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The semiconductor industry provides a host of very challenging problems in production planning and scheduling because of the unique features of the wafer fab. This research addresses the need to develop an approach, which can be used to generate optimal or near-optimal solutions to the scheduling problem of a wafer fab, by using Mathematical Programming for a general case of a wafer fab. The problem is approached in two steps. First, the number of lots of different products to be released into the system during each planning period is determined, such that the total tardiness of the product orders is minimized over the planning horizon. Second, the schedule of these lots is determined so that the cycle time of each lot released into the system is minimized. Thus, the performance measures based both on due dates and cycle time are considered. The lot release, tardiness problem is formulated as an integer linear program, and a 3-phase procedure, which utilizes a variation of the Wilkerson-Irwin algorithm, is developed. The performance of this 3-phase procedure is further improved by using insights from classical scheduling theory. The scheduling problem is formulated as a 0-1 integer linear program. An algorithm is developed for tightening the LP relaxation of this 0-1 integer linear programming model (of the scheduling problem) leading to a better performance of the branch and bound procedure used for its solution. Lagrangian relaxation is applied on a carefully chosen set of constraints in the scheduling problem, and a Lagrangian heuristic is developed for scheduling the jobs in each period of the planning horizon. Several useful insights are developed throughout to further improve the performance of the proposed algorithm. Experiments are conducted for both the tardiness and the scheduling problems. Five experiments are conducted for the tardiness problem. Each experiment has a different combination of number of products, machines, and work orders in a small sized wafer fab (2 to 6 products, 8 to 10 station families, 15 to 30 workstations, 9 to19 work orders, and 100 to 250 lots per work order). The solutions obtained by the 3-phase procedure are compared to the optimal solutions of the corresponding tardiness problems, and the tardiness per work order for the 3-phase procedure is 0% to 25% greater than the optimal solution. But the time required to obtain the optimal solution is 22 to 1074 times greater than the time required to obtain the solution through the 3-phase procedure. Thus, the 3-phase procedure can generate almost optimal solutions and requires much smaller computation time than that required by the optimal solution. Four experiments are conducted to test the performance of the scheduling problem. Each experiment has a different combination of number of products, machines, routes, bottleneck stations, processing times, and product mix entering the system each day in a small sized wafer fab (2 products, 8 station families, 18 workstations, and 8 to 10 lots released per day into the system). The solution quality of the schedule generated by the Lagrangian heuristic is compared to the solution provided by the standard dispatching rules available in practice. In each experiment, the cycle time of a product for each dispatching rule is divided by the best cycle time for that product over all the dispatching rules in that experiment. This ratio for the Lagrangian heuristic in each experiment and over all the experiments varies from 100% to 104%. For the standard dispatching rules, this ratio ranges from 100% to 120% in each experiment and also over all the experiments. The average of the ratio over all the experiments is the least for the Lagrangian heuristic. This indicates that for the experiments conducted, the Lagrangian heuristic consistently provides a solution that is, or is close to, the best solution and, hence, quite competitive when compared to the standard dispatching rules. / Master of Science

Este trabalho trata do problema de sequenciamento e programação de atividades em máquinas diferentes em paralelo, considerando elegibilidade de máquina, e tempo de liberação das máquinas e das atividades com o objetivo de minimizar o custo de atraso total. Tal problema é descrito pela literatura como NP-hard. Foi proposto um método otimizante que envolve modelagem matemática, um algoritmo de geração de colunas e, além disso, uma heurística para tratar problemas com instancias maiores. O algoritmo de geração de colunas é baseado no método proposto por Akker, Hurkens e Savelsbergh (2000), que foi adaptado para o problema de múltiplas máquinas diferentes. Assim, o método foi aplicado em instâncias da literatura e em instâncias geradas para este trabalho de até 25 atividades e 4 máquinas. Os resultados foram analisados e observou-se que o modelo de programação inteira mista e eficiente para encontrar limitantes superiores de boa qualidade. Por