way some variants of the high school timetabling problem. Although we pay special attention to problems arising in Brazilian institutions, the proposed methods can also be applied to problems from different countries.

A geração de quadros de horários escolares é um problema clássico de otimização que tem sido largamente estudado devido a sua importâncias prática e teórica. O problema consiste em alocar um conjunto de aulas entre professor-turma em períodos de tempo pré-determinados, satisfazendo diferentes tipos de requisitos. Devido a natureza combinatória do problema, a resolução de instâncias médias e grandes torna-se uma tarefa desafiadora. Quando recursos são escassos, mesmo uma solução factível pode ser difícil de ser encontrada. Várias técnicas tem sido propostas na literatura científica para resolver o problema de geração de quadros de horários escolares, no entanto, métodos robustos ainda não existem. Visto que o uso de métodos exatos, como por exemplo, técnicas de programação matemática, não podem ser utilizados na prática, para resolver instâncias grandes da realidade, meta-heurísticas e meta-heurísticas híbridas são usadas com frequência como abordagens de resolução. Nesta pequisa, são desenvolvidas técnicas que combinam programação matemática e heurísticas, denominadas mateheurísticas, para resolver de maneira eficiente e robusta algumas variações de problemas de geração de quadros de horários escolares. Embora neste trabalho sejam abordados problemas encontrados no contexto de instituições brasileiras, os métodos propostos também podem ser aplicados em problemas similares oriundo de outros países. / The school timetabling is a classic optimization problem that has been extensively studied due to its practical and theoretical importance. It consists in scheduling a set of class-teacher meetings in a prefixed period of time, satisfying requirements of different types. Given the combinatorial nature of this problem, solving medium and large instances of timetabling to optimality is a challenging task. When resources are tight, it is often difficult to find even a feasible solution. Several techniques have been developed in the scientific literature to tackle the high school timetabling problem, however, robust solvers do not exist yet. Since the use of exact methods, such as mathematical programming techniques, is considered impracticable to solve large real world instances, metaheuristics and hybrid metaheuristics are the most used solution approaches. In this research we develop techniques that combine mathematical programming and heuristics, so-called matheuristics, to solve efficiently and in a robust way some variants of the high school timetabling problem. Although we pay special attention to problems arising in Brazilian institutions, the proposed methods can also be applied to problems from different countries.

Todo início de período letivo, gestores de instituições de ensino se deparam com um típico problema: montar as grades horárias das turmas, segundo as demandas de aulas de suas disciplinas e considerando as restrições de disponibilidade horária de todos os envolvidos. Conhecido na literatura como School Timetabling Problem (STP), este típico problema de otimização combinatória é reconhecidamente complexo por conta do seu elevado número de variáveis e restrições. Devido à dependência das regras do sistema educacional de cada país, o STP pode ter inúmeras variantes, cada uma com o seu próprio conjunto de particularidades. Este trabalho se propõe a oferecer um modelo para o STP considerando o sistema educacional brasileiro, visando alocar não apenas professores, mas também determinando que disciplina cada professor deve ministrar e alocando os locais de aula. O modelo proposto, baseado na meta-heurística simulated annealing, foi concebido para que cada instituição de ensino usuária tenha liberdade para definir a penalidade de cada tipo possível de inconformidade ou restrição, de modo que o algoritmo empregado possa encontrar uma solução com o menor custo possível. / Every beginning of term, educational institution managers face a typical problem: planning the classes' timetable, according to their lesson demands for each subject, considering, furthermore, the schedule constrains of all actors. Known as school timetabling problem (STP), this typical combinatorial optimization problem is remarkably complex due to the high number of variables and constraints. Owing to the rules of each country's educational system, STP can have uncountable variants, each one with their own set of features. This dissertation searches to offer a model to STP considering the Brazilian Educational System, focusing on allocating not only the teachers but also determining which subject each teacher should teach and allocating classrooms, laboratories and the like. The propesed model, based on the metaheuristic simulated annealing, was conceived so that each educational institution using this model has the freedom to define which penalty will be applied to each possible kind of noncomformity and constraint, in order for the applied algorithm to find a solution at the lowest cost as possible.

