A new method is developed to schedule jobs on parallel machines with availability constraints. The objective of the problem is to minimize the makespan of the total production schedule. Without the availability constraints the scheduling of machines is a Pm || Cmax problem. The scheduling of this problem was the topic of many earlier papers. The main contribution of this research is that the schedule of the jobs on parallel machines with availability constraints is determined within a single implicit enumer- ation algorithm. Within the general enumeration scheme, the loads of each machine are enumerated in a lexicographic order. An exact integer linear programming model is provided, too. The difficulty of the problem depends on the properties of the pro- cessing times, the number of machines, and the number of availability constraints on the machines. In some subclasses, problems with very large number of jobs are solved. The largest problems solved within one hour limit have 1, 000, 000 jobs.

Nessa dissertação apresentamos um problema de programação da produção, motivado por uma indústria alimentícia caracterizada pela perecibilidade dos produtos, sequenciamento da produção dos lotes e pela necessidade de sincronização de recursos escassos para operação das linhas de produção. Em indústrias desse ramo, existem altos custos associados a estocagem dos produtos, a fim de evitar sua perda, de modo que é essencial a boa gestão dos processos industriais e do estoque. Modelos matemáticos de programação inteira mista foram desenvolvidos para tratar o problema, bem como o estudo da inclusão de diversas restrições da literatura para o tratamento da perecibilidade. Testes computacionais foram realizados para as validações dos modelos matemáticos, entretanto, devido à dificuldade de determinar soluções de boa qualidade pelo solver de otimização, foram propostos métodos heurísticos baseados na formulação matemática. Com o objetivo de mostrar o desempenho das heurísticas, comparamos as suas performances na resolução de instâncias da literatura e exemplares baseados no cenário produtivo da indústria com os resultados do solver. / In this dissertation we present a lot sizing and scheduling problem motivated by a food industry characterized by the perishability of the products, sequencing the production of the lots and by the need of synchronization of scarce resources for the operation of the production lines. In this type of industry, there are high costs associated with stocking the products in order to avoid their loss, so that good management of industrial processes and inventory is essential. Mathematical models of mixed integer programming were developed to treat the problem, as well as the study of the inclusion of several restrictions of the literature for the treatment of perishability. Computational tests were performed for the validations of the mathematical models, however, due to the difficulty of determining solutions of good quality by the optimization solver, heuristic methods based on the mathematical formulation were proposed. In order to show the performance of the heuristics, we compare their performances in solving instances of the literature and exemplars based on the productive scenario of the industry with the results of solver.

Escalonamento de processos é um tipo de problema de otimização combinatória no qual devemos alocar máquinas à tarefas por períodos específicos de tempo. A literatura contém diversos estudos propondo técnicas para resolver modelos de escalonamento de processos como o job shop e o open shop. Esses modelos permitem que os passos no processo produtivo sejam ou completamente ordenados ou sem ordenação alguma. Com o aumento da complexidade das aplicações industriais no encontramos, mais recentemente, diversos trabalhos que propõe problemas de escalonamento de processos mais gerais para modelar mais precisamente os processos produtivos. O mixed shop, group shop e partial shop são exemplos de tais modelos. Nesse trabalho nós propomos uma busca tabu iterada para o partial shop, que é um modelo geral que inclui diversos modelos mais restritivos. Os componentes novos mais importantes da técnica são o gerador de solução inicial, a vizinhança e o limite inferior para a vizinhança. Em experimentos computacionais nós conseguimos demonstrar que a heurística genérica e única é capaz de competir, e as vezes superar, as técnicas de estado de arte desenvolvidas especificamente para partial, open, mixed e group shop. Algumas vezes uma máquina é o gargalo de um processo produtivo, e é replicada. Na literatura o caso das máquinas paralelas foi incluído em diversas extensões de problemas de escalonamento de processos. Nessa tese nós também propomos uma técnica para escalonar as máquinas paralelas, sem incluí-las explicitamente na representação do problema. Nós usamos técnicas gerais para os casos sem máquinas paralelas para produzir uma busca heurística tabu rápida, e estado da arte, para o caso do job shop com máquinas paralelas. / Shop scheduling is a combinatorial optimization type of problem in which we must allocate machines to jobs for specific periods time. A set of constraints defines which schedules are valid, and we must select one that minimizes or maximizes an objective function. In this work we use the makespan, which is the time the last job finishes. The literature contains several studies proposing techniques to solve shop problems such as the job shop and open shop. These problems allow the steps of the production processes to be either fully ordered or not ordered at all. With increasing complexity and size of industrial applications we find, more recently, several works which propose more general shop problems to model the production processes more accurately. The mixed shop, group shop and partial shop are examples of such problems In this work we propose an iterated tabu search for the partial shop, which is a general problem and includes several other more restrictive shop problems. The most important novel components of the solver are the initial solution generator, the neighbourhood, and the lower bound for the neighbourhood. In computational experiments we were able to show that the general partial shop solver is able to compete with, and sometimes surpass, the state-of-the-art solvers developed specifically for the partial, open, mixed and group shops. Sometimes a machine is a bottleneck in the production process, and is replicated. In the literature the parallel machines case has being included in several extensions of shop problems. In this thesis we also propose a technique to schedule the parallel machines heuristically, without including them explicitly in the representation of the problem. We use general techniques for the non-parallel machine cases to produce a fast tabu search heuristic results for the job shop with parallel machines.

Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2001-02-17Bitstream added on 2014-06-13T19:07:26Z : No. of bitstreams: 1 fiorotto_dj_me_sjrp.pdf: 485977 bytes, checksum: 8cd2b3ba49a25a9c6a863795f27811c3 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O problema de dimensionamento de lotes é um problema de otimização da produção, em que o objetivo é planejar a quantidade de itens a ser produzida em várias, ou única, máquinas em cada período ao longo do horizonte de tempo, de modo a tender uma demanda e otimizar uma função objetivo. Este trabalho aborda o problema de dimensionamento de lotes em um único estágio em um ambiente com máquinas paralelas distintas. Cada item pode ser produzido em qualquer máquina, acarretando um tempo de preparação que é gasto antes de começar a produção. O objetivo do trabalho consiste em obter limitantes inferiores de boa qualidade para este problema. Para tanto, é desenvolvido um método de solução baseado numa reformulação do problema a e na relaxação lagrangiana de um conjunto de restrições. Alguns resultados computacionais são apresentados algumas propostas futuras para a continuidade do trabalho. / The lot-sizing problem is a production optimization problem, where the objective is to plan the quantity of items to be produced in multiple, or single, machines in each period over a time horizon, in order to satisfy a demand and optimize an objective function. This work addresses the single stage parallel machine lot-sizing problem. Each item can be produced on any machine, and incur a setup time before to start the production. The objective of this work is to lower bounds of good quality for this problem. A solution method is developed based on a reformulation of the problem and the Lagrangian relaxation of a set of constrainsts. Some computational results are presented comparing the proposed method with a method from the literature, and, some future researches are proposed.

In this thesis, we consider a rescheduling problem on non-identical parallel machines with controllable processing times. A period of unavailability occurs on one of the machines due to a machine failure, material shortage or broken tool. These disruptions may cause the original schedule to become inecient and sometimes infeasible. In order to generate a new and feasible schedule, we are dealing with two conflicting measures called the eciency and stability measures simultaneously. The eciency measure evaluates the satisfaction of a desired objective function value and the stability measure evaluates the amount of change between the schedule before and after the disruption. In this study, we measure stability by the number of disrupted jobs. In this thesis, the job is referred as a disrupted job if it completes processing after its planned completion time in the original schedule. The eciency is measured by the additional manufacturing cost of jobs. Decreasing number of disrupted jobs requires compressing the processing time of a job which cause an increase in its additional manufacturing cost. For that reason we cannot minimize these objectives at the same time. In order to handle this, we developed a mixed integer programming model for the considered problem by applying the epsilon-constraint approach. This approach makes focusing on the single objective possible to get efficient solutions. Therefore, we studied the problem of minimizing additional manufacturing cost subject to a limit on the number of disrupted jobs. We also considered a convex compression cost function for each job and solved a cost minimization problem by applying conic quadratic reformulation for the model. The convexity of cost functions is a major source of diculty in finding optimal integer solutions in this problem, but applying strengthened conic reformulation has eliminated this diculty. In addition, we prepare an improvement search algorithm in order to find good solution in reasonable CPU times. We use our heuristic procedure on optimality properties we showed for a single machine subproblem. We made computational experiments on small and medium scale test problems. Afterwards, we compare the performance of the improvement search algorithm and mathematical model for their solution quality and durations.