outro lado, o algoritmo de geração de colunas é eficiente para encontrar limitantes inferiores para o problema. Desta forma, o método proposto utiliza o modelo MILP e o algoritmo de geração de colunas de maneira a se complementar. Assim, soluções ótimas foram encontradas para 84% das instancias geradas, sendo que o GAP médio para as instancias restantes foi de 2,1%. A heurística proposta e baseada na ideia de heurística construtiva probabilística, que foi apresentada por Arcus (1965). Ela foi executada na massa de dados gerada, resultando em um GAP médio de 10,6%. / This paper deals with the problem of scheduling activities in unrelated parallel parallel, considering machine eligibility, and machine and activity release time in order to minimize total weighted tardiness.Such a problem is described in the literature as NPhard. It has been proposed an optimizing method that involves mathematical modeling and a column generation algorithm, in addition, it is proposed a heuristic to treat problems with larger instances. The column generation algorithm was based on the method proposed by Akker, Hurkens e Savelsbergh (2000), which has been adapted to the problem of multiple diferent machines. Thus, the method was applied in instances of the literature and in instances generated for this paper up to 25 jobs and 4 machines. The results were analyzed and it was noted that the mixed integer programming model is eficient to find good quality upper bounds. On the other hand, the column generation algorithm is eficient to find lower bounds for the problem. Therefore, the proposed method uses the MILP model and the column generation algorithm to complement each other. Thus, optimal solutions were found for 84 % of the generated instances, with the mean GAP for the remaining instances being 2.1 %. The proposed heuristic is based on the idea of probabilistic constructive heuristics, which was presented by Arcus (1965). It was run on the mass of data generated, resulting in an average GAP of 10,6%.

Este trabalho trata do problema de sequenciamento e programação de atividades em máquinas diferentes em paralelo, considerando elegibilidade de máquina, e tempo de liberação das máquinas e das atividades com o objetivo de minimizar o custo de atraso total. Tal problema é descrito pela literatura como NP-hard. Foi proposto um método otimizante que envolve modelagem matemática, um algoritmo de geração de colunas e, além disso, uma heurística para tratar problemas com instancias maiores. O algoritmo de geração de colunas é baseado no método proposto por Akker, Hurkens e Savelsbergh (2000), que foi adaptado para o problema de múltiplas máquinas diferentes. Assim, o método foi aplicado em instâncias da literatura e em instâncias geradas para este trabalho de até 25 atividades e 4 máquinas. Os resultados foram analisados e observou-se que o modelo de programação inteira mista e eficiente para encontrar limitantes superiores de boa qualidade. Por outro lado, o algoritmo de geração de colunas é eficiente para encontrar limitantes inferiores para o problema. Desta forma, o método proposto utiliza o modelo MILP e o algoritmo de geração de colunas de maneira a se complementar. Assim, soluções ótimas foram encontradas para 84% das instancias geradas, sendo que o GAP médio para as instancias restantes foi de 2,1%. A heurística proposta e baseada na ideia de heurística construtiva probabilística, que foi apresentada por Arcus (1965). Ela foi executada na massa de dados gerada, resultando em um GAP médio de 10,6%. / This paper deals with the problem of scheduling activities in unrelated parallel parallel, considering machine eligibility, and machine and activity release time in order to minimize total weighted tardiness.Such a problem is described in the literature as NPhard. It has been proposed an optimizing method that involves mathematical modeling and a column generation algorithm, in addition, it is proposed a heuristic to treat problems with larger instances. The column generation algorithm was based on the method proposed by Akker, Hurkens e Savelsbergh (2000), which has been adapted to the problem of multiple diferent machines. Thus, the method was applied in instances of the literature and in instances generated for this paper up to 25 jobs and 4 machines. The results were analyzed and it was noted that the mixed integer programming model is eficient to find good quality upper bounds. On the other hand, the column generation algorithm is eficient to find lower bounds for the problem. Therefore, the proposed method uses the MILP model and the column generation algorithm to complement each other. Thus, optimal solutions were found for 84 % of the generated instances, with the mean GAP for the remaining instances being 2.1 %. The proposed heuristic is based on the idea of probabilistic constructive heuristics, which was presented by Arcus (1965). It was run on the mass of data generated, resulting in an average GAP of 10,6%.

