One of the problems of real-life production scheduling is dynamics of manufacturing environments with new production demands and breaking machines during the schedule execution. Simple rescheduling from scratch in response to unexpected events occurring on the shop floor may require excessive computation time. Moreover, the recovered schedule may be prohibitively deviated from the ongoing schedule. This thesis reviews existing approaches in the field of dynamic scheduling and proposes techniques how to modify a schedule to accommodate disturbances such as resource failure, hot order arrival or order cancellation. The importance is put on the speed of suggested procedures as well as on a minimum modification from the original schedule. The scheduling model is motivated by the FlowOpt project, which is based on the Temporal Networks with Alternatives. The algorithms are written in the C# language.

Nesta tese, dois diferentes problemas de programação da produção são abordados, o Flexible JobShop Scheduling Problem com Flexibilidade de sequenciamento e o Flowshop Scheduling Problem com tempos de espera e permutação de sequência. Para ambos, inicialmente um algoritmo list scheduling (LS) que explora características do problema é desenvolvido e então estendido para um método do tipo Beam Search (BS) que utiliza o LS em seus principais elementos: (1) expansão dos níveis, (2) avaliação local dos candidatos e (3) avaliação global dos candidatos. Todos os métodos propostos são determinísticos e seus pseudocódigos são cuidadosamente descritos para garantir a replicabilidade dos resultados reportados. O desempenho dos métodos propostos são avaliados utilizando instâncias e outros métodos heurísticos da literatura. Os resultados computacionais obtidos mostram a eficiência das heurísticas propostas que superaram os métodos da literatura utilizando pouco tempo computacional. / In this thesis two diferent scheduling problems were addressed, the Flexible Job Shop Scheduling Problem with sequence Flexibility and the Flowshop Scheduling Problem with waiting times and sequence permutation. For both problems, firstly, a list scheduling (LS) algorithm which exploit features of the problem was developed and then it was extedend to a Beam Search (BS) method which use the LS in his main features: (1) level expansion, (2) local evaluation and (3) global evaluation. All the proposed methods are deterministics and their pseudocodes are carefully described to ensure the replicability of the reported results. The performance of the proposed methods was evaluated using instances and other heuristic methods found in literature. The computational results show the eficiency of the proposed heuristics, which outperformed the literature methods while using low computational time.

The purpose of this study was to examine whether the use of a middle school flexible interdisciplinary block schedule would increase eighth-grade students' reading scores, as measured by the Oregon Assessment of Knowledge and Skills (OAKS). A 90-minute middle school flexible interdisciplinary block schedule served as the independent variable and was evaluated to determine its impact on student reading achievement. Extant data from the OAKS was used to assess student learning. Extant data from two groups of students were examined. The treatment group had their eighth-grade language arts and social studies classes scheduled into 90-minute flexible interdisciplinary block periods, taught by the same teacher. The comparison group had their eighth-grade language arts and social studies classes scheduled into traditional 45-minute departmentalized periods, taught by two separate teachers. The overall amount of time allocated to language arts and social studies instruction within the academic year was the same for both groups. However, the way the time was flexed and utilized within the class periods differed between the two groups. Research Question 1 addressed the possible increase in mean OAKS reading scores over time. Research Question 2 addressed the possible differences in the mean OAKS Reading Achievement Standards cut scores over time. The results of the two-year treatment condition of a FIBS for language arts instruction did not result in statistically significant results, as measured by the OAKS. The results suggest that there may not be a significant achievement difference between schools that implement an interdisciplinary scheduled compared to schools that implement a traditional, departmental approach.

