97 research outputs found

    Improvement to an existing multi-level capacitated lot sizing problem considering setup carryover, backlogging, and emission control

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    This paper presents a multi-level, multi-item, multi-period capacitated lot-sizing problem. The lot-sizing problem studies can obtain production quantities, setup decisions and inventory levels in each period fulfilling the demand requirements with limited capacity resources, considering the Bill of Material (BOM) structure while simultaneously minimizing the production, inventory, and machine setup costs. The paper proposes an exact solution to Chowdhury et al. (2018)\u27s[1] developed model, which considers the backlogging cost, setup carryover & greenhouse gas emission control to its model complexity. The problem contemplates the Dantzig-Wolfe (D.W.) decomposition to decompose the multi-level capacitated problem into a single-item uncapacitated lot-sizing sub-problem. To avoid the infeasibilities of the weighted problem (WP), an artificial variable is introduced, and the Big-M method is employed in the D.W. decomposition to produce an always feasible master problem. In addition, Wagner & Whitin\u27s[2] forward recursion algorithm is also incorporated in the solution approach for both end and component items to provide the minimum cost production plan. Introducing artificial variables in the D.W. decomposition method is a novel approach to solving the MLCLSP model. A better performance was achieved regarding reduced computational time (reduced by 50%) and optimality gap (reduced by 97.3%) in comparison to Chowdhury et al. (2018)\u27s[1] developed model

    Scheduling Hybrid Flow Lines of Aerospace Composite Manufacturing Systems

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    Composite manufacturing is a vital part of aerospace manufacturing systems. Applying effective scheduling within these systems can cut the costs in aerospace companies significantly. These systems can be characterized as two-stage Hybrid Flow Shops (HFS) with identical, non-identical and unrelated parallel discrete-processing machines in the first stage and non-identical parallel batch-processing machines in the second stage. The first stage is normally the lay-up process in which the carbon fiber sheets are stacked on the molds (tools). Then, the parts are batched based on the compatibility of their cure recipe before going to the second stage into the autoclave for curing. Autoclaves require enormous capital investment and maximizing their utilization is of utmost importance. In this thesis, a Mixed Integer Linear Programming (MILP) model is developed to maximize the utilization of the resources in the second stage of this HFS. CPLEX, with an underlying branch and bound algorithm, is used to solve the model. The results show the high level of flexibility and computational efficiency of the proposed model when applied to small and medium-size problems. However, due to the NP-hardness of the problem, the MILP model fails to solve large problems (i.e. problems with more than 120 jobs as input) in reasonable CPU times. To solve the larger instances of the problem, a novel heuristic method along with a Genetic Algorithm (GA) are developed. The heuristic algorithm is designed based on a careful observation of the behavior of the MILP model for different problem sets. Moreover, it is enhanced by adding a number of proper dispatching rules. As its output, this heuristic algorithm generates eight initial feasible solutions which are then used as the initial population of the proposed GA. The GA improves the initial solutions obtained from the aforementioned heuristic through its stochastic iterations until it reaches the satisfactory near-optimal solutions. A novel crossover operator is introduced in this GA which is unique to the HFS of aerospace composite manufacturing systems. The proposed GA is proven to be very efficient when applied to large-size problems with up to 300 jobs. The results show the high quality of the solutions achieved by the GA when compared to the optimal solutions which are obtained from the MILP model. A real case study undertaken at one of the leading companies in the Canadian aerospace industry is used for the purpose of data experiments and analysis

    Makespan Minimization in Re-entrant Permutation Flow Shops

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    Re-entrant permutation flow shop problems occur in practical applications such as wafer manufacturing, paint shops, mold and die processes and textile industry. A re-entrant material flow means that the production jobs need to visit at least one working station multiple times. A comprehensive review gives an overview of the literature on re-entrant scheduling. The influence of missing operations received just little attention so far and splitting the jobs into sublots was not examined in re-entrant permutation flow shops before. The computational complexity of makespan minimization in re-entrant permutation flow shop problems requires heuristic solution approaches for large problem sizes. The problem provides promising structural properties for the application of a variable neighborhood search because of the repeated processing of jobs on several machines. Furthermore the different characteristics of lot streaming and their impact on the makespan of a schedule are examined in this thesis and the heuristic solution methods are adjusted to manage the problem’s extension