In this paper we propose an improved algorithm to search optimal solutions to the single machine total weighted tardiness scheduling problem. We propose using longest common sequence to combine with the random key method. Numerical simulation shows that the scheme we proposed could improve the search efficiency of genetic algorithm in this problem for some cases.

Submitted by Fernando Souza (fernandoafsou@gmail.com) on 2017-08-16T11:42:54Z No. of bitstreams: 1 arquivototal.pdf: 2606529 bytes, checksum: e6d5e9c7169bad77fb641468b804b962 (MD5) / Made available in DSpace on 2017-08-16T11:42:54Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2606529 bytes, checksum: e6d5e9c7169bad77fb641468b804b962 (MD5) Previous issue date: 2016-07-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The problem of scheduling on a single machine, proven to be NP-hard, consists of de ning the job grouping in batches and of the sequence in which these batches will be processed on a machine. Each job is associated with a release date, a processing time, a due date, a priority level in relation to the others and a size. The machine is able to process a group of jobs (batch) simultaneously, provided that the sum of the job sizes belonging to the referred batch does not exceed the machine capacity. Each job must be processed only once and only one batch is processed at a time on the machine. In this work, we consider the objective as the minimization of total weighted tardiness, where the tardiness of a job is the di erence between its completion time and its due date, in case the job processing is nished after its due date and hence is late, or equals zero, otherwise. In the literature, this problem is usually referred to as 1jbatch; rj ; sj ; comptjPwjTj . When all jobs are available to be processed at time zero, the problem is usually represented as 1jbatch; sj ; comptjPwjTj . These problems are still poorly explored in the literature and in addition, cover a large number of variant forms. There are few studies involving the application of exact methods for solving both. Only one mathematical formulation was identi ed in the literature for these problems. Hence, four time-indexed formulations were developed to solve the aforementioned problems, one of which is capable of dealing with both problems. The results achieved by the developed models were compared between themselves and with the results of the model available in the literature. These computational results reveal that two of the proposed models obtained higher performance both in terms of quality of the solution, particularly regarding the achieved lower bounds, and in numbers of open nodes and of proven optimal solutions. / O problema de sequenciamento de lotes da produ c~ao em uma m aquina, comprovadamente tido como NP-dif cil, consiste na de ni c~ao do agrupamento de tarefas em lotes e da sequ^encia em que estes ser~ao processados em uma m aquina. Cada tarefa est a associada a uma data de libera c~ao, um tempo de processamento, uma data de entrega, um n vel de prioridade em rela c~ao as demais, e um tamanho. A m aquina e capaz de processar um conjunto de tarefas (lote) simultaneamente, contanto que a soma dos tamanhos das tarefas pertencentes ao referido lote respeite a capacidade da m aquina. Cada tarefa deve ser processada apenas uma vez e somente um lote e processado por vez na m aquina. Neste trabalho, considera-se como objetivo a minimiza c~ao do total de atrasos ponderados, onde o atraso de uma tarefa e igual ao seu tempo de t ermino menos a sua data de entrega, caso o processamento da tarefa seja nalizado ap os a sua data da entrega e, portanto, em atraso, e e igual a zero, caso contr ario. Na literatura, este problema e geralmente referenciado como 1jbatch; rj ; sj ; comptjPwjTj . Quando todas as tarefas est~ao dispon veis para serem processadas no instante de tempo zero, o problema e usualmente representado por 1jbatch; sj ; comptjPwjTj . Estes s~ao problemas ainda pouco investigados na literatura e, al em disso, abordam uma grande quantidade de variantes. Existem poucos trabalhos envolvendo a aplica c~ao de m etodos exatos para a resolu c~ao de ambos. Apenas uma formula c~ao matem atica foi identi cada na literatura para estes problemas. Dessa forma, quatro formula c~oes matem aticas com vari aveis indexadas no tempo foram desenvolvidas para resolver os problemas mencionados anteriormente, das quais uma e capaz de tratar de ambos os problemas. Os resultados alcan cados por meio dos modelos desenvolvidos foram comparados entre si e com os resultados do modelo dispon vel na literatura. Tais resultados computacionais demonstram que dois dos modelos propostos obtiveram desempenho superior tanto em termos de qualidade da solu c~ao, em especial em rela c~ao aos limites inferiores alcan cados, quanto em n umeros de n os abertos e quantidade de solu c~oes otimas comprovadas.