Este trabalho propõe uma heurística construtiva determinística e uma heurística construtiva probabilística para resolver o problema de programação de projetos com custo de disponibilidade de recursos e custo de penalidade por atraso no término do projeto (RACPT - Resource Availability Cost Problem with Tardiness). Os algoritmos combinam a flexibilidade da atividade com a flexibilidade do recurso para selecionar a próxima atividade a ser programada. A data de início de uma atividade é a data mais cedo em que sua execução não gera o maior pico de utilização dos recursos ou a data mais cedo na qual o custo total do projeto for menor. A melhor versão das heurísticas foi obtida após o teste de várias regras de prioridade, conforme a revisão bibliográfica realizada. As heurísticas propostas foram testadas em 360 instâncias de testes e seus resultados foram comparados aos obtidos pela formulação matemática baseada em strip packing e restrições disjuntivas implementada no programa CPLEX. A heurística construtiva determinística gera uma solução viável rapidamente, porém de baixa qualidade. Já a heurística construtiva probabilística gera soluções ótimas ou próximas da ótima para problemas pequenos ou para problemas fáceis e gera soluções muito melhores do que o CPLEX na metade do tempo computacional para os problemas médios e grandes ou para problemas difíceis. Dado os bons resultados obtidos e à implementação no programa VBA for Microsoft Excel, a heurística construtiva probabilística proposta é um método bom e prático para resolução do RACPT. / This work proposes a deterministic constructive heuristic and a probabilistic constructive heuristic for solving the resource availability cost problem with tardiness (RACPT). The algorithms combine the flexibility of an activity with the flexibility of a resource to select the next activity to be scheduled. The start time of the activity is the earliest date in which the activity\'s execution does not create resources usage peak or the earliest date with the lowest total project cost. We tested several priority rules according to the literature review and determined the best version of the heuristics. Afterwards, we tested the proposed heuristics in 360 instances and compared its results with the solutions obtained by the optimization software CPLEX. The RACPT implementation on CPLEX utilized a mathematical formulation based on strip packing concepts and disjunctive constraints. The computational results showed that the deterministic constructive heuristic generates feasible solutions of poor quality in low computational time. The probabilistic constructive heuristic achieved better results. For small instances or easy problems, it found optimal or near-optimal solutions. For medium and large instances or hard problems, it obtained better results than CPLEX in half-computational time. We believe that the probabilistic constructive heuristic is a good and practical method for solving the RACPT. The proposed algorithm produced good results in reasonable computational time and was implemented on the popular software VBA for Microsoft Excel.

Problemas de sequenciamento são muito comuns, eles existem sempre que há uma escolha sobre a ordem em que várias tarefas podem ser realizadas. Seja o negócio uma companhia aérea, um hotel, um fabricante de computadores ou uma universidade, esses problemas fazem parte do cotidiano. A aplicação das técnicas de sequenciamento permite, por exemplo, a redução dos custos e o aumento na agilidade da cadeia de suprimentos, afetando as operações no inicio e no fim da cadeia de suprimentos pelo mundo inteiro. Este trabalho parte da intenção de abordar os princípios e as técnicas de Scheduling, com a finalidade de propor um modelo de sequenciamento para a solução de um problema em sistemas produtivos do tipo job shop com n tarefas e m máquinas, considerando os tempos de setup dependentes da sequência e tendo como horizonte de planejamento o curto prazo. O objetivo é o de minimizar a perda dos tempos não produtivos. Neste contexto, a pesquisa apresenta um enfoque tanto exploratório, quanto aplicado. Pode ser considerado exploratório, uma vez que a revisão da literatura é referência central para o desenvolvimento do modelo matemático. É aplicado considerando-se o desenvolvimento do modelo e avaliação de sua aplicabilidade. Sendo assim, a partir da definição do problema e desenvolvimento do modelo por meio do uso de técnicas matemáticas e abordagens da pesquisa operacional constatou-se que as conclusões tiradas podem inferir decisões para o problema real. Sendo que, as considerações aqui feitas têm por finalidade relatar os fatos constatados nos experimentos realizados, visando contribuir com futuras pesquisas na área. / Sequencing problems are very common, they happen every time there is a choice regarding the order in which several tasks can be performed. The business can be an airline, a hotel, a computer manufacturer or a university; these issues are part of their routine. The application of the sequencing techniques allows, for example, reducing the costs and fastening the supply chain all over the world. This work has an approach to Scheduling principles and techniques, with the objective of proposing a sequencing model for the solution of a problem in productive systems such as job shop with n tasks and m machines, considering setup times dependent on the sequence and adopting a short term planning. The goal is to minimize the waste of unproductive time. In this context, the research presents an approach both exploratory and applied. It can be considered exploratory, once that the literature review is a main reference to the development of a mathematical model. It is applied when we consider the development of the model and evaluation of its applicability. Thus, from the problem definition and the model development by the use of mathematical techniques and approaches of the operational research, we found that the conclusions drawn from the model might infer decisions for a real problem. The considerations shown here aim to report the facts given in the conducted experiments, intending to contribute to future researches in the area.