Effective production scheduling is essential for improved performance. Scheduling strategies for various shop configurations and performance criteria have been widely studied. Scheduling in parallel machines (PM) is one among the many scheduling problems that has received considerable attention in the literature. An even more complex scheduling problem arises when there are several PM families and jobs are capable of being processed in more than one such family. This research addresses such a situation, which is defined as an Associative Parallel Machine scheduling (APMS) problem. This research presents the SAPT-II algorithm that solves a highly constrained APMS problem with the objective to minimize average flow time. A case example from a make-to-order industrial product manufacturer is used to illustrate the complexity of the problem and evaluate the effectiveness of the scheduling algorithm.

Orientador: Silvio Alexandrede Araujo / Banca: Bernardo Sobrinho Simões de Almada Lobo / Banca: Franklina Maria Bragion Toledo / Resumo: O problema de dimensionamento de lotes é um problema de otimização da produção, em que o objetivo é planejar a quantidade de itens a ser produzida em várias, ou única, máquinas em cada período ao longo do horizonte de tempo, de modo a tender uma demanda e otimizar uma função objetivo. Este trabalho aborda o problema de dimensionamento de lotes em um único estágio em um ambiente com máquinas paralelas distintas. Cada item pode ser produzido em qualquer máquina, acarretando um tempo de preparação que é gasto antes de começar a produção. O objetivo do trabalho consiste em obter limitantes inferiores de boa qualidade para este problema. Para tanto, é desenvolvido um método de solução baseado numa reformulação do problema a e na relaxação lagrangiana de um conjunto de restrições. Alguns resultados computacionais são apresentados algumas propostas futuras para a continuidade do trabalho. / Abstract: The lot-sizing problem is a production optimization problem, where the objective is to plan the quantity of items to be produced in multiple, or single, machines in each period over a time horizon, in order to satisfy a demand and optimize an objective function. This work addresses the single stage parallel machine lot-sizing problem. Each item can be produced on any machine, and incur a setup time before to start the production. The objective of this work is to lower bounds of good quality for this problem. A solution method is developed based on a reformulation of the problem and the Lagrangian relaxation of a set of constrainsts. Some computational results are presented comparing the proposed method with a method from the literature, and, some future researches are proposed. / Mestre