Submitted in fulfillment of the academic requirements for the degree of Master of Technology in Construction Management, Durban University of Technology, Durban, South Africa, 2015. / On-time completion and conformity with assigned cost of every project are the most important factors in the success of project plans. Cost overruns and time overrun (delays) have been critical problems of many projects around the world in general and in South Africa in particular. The main objectives of this research are to assess the dominant causes of cost and time overruns, identifying possible and practical measures that can minimize overruns in office building construction projects around eThekwini Municipal area of Kwazulu-Natal. These objectives are achieved through the implementation of the research methodologies that are mainly literature review and questionnaire survey conducted to identify and evaluate the significant factors contributing to delay and cost overruns within the projects of interest. A review of literature identified eighty-five variables for delay, grouped in nine major categories and nine variables for cost overruns ranked in their order of importance in three sets based on the responses from the professionals working for the client, consultants and contractors. The agreement among the sets of rankings for delay and cost overruns has also been tested using statistical methods. The result indicates that there is strong agreement on ranking the importance of the individual variables of delay and cost overruns between parties. From each of the three sets of rankings, the twenty most important variables of delay and the three most important variables of cost overrun are identified as critical. Based on overall results, the top five most important causes are contractor’s cash flow problems, delay in progress payments by the client, poor site supervision and management by contractor, inefficient quality control by the contractor during construction leading to rework due to errors, and contractor’s difficulties in financing the project. Out of the 20 most important delay causing variables, three are found to be common between all parties. These are delay in progress payments by the client, delay in delivery and late ordering of material, and insufficient skill of labour. Furthermore, the study reveals that all stakeholders of construction parties are deeply involved in contributing to the causes of the problems. Thus, in order to eliminate or minimize cost and time extension of office construction projects in the eThekwini Municipal area, a joint effort based on teamwork is essential through effective project planning, controlling and monitoring which boils down to putting in place best practice construction project management.

Em um contexto industrial, a programação da produção tem como objetivo alocar recursos para operações de forma a aumentar a eficiência operacional do processo de fabricação. Esta programação pode ser modelada na forma de problemas de sequenciamento de tarefas, que são resolvidos visando minimizar um determinado critério de desempenho. A aplicação de métodos exatos nestes problemas possibilita encontrar a solução ótima, tanto para aplicação direta como para a validação de métodos heurísticos e metaheurísticas. Entretanto, a literatura mostra que os métodos exatos, tanto a resolução do problema pela modelagem em programação linear-inteira mista como o branch-and-bound, têm sua aplicação restrita à problemas de menores tamanhos. O objetivo deste trabalho é propor novas formulações de limitantes inferiores para a aplicação do branch-and-bound em problemas de flowshop permutacional visando aumentar sua eficiência e aplicabilidade. Os limitantes propostos são avaliados em problemas de flowshop permutacional com tempos de setup dependente da sequência, tendo como critérios de desempenho o tempo de fluxo total e o atraso total. A avaliação da aplicabilidade de cada limitante é feita através do número de nós explorados e o tempo computacional gasto pelo branch-and-bound para resolver problemas de diversos tamanhos. / In an industrial context, production sequencing aims at allocating resources for job processing while increasing manufacturing efficiency. This task can be modelled in the form of scheduling problems, which are solved by minimizing a pre-determined performance criterion. The use of exact methods allows the optimal solution to be found, which can be applied directly in the manufacturing shop or used to validate heuristic and metaheuristic methods. However, the literature shows that MILP and branch-and-bound, both exact methods, are restrained to small-sized scheduling problems. The aim of this project is to propose new lower bound formulations to be used in the branch-and-bound method for permutational flowshop probems, in order to extend its efficiency and applicability. The proposed bounds are tested in permutational flowshop problems with sequence dependent setup times, and using as performance criteria the total flow time and the total tardiness. The evaluation of each lower bounds applicability is done considering the number of explored nodes and the required computational time for the branch-and-bound to solve problem instances of different sizes.