Todo início de período letivo, gestores de instituições de ensino se deparam com um típico problema: montar as grades horárias das turmas, segundo as demandas de aulas de suas disciplinas e considerando as restrições de disponibilidade horária de todos os envolvidos. Conhecido na literatura como School Timetabling Problem (STP), este típico problema de otimização combinatória é reconhecidamente complexo por conta do seu elevado número de variáveis e restrições. Devido à dependência das regras do sistema educacional de cada país, o STP pode ter inúmeras variantes, cada uma com o seu próprio conjunto de particularidades. Este trabalho se propõe a oferecer um modelo para o STP considerando o sistema educacional brasileiro, visando alocar não apenas professores, mas também determinando que disciplina cada professor deve ministrar e alocando os locais de aula. O modelo proposto, baseado na meta-heurística simulated annealing, foi concebido para que cada instituição de ensino usuária tenha liberdade para definir a penalidade de cada tipo possível de inconformidade ou restrição, de modo que o algoritmo empregado possa encontrar uma solução com o menor custo possível. / Every beginning of term, educational institution managers face a typical problem: planning the classes' timetable, according to their lesson demands for each subject, considering, furthermore, the schedule constrains of all actors. Known as school timetabling problem (STP), this typical combinatorial optimization problem is remarkably complex due to the high number of variables and constraints. Owing to the rules of each country's educational system, STP can have uncountable variants, each one with their own set of features. This dissertation searches to offer a model to STP considering the Brazilian Educational System, focusing on allocating not only the teachers but also determining which subject each teacher should teach and allocating classrooms, laboratories and the like. The propesed model, based on the metaheuristic simulated annealing, was conceived so that each educational institution using this model has the freedom to define which penalty will be applied to each possible kind of noncomformity and constraint, in order for the applied algorithm to find a solution at the lowest cost as possible.

Goal programming is an approach for solving decision problems. The aim of this doctoral thesis is to show the practical use of this approach for solving real problems. The first chapter brings a brief introduction to multicriteria decision making. The second chapter is devoted to goal programming, its history, theory, criticism and also to its practical applications. The third chapter deals with description of a model for optimisation of white mass production. This model utilises the goal programming principle to deal with measuring deviations of raw materials' composition. A part of this chapter is a presentation of OPTIPROT, an application that implements the mentioned model. In the fourth chapter there are described three mathematical models for timetabling at a department level; two multistage models and one complex model. All three models are formulated utilising goal programming. In this chapter there is also described an application that implements the complex model for timetabling.

In this dissertation, we address three different combinatorial optimization problems (COPs), each of which has specific real-life applications. Owning to their specific nature, these problems are different from those discussed in the literature. For each of these problems, we present a mathematical programming formulation, analyze the problem to determine its useful, inherent structural properties, and develop an efficient methodology for its solution by exploiting these properties. The first problem that we address is the course timetabling problem encountered at Virginia Tech. The course timetabling problem for a university is a difficult problem and has been studied by many researchers over the years. As a result, a plethora of models and approaches have been reported in the literature. However, most of these studies have focused on applications pertaining to course scheduling for a single or at most few departments of a university. The sheer size of the university-wide timetabling problem that we address, involving thousands of courses to be scheduled in hundreds of classrooms in each semester, makes it a challenging problem. We employ an appropriate decomposition technique that relies on some inherent structural properties of the problem both during the modeling and algorithmic development phases. We show the superiority of the schedules generated by our methodology over those that are currently being used. Also, our methodology requires only a reasonable amount of computational time in solving this large-size problem. A facility layout problem involving arbitrary-shaped departments is the second problem that we investigate in this dissertation. We designate this problem as the arbitrary-shaped facility layout problem (ASFLP). The ASFLP deals with arranging a given set of departments (facilities, workstations, machines) within the confines of a given floor space, in order to optimize a desired metric, which invariably relates to the material handling cost. The topic of facility planning has been addressed rather extensively in the literature. However, a major limitation of most of the work reported in the literature is that they assume the shape of a department to be a rectangle (or even a square). The approach that relies on approximating an arbitrary-shaped department by a rectangle might result in an unattractive solution. The key research questions for the ASFLP are: (1) how to accurately model the arbitrary-shaped departments, and (2) how to effectively and efficiently determine the desired layout. We present a mixed-integer programming model that maintains the arbitrary shapes of the departments. We use a meta-heuristic to solve the large-size instances of the ASFLP in a reasonable amount of time. The third problem that we investigate is a supply chain scheduling problem. This problem involves two stages of a supply chain, specifically, a manufacturer and one or more customers. The key issue is to achieve an appropriate coordination between the production and distribution functions of the manufacturer so as to minimize the sum of the shipping and job tardiness costs. We, first, address a single customer problem, and then, extend our analysis to the case of multiple customers. For the single-customer problem, we present a polynomial-time algorithm to solve it to optimality. For the multiple-customer problem, we prove that this problem is NP-hard and solve it by appropriately decomposing it into subproblems, one of which is solvable in polynomial time. We propose a branch-and-bound-based methodology for this problem that exploits its structural properties. Results of an extensive computational experimentation are presented that show the following: (1) our algorithms are efficient to use and effective to implement; and (2) significant benefits accrue as a result of integrating the production and distribution functions. / Ph. D.