Scheduling on unrelated parallel machines is a common problem in many systems (as semi-conductors manufacturing,multiprocessor computer applications, textile industry, etc.). In this thesis, we consider two variantsof this problem under uncertain processing time. In the first case, each job can be split into continuoussub-jobs and processed independently on the machines with allowed overlappinf. In the second case whichis termed preemption, we prohibit the overlapping. From a mathematical viewpoint, the splitting problem isa relaxed version of the preemptive problem. The objective is to minimize the makespan.The deterministic linear formulations provided by the literature allow to solve these problems in polynomialtimes under the hypothesis of certainty. But, when we consider uncertain processing times, thesealgorithms suffer from some limitations. Indeed, the solutions compouted based on a nominal instance,supposed to be certain, turn usually to be suboptimal when applied to the actual realization of processingtimes.We incorporate the uncertain processing times in these problems without making any assumption ontheir distribution. Hence, we use discrete scenarios to represent the uncetain processing times and we adopta proactive approach to provide robust solutions. We use special case policies that are commongly used inthe industry to compute robust solutions. We show that the solutions based on some of those policies arepotentially good in terms of robustness according to the worst-case makespan, especially the scenario smaxsolution under which all the processing times are set to their maximal values. However, the robustness costsof these solutions are not satisfying. Thus, we propose to compute optimal robust solutions. For this purpose,we use a mathematical trick that allows us to formulate and solve, in polynomila times, the robust versionsof the considered scheduling problems. Moreover, the computational results affirm that the robustness costof the optimal solution is not usually very high.Moreover, we evaluate the stability of the robust solutions under a new scenario induced by variations.In fact, the decision-maker is only responsible for the consequences of the decisions when the processingtime realizations are within the represented uncertainty set. Thus, we define stability of a robust solution asits ability to cover a new scenario with minor deviations regarding its structure and its performance.The global motivation of this thesis is then to provide a decision support to help decision maker computerobust solutions and choose among these robust solutions those with the most stable structure and the moststable performance. / Scheduling on unrelated parallel machines is a common problem in many systems (as semi-conductors manufacturing,multiprocessor computer applications, textile industry, etc.). In this thesis, we consider two variantsof this problem under uncertain processing time. In the first case, each job can be split into continuoussub-jobs and processed independently on the machines with allowed overlappinf. In the second case whichis termed preemption, we prohibit the overlapping. From a mathematical viewpoint, the splitting problem isa relaxed version of the preemptive problem. The objective is to minimize the makespan.The deterministic linear formulations provided by the literature allow to solve these problems in polynomialtimes under the hypothesis of certainty. But, when we consider uncertain processing times, thesealgorithms suffer from some limitations. Indeed, the solutions compouted based on a nominal instance,supposed to be certain, turn usually to be suboptimal when applied to the actual realization of processingtimes.We incorporate the uncertain processing times in these problems without making any assumption ontheir distribution. Hence, we use discrete scenarios to represent the uncetain processing times and we adopta proactive approach to provide robust solutions. We use special case policies that are commongly used inthe industry to compute robust solutions. We show that the solutions based on some of those policies arepotentially good in terms of robustness according to the worst-case makespan, especially the scenario smaxsolution under which all the processing times are set to their maximal values. However, the robustness costsof these solutions are not satisfying. Thus, we propose to compute optimal robust solutions. For this purpose,we use a mathematical trick that allows us to formulate and solve, in polynomila times, the robust versionsof the considered scheduling problems. Moreover, the computational results affirm that the robustness costof the optimal solution is not usually very high.Moreover, we evaluate the stability of the robust solutions under a new scenario induced by variations.In fact, the decision-maker is only responsible for the consequences of the decisions when the processingtime realizations are within the represented uncertainty set. Thus, we define stability of a robust solution asits ability to cover a new scenario with minor deviations regarding its structure and its performance.The global motivation of this thesis is then to provide a decision support to help decision maker computerobust solutions and choose among these robust solutions those with the most stable structure and the moststable performance.

A concorrência nos mercados mundiais impõe a necessidade de aumento da competitividade das empresas que desejam assumir posições de liderança nos segmentos em que atuam. Neste ínterim, a programação de tarefas contribui para que as empresas promovam a eficiente utilização dos recursos produtivos visando a realização de seus objetivos estratégicos. Esta dissertação enfoca a programação de tarefas em máquinas paralelas não-relacionadas e com tempos de setup dependentes da sequência de processamento. Primeiramente é abordado o objetivo de minimização do atraso total e do tempo total para a conclusão de um conjunto de tarefas, através de uma heurística de três etapas que (i) ordena as tarefas pelo WSPT (Weighted Shortest Processing Time), (ii) aloca as tarefas às máquinas e (iii) aprimora a solução proposta pela etapa (ii) através de Tabu Search. Quando aplicada em um ambiente de manufatura real composto por duas máquinas paralelas não-relacionadas no processo de metalização de filmes plásticos em alto vácuo, a heurística resulta em um desvio de 1,1% para o tempo total de processamento das tarefas e 4,6% para o atraso total, em comparação ao resultado ótimo obtido por enumeração. Na sequência, o objetivo passa a ser a minimização simultânea do atraso e do adiantamento das tarefas através de uma heurística de três etapas que (i) caracteriza o conjunto de tarefas por um conjunto de métricas, (ii) aloca as tarefas às máquinas através de uma versão modificada do ATCS (Apparent Tardiness Cost with Setup) de Lee e Pinedo (1997), e (iii) aprimora a solução final com Tabu Search. A aplicação em dados reais resulta em 14% de desvio em relação à solução ótima obtida por enumeração. Quando aplicada em cenários com data de entrega, tempos de processamento e setup simulados, a heurística resulta em desvio médio de 18% da solução ótima gerada por enumeração para pelo menos 70% das simulações. / The competition in worldwide markets lead the companies to increase the competitiveness in order to take leading positions in their industries. In this sense, scheduling plays an important role leading the companies to reach their strategic goals through efficient utilization of manufacturing resources. This dissertation focuses on the scheduling unrelated parallel machines with sequence dependent setup times. First goal is to minimize the completion time and total weighted tardiness, through a three phase heuristic which (i) sort the jobs with WSPT, (ii) allocate the jobs to the machines and (iii) improve final solution with Tabu Search. Once applied to a real manufacturing environment composed by two unrelated parallel machines, in high vacuum plastic films metallisation process, the heuristic results in 1.1% of deviation from total weighted completion time and 4.6% of deviation from weighted tardiness, in relation to the optimal solution obtained from total enumeration. Next goal is the simultaneous minimization of weighted earliness and tardiness, through a three phase heuristic which (i) characterize the jobs, (ii) allocate the jobs to the machines with a modified version of Lee and Pinedo’s (1997) ATCS and (iii) improve final solution with Tabu Search. The application in real data results in 14% of deviation from the optimal solution obtained by enumeration. When applied to simulated scenarios of due date, processing and setup time, the heuristic results in average deviation of 18% from optimal solution obtained by enumeration to at least 70% of the simulations.