    A SearchCol Algorithm for the unrelated parallel machine scheduling problem with job splitting

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    Dissertação de mestrado em Engenharia IndustrialIn this dissertation, the unrelated parallel machine scheduling problem with job splitting and sequence independent setup times is addressed, implementing a method to solve it in a recently proposed framework, SearchCol, short for ‘Metaheuristic search by Column Generation’. The study of scheduling problems is of high relevance due to its real-world application in multiple fields, as documented in its vast literature, and also due to its high complexity derived from the diverse environments, variables, restrictions and the combinations of these in different systems. The problem consists in finding a scheduling plan for a set of independent jobs on a set of unrelated parallel machines, considering jobs and machines release dates, sequence independent setup times and the job splitting property, with due date related objectives. The introduction of setup times and job splitting properties in unrelated environments has not been extensively studied, even though its use can play an important role in scheduling. A mixed integer programming model is developed featuring the aforementioned properties, which is then decomposed by machine using the Dantzig-Wolfe decomposition. To solve the decomposed model a hybrid approach entitled SearchCol is applied, which results from the interaction between column generation and metaheuristics. Problem specific heuristics to use in the column generation component of the SearchCol are also developed and diverse alternatives within the global algorithm are tested. A problem specific algorithm for one of the main SearchCol components is also suggested. To evaluate the effectiveness of the model and the proposed algorithms, computational tests are performed and their solutions analysed for a set of test instances.O trabalho que se apresenta nesta dissertação, aborda o problema de escalonamento em máquinas paralelas não relacionadas com dimensionamento de lotes e tempos de preparação independentes da sequência, recorrendo a uma ferramenta recentemente proposta, designada por SearchCol, abreviatura de ‘Metaheuristic Search by Column Generation’. O estudo de problemas de escalonamento revela-se de grande importância devido à sua aplicação em diferentes áreas, documentado na sua vasta literatura, e também devido à sua elevada complexidade decorrente das diversas configurações e tipos de máquinas, variáveis e restrições, bem como as combinações destas nos diversos sistemas. O problema consiste na determinação de um plano de produção para um conjunto de tarefas independentes em máquinas paralelas não relacionadas, considerando tempos de disponibilidade de tarefas e máquinas, tempos de preparação independentes da sequência e o dimensionamento de lotes. O estudo deste problema com incorporação de tempos de preparação e da propriedade de dimensionamento de lotes em máquinas paralelas não relacionadas não é comum na literatura, apesar de se revelar de extrema importância em problemas de escalonamento. Um modelo de programação inteira mista é desenvolvido para o problema e é também efectuada uma decomposição por máquina através da decomposição de Dantzig-Wolfe. Para resolver o problema, estuda-se uma abordagem híbrida que consiste na interação entre a técnica de geração de colunas e metaheurísticas, de seu nome SearchCol. São desenvolvidas heurísticas específicas para o problema, as quais são usadas na componente de geração de colunas do SearchCol, sendo testadas também diversas alternativas e ferramentas no contexto do algoritmo global. Além disso, um algoritmo específico para o problema é também sugerido, para incluir num dos principais componentes do SearchCol. Para avaliar o desempenho e qualidade dos modelos e algoritmos propostos, são realizados testes computacionais e analisadas as suas soluções para um conjunto de instâncias de teste.Fundação para a Ciência e a Tecnologia (FCT) - Project ref. PTDC/EIA-EIA/100645/2008.This work was partially funded by the FEDER through the Programme COMPETE