Neste trabalho abordamos o problema de programação de tarefas em um ambiente flow shop permutacional com mais de duas máquinas. Restringimos o estudo para o caso em que todas as tarefas têm uma data de entrega comum e restritiva, e onde o objetivo é minimizar a soma total dos adiantamentos e atrasos das tarefas em relação a tal data de entrega. É assumido também um ambiente estático e determinístico. Havendo soluções com o mesmo custo, preferimos aquelas que envolvem menos tempo de espera no buffer entre cada máquina. Devido à dificuldade de resolver o problema, mesmo para instâncias pequenas (o problema pertence à classe NP-difícil), apresentamos uma abordagem heurística para lidar com ele, a qual está baseada em busca local e faz uso de um algoritmo linear para atribuir datas de conclusão às tarefas na última máquina. Este algoritmo baseia-se em algumas propriedades analíticas inerentes às soluções ótimas. Além disso, foi desenvolvida uma formulação matemática do problema em programação linear inteira mista (PLIM) que vai permitir validar a eficácia da abordagem. Examinamos também o desempenho das heurísticas com testes padrões (benchmarks) e comparamos nossos resultados com outros obtidos na literatura. / In this work we approach the permutational flow shop scheduling problem with more than two machines. We restrict the study to the case where all the jobs have a common and restrictive due date, and where the objective is to minimize the total sum of the earliness and tardiness of jobs relative to the due date. A static and deterministic environment is also assumed. If there are solutions with the same cost, we prefer those that involve less buffer time between each machine. Due to the difficulty of solving the problem, even for small instances (the problem belongs to the NP-hard class), we present a heuristic approach to dealing with it, which is based on local search and makes use of a linear algorithm to assign conclusion times to the jobs on the last machine. This algorithm is based on some analytical properties inherent to optimal solutions. In addition, a mathematical formulation of the problem in mixed integer linear programming (MILP) was developed that will validate the effectiveness of the approach. We also examined the performance of our heuristics with benchmarks and compared our results with those obtained in the literature.

In mobile and wireless networks, data broadcasting for popular data items enables the efficient utilization of the limited wireless bandwidth. However, efficient data scheduling schemes are needed to fully exploit the benefits of data broadcasting. Towards this goal, several broadcast scheduling policies have been proposed. These existing schemes have mostly focused on either minimizing response time, or drop rate, when requests are associated with hard deadlines. The inherent inaccuracy of hard deadlines in a dynamic mobile environment motivated us to use Service Level Agreements (SLAs) where a user specifies the utility of data as a function of its arrival time. Moreover, SLAs provide the mobile user with an already familiar quality of service specification from wired environments. Hence, in this dissertation, we propose SAAB, an SLA-aware adaptive data broadcast scheduling policy for maximizing the system utility under SLA-based performance measures. To achieve this goal, SAAB considers both the characteristics of disseminated data objects as well as the SLAs associated with them. Additionally, SAAB automatically adjusts to the system workload conditions which enables it to constantly outperform existing broadcast scheduling policies.