Escalonamento de processos é um tipo de problema de otimização combinatória no qual devemos alocar máquinas à tarefas por períodos específicos de tempo. A literatura contém diversos estudos propondo técnicas para resolver modelos de escalonamento de processos como o job shop e o open shop. Esses modelos permitem que os passos no processo produtivo sejam ou completamente ordenados ou sem ordenação alguma. Com o aumento da complexidade das aplicações industriais no encontramos, mais recentemente, diversos trabalhos que propõe problemas de escalonamento de processos mais gerais para modelar mais precisamente os processos produtivos. O mixed shop, group shop e partial shop são exemplos de tais modelos. Nesse trabalho nós propomos uma busca tabu iterada para o partial shop, que é um modelo geral que inclui diversos modelos mais restritivos. Os componentes novos mais importantes da técnica são o gerador de solução inicial, a vizinhança e o limite inferior para a vizinhança. Em experimentos computacionais nós conseguimos demonstrar que a heurística genérica e única é capaz de competir, e as vezes superar, as técnicas de estado de arte desenvolvidas especificamente para partial, open, mixed e group shop. Algumas vezes uma máquina é o gargalo de um processo produtivo, e é replicada. Na literatura o caso das máquinas paralelas foi incluído em diversas extensões de problemas de escalonamento de processos. Nessa tese nós também propomos uma técnica para escalonar as máquinas paralelas, sem incluí-las explicitamente na representação do problema. Nós usamos técnicas gerais para os casos sem máquinas paralelas para produzir uma busca heurística tabu rápida, e estado da arte, para o caso do job shop com máquinas paralelas. / Shop scheduling is a combinatorial optimization type of problem in which we must allocate machines to jobs for specific periods time. A set of constraints defines which schedules are valid, and we must select one that minimizes or maximizes an objective function. In this work we use the makespan, which is the time the last job finishes. The literature contains several studies proposing techniques to solve shop problems such as the job shop and open shop. These problems allow the steps of the production processes to be either fully ordered or not ordered at all. With increasing complexity and size of industrial applications we find, more recently, several works which propose more general shop problems to model the production processes more accurately. The mixed shop, group shop and partial shop are examples of such problems In this work we propose an iterated tabu search for the partial shop, which is a general problem and includes several other more restrictive shop problems. The most important novel components of the solver are the initial solution generator, the neighbourhood, and the lower bound for the neighbourhood. In computational experiments we were able to show that the general partial shop solver is able to compete with, and sometimes surpass, the state-of-the-art solvers developed specifically for the partial, open, mixed and group shops. Sometimes a machine is a bottleneck in the production process, and is replicated. In the literature the parallel machines case has being included in several extensions of shop problems. In this thesis we also propose a technique to schedule the parallel machines heuristically, without including them explicitly in the representation of the problem. We use general techniques for the non-parallel machine cases to produce a fast tabu search heuristic results for the job shop with parallel machines.