    Lotsizing and scheduling in the glass container industry

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    Manufacturing organizations are keen to improve their competitive position in the global marketplace by increasing operational performance. Production planning is crucial to this end and represents one of the most challenging tasks managers are facing today. Among a large number of alternatives, production planning processes help decision-making by tradingoff conflicting objectives in the presence of technological, marketing and financial constraints.Two important classes of such problems are lotsizing and scheduling. Proofs from complexity theory supported by computational experiments clearly show the hardness of solving lotsizing and scheduling problems.Motivated by a real-world case, the glass container industry production planning and scheduling problem is studied in depth. Due to its inherent complexity and to the frequent interdependencies between decisions that are made at and affect different organizational echelons, the system is decomposed into a two-level hierarchically organized planning structure: long-term and short-term levels.This dissertation explores extensions of lotsizing and scheduling problems that appear in both levels. We address these variants in two research directions. On one hand, we develop and implement different approaches to obtain good quality solutions, as metaheuristics (namely variable neighborhood search) and Lagrangian-based heuristics, as well as other special-purpose heuristics. On the other hand, we try to combine new stronger models and valid inequalities based on the polyhedral structure of these problems to tighten linear relaxations and speed up the solution process.Manufacturing organizations are keen to improve their competitive position in the global marketplace by increasing operational performance. Production planning is crucial to this end and represents one of the most challenging tasks managers are facing today. Among a large number of alternatives, production planning processes help decision-making by tradingoff conflicting objectives in the presence of technological, marketing and financial constraints.Two important classes of such problems are lotsizing and scheduling. Proofs from complexity theory supported by computational experiments clearly show the hardness of solving lotsizing and scheduling problems.Motivated by a real-world case, the glass container industry production planning and scheduling problem is studied in depth. Due to its inherent complexity and to the frequent interdependencies between decisions that are made at and affect different organizational echelons, the system is decomposed into a two-level hierarchically organized planning structure: long-term and short-term levels.This dissertation explores extensions of lotsizing and scheduling problems that appear in both levels. We address these variants in two research directions. On one hand, we develop and implement different approaches to obtain good quality solutions, as metaheuristics (namely variable neighborhood search) and Lagrangian-based heuristics, as well as other special-purpose heuristics. On the other hand, we try to combine new stronger models and valid inequalities based on the polyhedral structure of these problems to tighten linear relaxations and speed up the solution process

    Flexible jobshop scheduling problem with resource recovery constraints.

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    Objectives and methods of study: The general objective of this research is to study a scheduling problem found in a local brewery. The main problem can be seen as a parallel machine batch scheduling problem with sequence-dependent setup times, resource constraints, precedence relationships, and capacity constraints. In the first part of this research, the problem is characterized as a Flexible Job-shop Scheduling Problem with Resource Recovery Constraints. A mixed integer linear formulation is proposed and a large set of instances adapted from the literatura of the Flexible Job-shop Scheduling Problem is used to validate the model. A solution procedure based on a General Variable Neighborhood Search metaheuristic is proposed, the performance of the procedure is evaluated by using a set of instances adapted from the literature. In the second part, the real problem is addressed. All the assumptions and constraints faced by the decision maker in the brewery are taken into account. Due to the complexity of the problem, no mathematical formulation is presented, instead, a solution method based on a Greedy Randomize Adaptive Search Procedure is proposed. Several real instances are solved by this algorithm and a comparison is carried out between the solutions reported by our GRASP and the ones found through the procedure followed by the decision maker. The computational results reveal the efficiency of our method, considering both the processing time and the completion time of the scheduling. Our algorithm requires less time to generate the production scheduling (few seconds) while the decision maker takes a full day to do it. Moreover, the completion time of the production scheduling generated by our algorithm is shorter than the one generated through the process followed by the decision maker. This time saving leads to an increase of the production capacity of the company. Contributions: The main contributions of this thesis can be summarized as follows: i) the introduction of a variant of the Flexible Job-shop Scheduling Problem, named as the Flexible Job-shop Scheduling Problem with Resource Recovery Constraints (FRRC); ii) a mixed integer linear formulation and a General Variable Neighborhood Search for the FRRC; and iii) a case study for which a Greedy Randomize Adaptive Search Procedure has been proposed and tested on real and artificial instances. The main scientific products generated by this research are: i) an article already published: Sáenz-Alanís, César A., V. D. Jobish, M. Angélica Salazar-Aguilar, and Vincent Boyer. “A parallel machine batch scheduling problem in a brewing company”. The International Journal of Advanced Manufacturing Technology 87, no. 1-4 (2016): 65-75. ii) another article submitted to the International Journal of Production Research for its possible publication; and iii) Scientific presentations and seminars