I den här studien undersöks schemaläggningsprocesser i gymnasieskolan. Schemaläggning i skolan är en komplex verksamhet som har stor påverkan på lärares arbetsvillkor och elevers förutsättningar för lärande. Därför är det av stor betydelse att schemaläggningen håller hög kvalitet. Till följd av skolreformer på 1990-talet decentraliserades beslutsfattandet över schemaläggningen. Decentraliseringen ställer stora krav på enskilda skolors ansvarstagande, vilket innebär att lokala förutsättningar får stor betydelse för schemaläggningens resultat. Det är därför av intresse att undersöka vilka faktorer som främjar skolors schemaläggning. Syftet med studien är att undersöka vilka villkor som behöver uppfyllas för attschemaläggningsprocessen i en gymnasieskola ska vara effektiv. Effektiva schemaläggningsprocesser definieras med utgångspunkt från tidigare schemaläggningsforskning. Studien har genomförts i form av en flerfallsstudie där två komparativt utvalda gymnasieskolor undersökts och jämförts. Intervju användes som datainsamlingsmetod och data analyserades med kvalitativ innehållsanalys. Faktorer som påverkar och begränsar schemaläggningsprocesserna kunde på så sätt identifieras. Med utgångspunkt ifrån en jämförelse av resultaten från de båda fallen föreslogs fyra villkor som möjliggör effektiva schemaläggningsprocesser i gymnasieskolan. Två av dessa villkor behandlar hur schemaläggarens arbete bör struktureras: Schemaläggaren bör använda strategier för att hantera begränsande faktorer i schemaläggningen och schemaläggningsarbetet bör fokuseras på dess kärnuppdrag. De övriga två behandlar de strukturella förutsättningarna för schemaläggning: Skolan behöver ha stabilt elevunderlag och undervisningsgrupperna på skolan bör vara utformade på ett sätt som stödjer schemaläggningen. / In this study, timetabling processes in Swedish upper secondary schools were examined. School timetabling is a complex activity, with a great impact on working conditions for teachers and pupils’ learning conditions. Hence, it is of great importance that the timetabling is of high quality. As a result of the Swedish educational reforms in the 1990’s, timetabling decision-making was decentralized. This places great demands on responsibility of individual schools, which implies that local conditions are of great significance for the outcomes of timetabling. It is therefore of interest to examine the factors that promote school timetabling. The purpose of this study is to investigate the conditions that need to be fulfilled to ensure the efficacy of the timetabling process in an upper secondary school. Effective timetabling processes are defined based on previous research on school timetabling. The study has been conducted as a multiple case study, in which two comparatively chosen upper secondary schools were examined and compared. Interviews were used for data collection and data were analyzed using qualitative content analysis. In this way, factors that influence and constrain the timetabling processes could be identified. Based on a comparison of the results from both cases, four conditions were suggested that render timetabling processes effective. Two of the conditions deal with work structure of timetablers: Timetablers should apply strategies to handle timetabling constraints and the timetabling should be focused on its main task. The other two conditions deal with structural features necessary for effective timetabling: The school needs a stable pupil population and the class composition should be organized in a way that supports timetabling.