A presente pesquisa tem como objetivo estudar a integração entre dois temas clássicos da literatura de pesquisa operacional e gestão de operações: problemas de corte e empacotamento; e problemas de programação da produção. Ainda que sejam duas áreas intensamente exploradas e pesquisadas, e, ainda, que seja uma situação facilmente encontrada em sistemas de produção reais, abordagens de ambos problemas de forma coordenada ainda carecem de maiores pesquisas. Neste trabalho é feita uma revisão de ambos temas, com foco em problemas de bin packing e programação em ambiente de máquina única com objetivo de minimizar soma de atrasos e adiantamentos ponderados. Uma formulação matemática linear e inteira mista é proposta para o problema, contemplando as restrições que concernem a cada um e também à sua consideração simultânea. Como se trata de um problema que une dois outros, cada um NP-hard isoladamente, um método heurístico é proposto para obter uma solução interessante em tempos computacionais bastante reduzidos. Foram obtidas propriedades físicas de definição de data ideal de programação de um conjunto de itens atribuídos a um bin. Também é proposto um método para geração de um limitante inferior melhorado em relação a pacotes de otimização de mercado para o problema. Ambos métodos foram testados em uma massa de dados de 1.152 instâncias, geradas para retratar cenários de diferentes datas de entrega, setups, custos de atraso e adiantamento em relação à matéria-prima, tamanho de itens e número de itens na instância. Os resultados mostram-se largamente superiores aos obtidos por um otimizador genérico (CPLEX), embora ainda sejam gaps excessivamente grandes, o que reforça a dificuldade do problema. / The present research aims to explore the integration between two classic themes on operations research and operations management literature: cutting and packing problems; and production scheduling problems. Although they are intensive explored and researched areas and, besides, it\'s an easily found situation on real production systems, coordinated approaches of both themes still need deeper research. On this paper, it was done a review of both themes, focusing on bin packing problems and single-machine environment scheduling problems aiming to minimize total weighed earliness and tardiness. A mixed integer-linear mathematical formulation is proposed to the problem, including constraints referred to each problem and, also, to their simultaneous consideration. Once it\'s a problem that joins the other two, each one NP-hard solely, an heuristic method is proposed to obtain an interesting solution in reasonable computational times. Physical properties were identified, defining the best date to allocate a given lot of items to be processed together. Also, a lower bound generation method is proposed, improving the one generated by optimization softwares. Both methods were tested on a 1.152 instances mass of data, generated to represent well several scenarios of different due dates, setup times, earliness and tardiness costs compared to raw material, size of items and number the items the instance. Results show largely superiority the ones obtained by an optimization pack (CPLEX), although gaps are still excessively large, fact the reinforces problem\'s difficulty.

In modern software development, continuous integration has become a integral part of agile development methods, advocating that developers should integrate their code frequently. Configura currently has one dedicated machine, performing tasks such as building the software and running system tests each time a developer submits new code to the main repository. One of the main practices of continuous integration advocates for having a fast build in order to keep the feedback loop short for developers, leading to increased productivity. Configura’s build system, named Build Central, currently uses a sequential build procedure to execute said tasks and was becoming too slow to keep up with the number of requested builds. The primary method for speeding up this procedure was to utilize the multi-core architecture of the build machine. In order to accomplish this, the system would need to deploy a scheduling algorithm to distribute and order tasks correctly. In this thesis, six scheduling algorithms are implemented and compared. Four of these algorithms are based on the classic list scheduling approach, and two additional algorithms are proposed which are based on dynamic scheduling principles. In this particular system, the dynamic algorithms proved to have better performance compared to the static scheduling algorithms. Performance on Build Central, using four processing cores, was improved with approximately 3.4 times faster execution time on an average daily build, resulting in a large increase of the number of builds that can be performed each day.