    Multi-agent deep reinforcement learning based Predictive Maintenance on parallel machines

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    In the context of Industry 4.0, companies understand the advantages of performing Predictive Maintenance (PdM). However, when moving towards PdM, several considerations must be carefully examined. First, they need to have a sufficient number of production machines and relative fault data to generate maintenance predictions. Second, they need to adopt the right maintenance approach, which, ideally, should self-adapt to the machinery, priorities of the organization, technician skills, but also to be able to deal with uncertainty. Reinforcement learning (RL) is envisioned as a key technique in this regard due to its inherent ability to learn by interacting through trials and errors, but very few RL-based maintenance frameworks have been proposed so far in the literature, or are limited in several respects. This paper proposes a new multi-agent approach that learns a maintenance policy performed by technicians, under the uncertainty of multiple machine failures. This approach comprises RL agents that partially observe the state of each machine to coordinate the decision-making in maintenance scheduling, resulting in the dynamic assignment of maintenance tasks to technicians (with different skills) over a set of machines. Experimental evaluation shows that our RL-based maintenance policy outperforms traditional maintenance policies (incl., corrective and preventive ones) in terms of failure prevention and downtime, improving by ≈75% the overall performance

    Simultaneous lotsizing and scheduling - extensions and solution approaches

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    The present thesis focuses on simultaneous lotsizing and scheduling. A comprehensive review of the literature is presented in which the historical development of the subject and the current research gaps are, based on a classification scheme, described. Additionally, a review focusing on so-called secondary resources (e.g., setup operators or raw materials), which are considered alongside the primary production resource, is provided. The insights on different types of secondary resources help to develop a new model formulation generalizing and extending the currently used approaches, which are specific to certain settings. Some illustrative examples demonstrate the functional principle and flexibility of this new formulation which can thus be used in a wide range of applications. Finally, a new heuristic to solve large-scaled simultaneous lotsizing and scheduling problems is presented. The heuristic creates a modified multi-line master problem by aggregating products into groups. The resulting problem is less complex and its solution can be used to define single-line sub problems. These sub problems are solved by heuristics present in the literature and the results are then combined to form a solution to the original problem. Numerical tests show the applicability of the aforementioned approach to solve problems of practical relevance.Die vorliegende Ausarbeitung betrachtet das Thema der simultanen Losgrößen- und Reihenfolgeplanung tiefergehend. Ein ausführlicher Literaturüberblick zeigt unter Zuhilfenahme eines Klassifizierungsschemas den Entwicklungsverlauf und aktuelle Forschungslücken in diesem Bereich auf. Weiterhin wird ein auf zusätzliche Ressourcen (sogenannte secondary resources) fokussierter Literaturüberblick erstellt. Diese Ressourcen (z.B. Personal zur Umrüstung oder Rohmaterial) werden zusätzlich zu der primären Produktionsressource benötigt. Die Erkenntnisse zu den verschiedenen Typen von zusätzlichen Ressourcen werden verwendet, um ein generelles Modell zu entwickeln, welches die bisherigen, auf bestimmte Anwendungsfälle spezialisierten, Formulierungen abbildet und erweitert. Testläufe mit Beispielszenarien demonstrieren die Funktionalität und die Flexibilität der neuen Modellformulierung welche für einen Vielzahl von Anwendungsfällen verwendet werden kann. Abschließend wird eine neue Heuristik zum Lösen von simultanen Losgrößen- und Reihenfolgeplanungsproblemen praxisrelevanter Größen vorgestellt. Innerhalb der Heuristik wird durch Produktaggregation ein modifiziertes Mehrlinien-Masterproblem generiert. Das resultierende Problem ist weniger komplex und die dafür gefundene Lösung kann zum Erstellen von Einlinien-Teilproblemen verwendet werden. Diese Teilprobleme werden mit aus der Literatur bekannten Heuristiken gelöst. Die Ergebnisse werden zu einer Lösung für das ursprüngliche Problem zusammengefasst. Numerische Tests belegen die Tauglichkeit des Verfahrens zum Lösen von praxisrelevanten Problemen
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