Serial-batch scheduling – the special case of laser-cutting machines

The dissertation deals with a problem in the field of short-term production planning, namely the scheduling of laser-cutting machines. The object of decision is the grouping of production orders (batching) and the sequencing of these order groups on one or more machines (scheduling). This problem is also known in the literature as "batch scheduling problem" and belongs to the class of combinatorial optimization problems due to the interdependencies between the batching and the scheduling decisions. The concepts and methods used are mainly from production planning, operations research and machine learning

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Production Scheduling

Generally speaking, scheduling is the procedure of mapping a set of tasks or jobs (studied objects) to a set of target resources efficiently. More specifically, as a part of a larger planning and scheduling process, production scheduling is essential for the proper functioning of a manufacturing enterprise. This book presents ten chapters divided into five sections. Section 1 discusses rescheduling strategies, policies, and methods for production scheduling. Section 2 presents two chapters about flow shop scheduling. Section 3 describes heuristic and metaheuristic methods for treating the scheduling problem in an efficient manner. In addition, two test cases are presented in Section 4. The first uses simulation, while the second shows a real implementation of a production scheduling system. Finally, Section 5 presents some modeling strategies for building production scheduling systems. This book will be of interest to those working in the decision-making branches of production, in various operational research areas, as well as computational methods design. People from a diverse background ranging from academia and research to those working in industry, can take advantage of this volume

Planning and Scheduling Optimization

Although planning and scheduling optimization have been explored in the literature for many years now, it still remains a hot topic in the current scientific research. The changing market trends, globalization, technical and technological progress, and sustainability considerations make it necessary to deal with new optimization challenges in modern manufacturing, engineering, and healthcare systems. This book provides an overview of the recent advances in different areas connected with operations research models and other applications of intelligent computing techniques used for planning and scheduling optimization. The wide range of theoretical and practical research findings reported in this book confirms that the planning and scheduling problem is a complex issue that is present in different industrial sectors and organizations and opens promising and dynamic perspectives of research and development