The timetable is an essential part for the operations of railway traffic, and its quality is considered to have large impact on capacity utilization and reliability of the transport mode. The process of generating a timetable is most often a manual task with limited computer aid, and is known to be a complex planning problem due to inter-train dependencies. These inter-train dependencies makes it hard to manually generate feasible timetables, and also makes it hard to improve a given timetable as new conflicts and surprising effects easily can occur. As the demand for railway traffic is expected to continue grow, higher frequencies and more saturated timetables are required. However, in many European countries there is also an on-going public debate on the punctuality of the railway, which may worsen by increased capacity utilization. It is therefore also a need to increase the robustness of the services. This calls for increased precision of both the planning and the operation, which can be achieved with a higher degree of automation. The research in this thesis is aimed at improving the robustness of railway timetables by combining micro-simulation with mathematical optimization, two methods that today are used frequently by practitioners and researchers but rarely in combination. In this research a sequential approach based on simulating a given timetable and re-optimizing it to reduce the weighted sum of scheduled travel time and predicted average delay is proposed. The approach has generated promising results in simulation studies, in which it has been possible to substantially improve the punctuality and reduce the average delays by only increasing the advertised travel times slightly. Further, the results have also indicated a positive socio-economic benefit. This demonstrates the methods potential usefulness and motivates further research. / För järnvägen har tidtabellen en central roll, och dess kvalité har stor betydelse för kapacitet och tillförlitlighet. Processen att konstruera en tidtabell är ofta en uppgift som utförs manuellt med begränsat datorstöd och på grund av beroenden mellan enskilda tåg är det ofta ett tidskrävande och svårt arbete. Dessa tågberoenden gör det svårt att manuellt konstruera konfliktfria tidtabeller samtidigt som det också är svårt att manuellt förbättra en given tidtabell, vilket beror på att de är svårt att förutsäga vad effekten av en given ändring blir. Eftersom efterfrågan på järnväg fortsatt förväntas öka, finns det ett behov av att kunna köra fler tåg. Samtidigt pågår det redan i många europeiska länder en offentlig debatt om järnvägen punktlighet, vilken riskeras att försämras vid högre kapacitetsanvändning. Därför finns det även ett behov av att förbättra tidtabellernas robusthet, där robusthet syftar till en tidtabells möjlighet att stå emot och återhämta mindre förseningar. För att hantera denna målkonflikt kommer det behövas ökad precision vid både planering och drift, vilket kan uppnås med en högre grad av automation. Forskningen i denna avhandling syftar till att förbättra robustheten för tågtidtabeller genom att kombinera mikro-simulering med matematisk optimering, två metoder som redan används i hög grad av både yrkesverksamma trafikplanerare och forskare men som sällan kombineras. I den här avhandlingen förslås en sekventiell metod baserad på att simulera en given tidtabell och optimera den för att minska den viktade summan av planerad restid och predikterad medelförsening. Metoden har visat på lovande resultat i simuleringsstudier, där det har varit möjligt att uppnå en väsentligt bättre punktlighet och minskad medelförsening, genom att endast förlänga de planerade restiderna marginellt. Även förbättrad samhällsekonomisk nytta har observerats av att tillämpa den föreslagna metoden. Sammantaget visar detta metodens potentiella nytta och motiverar även fortsatt forskning. / <p>QC 20191112</p>

Made available in DSpace on 2015-03-05T14:01:22Z (GMT). No. of bitstreams: 0 Previous issue date: 12 / Bolsa para curso e programa de Pós Graduação / Este trabalho aborda o uso de uma metaheurística populacional para a solução do problema de otimização conhecido, na Pesquisa Operacional, como Programação de Horário de Cursos Baseada em Currículos. O problema de Programação de Horário de Cursos Baseada em Currículos consiste na construção das grades de horário de cursos em instituição de ensino que indicam em quais períodos semanais cada disciplina destes cursos deverá ocorrer, alocando professores e salas e respeitando um conjunto de requisitos organizacionais, pedagógicos e pessoais. Este trabalho apresenta uma formulação matemática para o problema e especifica um algoritmo de solução baseado na técnica metaheurística Busca Dispersa, combinada com o método de Reconexão por Caminhos. Além disso, é apresentado o registro de testes realizados com instâncias de problemas utilizadas na International Timetabling Competition e também em um problema real de uma instituição local de esino superior. / This paper discusses the use of a populational metaheuristic to solve the optimization problem known in Operational Research, as Curriculum Based Timetabling. The Curriculum Based Timetabling problem is the construction of schedule of courses in educational institutions that indicate which weekly times each subject of these courses should occur, allocating rooms and teachers and a respecting a set of organizational, pedagogical and personal requirements. This paper presents a mathematical formulation for the problem and specify a solution algorithm based on the Scatter Search metaheuristic technique, combined with the method Path Relinking. Furthermore, it is present the record of tests with instances of problems used in the International Timetabling Competition and also a real problem of a local institution.