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本文分為個部分：多技能員工調問題，和集合覆蓋、裝運和劃分混合問題多面體研究，其中第一部分問題啟發我們第二部分的探。 / 首先，我們研究在一個大型機場的國際客運站中客戶服務人員的調問題。員工有同的技能和技能水平。技能定義是二維的，包括操作技能和語言能。在學模型中，我們也考慮用餐和休息時間的調和多處工作地點。我們證明該問題是NP-hard 的。我們推導出有效等式，以方計算過程。我們的學模型能夠幫助規劃者做出決策，及可計算同型的活性對業務的影響。我們的模型也可以幫助決策者計劃長遠工作調和培訓。 / 多技能人員調問題啟發我們這篇文的第二部分：集合覆蓋、裝運和劃分混合問題多面體研究。我們首先證明如覆蓋（或裝運）的等式被删去，該多面體是相當於一個放寬的裝運（或覆蓋）多面體的投影。然後我們考慮混合奇穴多面體（即是一個由覆蓋和裝運等式組成的多面體），並採用圖方法研究，通過考慮同型的等式的互動，推導出混合奇穴等式和完全描繪多面體的特徵。我們再推導出集合覆蓋和裝運混合問題的混合奇穴等式。計算結果顯示，混合奇穴等式有助於減少計算時間。我們還提供子明如何用等式幫助決策。 / This thesis is divided into two parts: Multi-Skilled Staff-Scheduling Problem and a polyhedral study on the Mixed Set Covering, Packing and Partitioning Problem, where the first part is a motivating example of the latter. / In the multi-skilled staff-scheduling problem, we study the problem of scheduling customer service agents at an international terminal of a large airport. The staff members are heterogeneous with different skills and skill levels. The skill specification is two-dimensional, defined by operational skills and language proficiency. In the mathematical model, we also consider the scheduling of meal and rest breaks, and multiple locations. The problem is shown to be NP-hard. We derive valid inequalities to speed up the computational procedure. With our mathematical model, we are able to help schedule planners make decisions and examine the impacts of different types of flexibility on the level of service provided. Our model can also help decision makers with long-term work-schedule planning. / Motivated by the staff-scheduling problem, the second part of this thesis studies the polyhedral structure of the mixed set covering, packing and partitioning problem, i.e., a problem that contains set covering, set packing and set partitioning constraints. We first study the mixed odd hole polytope, which is the polytope associated with a mixed odd hole consisting of covering and packing "edges". Adopting a graphical approach and considering the "interactions" between the different types of inequalities, we derive the mixed odd hole inequality, thereby completely characterizing the mixed odd hole polytope. We then generalize the mixed odd hole inequality for the general mixed covering and packing polytope. Computational results show that the mixed odd hole inequalities are helpful in reducing solution time. We also provide examples of problem settings in which the inequalities can be used to help decision making. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Kuo, Yong Hong. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 119-129). / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter I --- Scheduling of Multi-skilled Staff Across Multiple Locations --- p.1 / Chapter 1 --- Introduction --- p.2 / Chapter 2 --- Literature Review --- p.8 / Chapter 3 --- Mathematical Model --- p.14 / Chapter 3.1 --- Problem Formulation --- p.14 / Chapter 3.2 --- Valid Inequalities --- p.20 / Chapter 3.3 --- Shift Scheduling and Longer-Term Work-Schedule Planning --- p.21 / Chapter 4 --- Computational Studies --- p.24 / Chapter 4.1 --- Dataset and Input Parameters --- p.24 / Chapter 4.1.1 --- Staffing Requirements and Shortage Penalties --- p.24 / Chapter 4.2 --- Computational Study: Managerial Insights --- p.26 / Chapter 4.2.1 --- Effect of Three Types of Flexibility --- p.26 / Chapter 4.2.2 --- Impact of Different Types of Flexibility --- p.28 / Chapter 4.3 --- Computational Study: Benefits Compared with Benchmarks --- p.33 / Chapter 4.3.1 --- Heuristic H1: CSA Assignment by Time Period --- p.35 / Chapter 4.3.2 --- Heuristic H2: CSA Assignment by Criticality --- p.35 / Chapter 4.3.3 --- Comparison with Benchmarks --- p.37 / Chapter 4.4 --- Computational Study: Computational Efficiency --- p.40 / Chapter 5 --- Conclusions --- p.44 / Chapter II --- On the Polyhedral Structure of the Mixed Set Covering, Packing and Partitioning Polytope --- p.47 / Chapter 6 --- Introduction --- p.48 / Chapter 7 --- Preliminaries --- p.51 / Chapter 8 --- Overview of Packing, Covering and Partitioning Polyhedra --- p.58 / Chapter 8.1 --- Set Packing Polytope --- p.58 / Chapter 8.1.1 --- Intersection Graph --- p.59 / Chapter 8.1.2 --- Lifting Procedures --- p.63 / Chapter 8.1.3 --- Facet-Producing Subgraphs --- p.66 / Chapter 8.2 --- Set Covering Polytope --- p.71 / Chapter 8.2.1 --- Polyhedral Structure and the Associated Graphs --- p.71 / Chapter 8.3 --- Set Partitioning Polytope --- p.76 / Chapter 8.4 --- Blocking and Anti-Blocking Pairs --- p.78 / Chapter 8.4.1 --- Blocking polyhedra --- p.78 / Chapter 8.4.2 --- Anti-blocking polyhedra --- p.80 / Chapter 8.5 --- Perfect, Ideal and Balanced Matrices --- p.81 / Chapter 8.5.1 --- Perfect Matrices --- p.81 / Chapter 8.5.2 --- Ideal Matrices --- p.83 / Chapter 8.5.3 --- Balanced Matrices --- p.84 / Chapter 9 --- Mixed Set Covering, Packing and Partitioning Polytope --- p.87 / Chapter 9.1 --- Mixed Set Partitioning and Covering/Packing Polytope --- p.87 / Chapter 9.2 --- Mixed Set Covering and Packing Polytope --- p.88 / Chapter 9.2.1 --- Mixed odd hole --- p.90 / Chapter 9.2.2 --- General Mixed Covering and Packing Polytope --- p.97 / Chapter 9.3 --- Computational Experiments --- p.108 / Chapter 9.4 --- Applications of the Mixed Odd Hole Inequality --- p.112 / Chapter 9.4.1 --- Railway Time-Tabling --- p.112 / Chapter 9.4.2 --- Team Formation --- p.113 / Chapter 9.4.3 --- Course Registration --- p.114 / Chapter 10 --- Conclusions --- p.117 / Bibliography --- p.119

The main goal of a scheduling process is to decide when and how to execute each of the project's activities. Despite large variety of researched scheduling problems, the majority of them can be described as generalisations of the resource-constrained project scheduling problem (RCPSP). Because of wide applicability and challenging difficulty, RCPSP has attracted vast amount of attention in the research community and great variety of heuristics have been adapted for solving it. Even though these heuristics are structurally different and operate according to diverse principles, they are designed to obtain only one solution at a time. In the recent researches on RCPSPs, it was proven that these kind of problems have complex multimodal fitness landscapes, which are characterised by a wide solution search spaces and presence of multiple local and global optima. The main goal of this thesis is twofold. Firstly, it presents a variation of the RCPSP that considers optimisation of projects in an uncertain environment where resources are modelled to adapt to their environment and, as the result of this, improve their efficiency. Secondly, modification of a novel evolutionary computation method Cuckoo Search (CS) is proposed, which has been adapted for solving combinatorial optimisation problems and modified to obtain multiple solutions. To test the proposed methodology, two sets of experiments are carried out. Firstly, the developed algorithm is applied to a real-life software development project. Secondly, the performance of the algorithm is tested on universal benchmark instances for scheduling problems which were modified to take into account specifics of the proposed optimisation model. The results of both experiments demonstrate that the proposed methodology achieves competitive level of performance and is capable of finding multiple global solutions, as well as prove its applicability in real-life projects.