Scheduling Hybrid Flow Lines of Aerospace Composite Manufacturing Systems

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

Bi-Criteria Batching and Scheduling in Hybrid Flow Shops

In this research, a bi-criteria batching and scheduling problem is investigated in hybrid flow shop environments, where unrelated-parallel machines are run simultaneously with different capacities and eligibilities in processing, in some stages. The objective is to simultaneously minimize a linear combination of the total weighted completion time and total weighted tardiness. The first favors the producer’s interest by minimizing work-in-process inventory, inventory holding cost, and energy consumption as well as maximizing machine utilization, while the second favors the customers’ interest by maximizing customers’ service level and delivery speed. In particular, it disregards the group technology assumptions (GTAs) by allowing for the possibility of splitting pre-determined groups of jobs into inconsistent batches in order to improve the operational efficiency. A comparison between the group scheduling and batch scheduling approaches reveals the outstanding performance of the batch scheduling approach. As a result, contrary to the GTAs, jobs belonging to a group might be processed on more than one machine as batches, but not all machines may be capable of processing all jobs. A sequence- and machine-dependent setup time is required between each of two consecutively scheduled batches belonging to different groups. Based on manufacturing company policy, the desired lower bounds on batch sizes are considered for the number of jobs assigned to batches. Although, the direction in which all jobs move through production line is the same, some jobs may skip some stages. Furthermore, to reflect real industry requirements, the job release times and the machine availability times are considered to be dynamic, which means not all machines and jobs are available at the beginning of the planning horizon.The problem is formulated with the help of four mixed-integer linear programming (MILP) models. Two out of four MILP models are formulated as two integrated phases, i.e., batching and scheduling phases, with respect to the precedence constraints between each pair of jobs batches and or the position concept within batches. The optimal combination between batch compositions of groups are determined in the batching phase, while the optimal assignment and sequence of batches on machines and sequence of jobs within batches are determined in the scheduling phase, with respect to a set of operational constraints. A batch composition of a group corresponding to a particular stage, determined in the batching phase of the MILP model, represents the number of batches assigned to the group as well as the number and type of jobs belonging to each batch of that group. Since the first and second MILP models lead to unmanageable solution space, the relaxed MILP model, which allocates one and only one job to each batch of each group in each stage, can be developed to focus on the non-dominated solution space. The optimal solutions of MILP models and relaxed MILP model are equal, if and only if the optimal solution of the relaxed MILP model does not violate the desired lower bounds on batch sizes. Since the relaxed MILP model cannot guarantee the optimal solution of the MILP models, a third MILP model is developed by integrating batching and scheduling phases. This MILP model eliminates an exhaustive combination enumeration between batch compositions of all groups in all stages. Although the third MILP model converges to the optimal solution slower than the relaxed MILP model, it guarantees finding the optimal solution of the first and second MILP models. A comparison between four MILP models shows the superior performance of the third MILP model. However, since the problem is strongly NP-hard, it is not possible to find its optimal solution within a reasonable time as the problem size increases from small to medium to large, even by the relaxed MILP model or the fourth MILP model. Therefore, several meta-heuristic algorithms based upon basic local search, basic population-based search, and hybridization of local search and population-based searches are developed, which move back and forth between batching and scheduling phases. Tabu Search (TS) is implemented as a basic local search algorithm, while Tabu Search Path-Relinking (TS PR) is implemented as a local search algorithm enhanced with a population-based structure. TS is incorporated into the framework of path-relinking to exploit the information on good solutions. The TS PR algorithm comprises several distinguishing features including relinking procedures to effectively explore trajectories connecting elite solutions and the methods used to choose the reference solution. Particle Swarm Optimization (PSO) is implemented as a basic population-based algorithm, while Particle Swarm Optimization enhanced with a local search algorithm (PSO LSA) is developed to realize the benefits of batching and, consequently, enhance the quality of solutions.Since there is interdependency between positions of a job in different stages of a hybrid flow shop in batch scheduling, a meta-heuristic algorithm is not capable of capturing these interdependencies and, subsequently, its efficacy can be diminished. In order to capture this interdependency, the non-, partial- complete-, and stage-based interdependency strategy are developed. In the stage-based-interdependency strategy, a complete sequence related to all of the stages is gradually determined, stage by stage. An initial solution finding mechanism is developed to trigger the search into the solution space and generate an initial population. The performances of these algorithms are compared to each other in order to identify which algorithm(s) outperforms the others. Nevertheless, the performances of the best algorithm(s) are evaluated with respect to a tight lower bound obtained from a branch-and-price (B&P) algorithm. The B&P algorithm uses Dantzig-Wolfe decomposition (DWD) to divide the original problem into a master problem and several sub-problems (SPs) corresponding to each stage. The original problem is decomposed into the SPs by three DWDs corresponding to the three MILP models. Although, by applying DWD technique in the first and second MILP models, an exhaustive combination enumeration between batch compositions of all groups in all stages is excluded and, as a result, the SPs are easier to solve than the original problem, they are still strongly NP-hard because of an enormous number of combinations between batch compositions of all groups in each stage. However, the DWD technique corresponding to the relaxed MILP model not only drastically reduces the number of variables and constraints in the SPs, but also eliminates the batching phase of the first and second MILP models. Decomposing the original problem based on the relaxed MILP model and implementing the B&P algorithm cannot guarantee optimal solutions or tight lower bounds of problems unless the number of violations in the desired lower bounds on batch sizes is not significant. Therefore, the third MILP model is decomposed by DWD so that the B&P algorithm is capable of finding tight lower bounds even for large-size instances of the problem. A comparison between the lower bounds obtained from the B&P algorithm and CPLEX reveals the impressive performance of the B&P algorithm, particularly for large-size problems. The evaluation of the best algorithms based upon these tight lower bounds developed by the B&P algorithm, uncovers the outstanding performance of hybrid algorithms compared to the results obtained from CPLEX.Keywords: Dantzig-Wolfe Decomposition, Mixed-Integer Linear Programming Model, Branch-and-Price Optimization Algorithm, Sequence- and Machine-Dependent Setup Time, Column Generation, Group Scheduling, Particle Swarm Optimization, Batching and Scheduling, Hybrid Flow Shop, Tabu Search, Desired Lower Bounds on Batch Sizes, Bi-Criteria Objective, Path-Relinkin

Bi-Criteria Batching and Scheduling in Hybrid Flow Shops

In this research, a bi-criteria batching and scheduling problem is investigated in hybrid flow shop environments, where unrelated-parallel machines are run simultaneously with different capacities and eligibilities in processing, in some stages. The objective is to simultaneously minimize a linear combination of the total weighted completion time and total weighted tardiness. The first favors the producer’s interest by minimizing work-in-process inventory, inventory holding cost, and energy consumption as well as maximizing machine utilization, while the second favors the customers’ interest by maximizing customers’ service level and delivery speed. In particular, it disregards the group technology assumptions (GTAs) by allowing for the possibility of splitting pre-determined groups of jobs into inconsistent batches in order to improve the operational efficiency. A comparison between the group scheduling and batch scheduling approaches reveals the outstanding performance of the batch scheduling approach. As a result, contrary to the GTAs, jobs belonging to a group might be processed on more than one machine as batches, but not all machines may be capable of processing all jobs. A sequence- and machine-dependent setup time is required between each of two consecutively scheduled batches belonging to different groups. Based on manufacturing company policy, the desired lower bounds on batch sizes are considered for the number of jobs assigned to batches. Although, the direction in which all jobs move through production line is the same, some jobs may skip some stages. Furthermore, to reflect real industry requirements, the job release times and the machine availability times are considered to be dynamic, which means not all machines and jobs are available at the beginning of the planning horizon.The problem is formulated with the help of four mixed-integer linear programming (MILP) models. Two out of four MILP models are formulated as two integrated phases, i.e., batching and scheduling phases, with respect to the precedence constraints between each pair of jobs batches and or the position concept within batches. The optimal combination between batch compositions of groups are determined in the batching phase, while the optimal assignment and sequence of batches on machines and sequence of jobs within batches are determined in the scheduling phase, with respect to a set of operational constraints. A batch composition of a group corresponding to a particular stage, determined in the batching phase of the MILP model, represents the number of batches assigned to the group as well as the number and type of jobs belonging to each batch of that group. Since the first and second MILP models lead to unmanageable solution space, the relaxed MILP model, which allocates one and only one job to each batch of each group in each stage, can be developed to focus on the non-dominated solution space. The optimal solutions of MILP models and relaxed MILP model are equal, if and only if the optimal solution of the relaxed MILP model does not violate the desired lower bounds on batch sizes. Since the relaxed MILP model cannot guarantee the optimal solution of the MILP models, a third MILP model is developed by integrating batching and scheduling phases. This MILP model eliminates an exhaustive combination enumeration between batch compositions of all groups in all stages. Although the third MILP model converges to the optimal solution slower than the relaxed MILP model, it guarantees finding the optimal solution of the first and second MILP models. A comparison between four MILP models shows the superior performance of the third MILP model. However, since the problem is strongly NP-hard, it is not possible to find its optimal solution within a reasonable time as the problem size increases from small to medium to large, even by the relaxed MILP model or the fourth MILP model. Therefore, several meta-heuristic algorithms based upon basic local search, basic population-based search, and hybridization of local search and population-based searches are developed, which move back and forth between batching and scheduling phases. Tabu Search (TS) is implemented as a basic local search algorithm, while Tabu Search Path-Relinking (TS PR) is implemented as a local search algorithm enhanced with a population-based structure. TS is incorporated into the framework of path-relinking to exploit the information on good solutions. The TS PR algorithm comprises several distinguishing features including relinking procedures to effectively explore trajectories connecting elite solutions and the methods used to choose the reference solution. Particle Swarm Optimization (PSO) is implemented as a basic population-based algorithm, while Particle Swarm Optimization enhanced with a local search algorithm (PSO LSA) is developed to realize the benefits of batching and, consequently, enhance the quality of solutions.Since there is interdependency between positions of a job in different stages of a hybrid flow shop in batch scheduling, a meta-heuristic algorithm is not capable of capturing these interdependencies and, subsequently, its efficacy can be diminished. In order to capture this interdependency, the non-, partial- complete-, and stage-based interdependency strategy are developed. In the stage-based-interdependency strategy, a complete sequence related to all of the stages is gradually determined, stage by stage. An initial solution finding mechanism is developed to trigger the search into the solution space and generate an initial population. The performances of these algorithms are compared to each other in order to identify which algorithm(s) outperforms the others. Nevertheless, the performances of the best algorithm(s) are evaluated with respect to a tight lower bound obtained from a branch-and-price (B&P) algorithm. The B&P algorithm uses Dantzig-Wolfe decomposition (DWD) to divide the original problem into a master problem and several sub-problems (SPs) corresponding to each stage. The original problem is decomposed into the SPs by three DWDs corresponding to the three MILP models. Although, by applying DWD technique in the first and second MILP models, an exhaustive combination enumeration between batch compositions of all groups in all stages is excluded and, as a result, the SPs are easier to solve than the original problem, they are still strongly NP-hard because of an enormous number of combinations between batch compositions of all groups in each stage. However, the DWD technique corresponding to the relaxed MILP model not only drastically reduces the number of variables and constraints in the SPs, but also eliminates the batching phase of the first and second MILP models. Decomposing the original problem based on the relaxed MILP model and implementing the B&P algorithm cannot guarantee optimal solutions or tight lower bounds of problems unless the number of violations in the desired lower bounds on batch sizes is not significant. Therefore, the third MILP model is decomposed by DWD so that the B&P algorithm is capable of finding tight lower bounds even for large-size instances of the problem. A comparison between the lower bounds obtained from the B&P algorithm and CPLEX reveals the impressive performance of the B&P algorithm, particularly for large-size problems. The evaluation of the best algorithms based upon these tight lower bounds developed by the B&P algorithm, uncovers the outstanding performance of hybrid algorithms compared to the results obtained from CPLEX.Keywords: Bi-Criteria Objective, Column Generation, Batch Scheduling, Tabu Search, Batching and Scheduling, Desired Lower Bounds on Batch Sizes, Path-Relinking, Branch-and-Price Optimization Algorithm, Particle Swarm Optimization, Group Scheduling, Hybrid Flow Shop, Dantzig-Wolfe Decomposition, Mixed-Integer Linear Programming Model, Sequence- and Machine-Dependent Setup Tim

Dynamic Control for Batch Process Systems Using Stochastic Utility Evaluation

Most research studies in the batch process control problem are focused on optimizing system performance. The methods address the problem by minimizing single criterion such as cycle time and tardiness, or bi-criteria such as cycle time and tardiness, and earliness and tardiness. This research demonstrates the use of Stochastic Utility Evaluation (SUE) function approach to optimize system performance using multiple criteria. In long production cycles, the earliness and tardiness weight (utility) of products vary depending on the time. As the time approaches the due-date, it affects contractual penalties, loss of customer goodwill and the storage period for the completed products. It is necessary to reflect the weight of products for earliness and tardiness at decision epochs to decide on the optimal strategy. This research explores how stochastic utility function using stochastic information can be derived and used to strategically improve existing approaches for the batch process control problem. This research first explores how SUE function can be applied to existing model for bi-objective problem such as cycle time and tardiness. Benchmark strategies using SUE function (NACH-SUE, MBS-SUE, No idle and full batch) are compared to each other. The experimental results show that NACH-SUE effectively improves mean cycle time and tardiness performance respectively than other benchmark strategies. Next, SUE function for earliness and tardiness is used in an existing model to develop a tri-objective problem. Typically, this problem is very complex to solve due to its trade-off relationship. However SUE function makes it relatively easy to solve the tri-objective problem since SUE function can be incorporated in an existing model. It is observed that SUE function can be effectively used for solving a tri-objective problem. Performance improvement for averaged value of cycle time, earliness and tardiness is observed under a comprehensive set of experimental conditions

PiCo: A Domain-Specific Language for Data Analytics Pipelines

In the world of Big Data analytics, there is a series of tools aiming at simplifying programming applications to be executed on clusters. Although each tool claims to provide better programming, data and execution models—for which only informal (and often confusing) semantics is generally provided—all share a common under- lying model, namely, the Dataflow model. Using this model as a starting point, it is possible to categorize and analyze almost all aspects about Big Data analytics tools from a high level perspective. This analysis can be considered as a first step toward a formal model to be exploited in the design of a (new) framework for Big Data analytics. By putting clear separations between all levels of abstraction (i.e., from the runtime to the user API), it is easier for a programmer or software designer to avoid mixing low level with high level aspects, as we are often used to see in state-of-the-art Big Data analytics frameworks. From the user-level perspective, we think that a clearer and simple semantics is preferable, together with a strong separation of concerns. For this reason, we use the Dataflow model as a starting point to build a programming environment with a simplified programming model implemented as a Domain-Specific Language, that is on top of a stack of layers that build a prototypical framework for Big Data analytics. The contribution of this thesis is twofold: first, we show that the proposed model is (at least) as general as existing batch and streaming frameworks (e.g., Spark, Flink, Storm, Google Dataflow), thus making it easier to understand high-level data-processing applications written in such frameworks. As result of this analysis, we provide a layered model that can represent tools and applications following the Dataflow paradigm and we show how the analyzed tools fit in each level. Second, we propose a programming environment based on such layered model in the form of a Domain-Specific Language (DSL) for processing data collections, called PiCo (Pipeline Composition). The main entity of this programming model is the Pipeline, basically a DAG-composition of processing elements. This model is intended to give the user an unique interface for both stream and batch processing, hiding completely data management and focusing only on operations, which are represented by Pipeline stages. Our DSL will be built on top of the FastFlow library, exploiting both shared and distributed parallelism, and implemented in C++11/14 with the aim of porting C++ into the Big Data world

Serial batch processing machine scheduling: a cement industry case study

Dissertação de mestrado em Engenharia de SistemasThis work arises in the Cement Industry in the process of scheduling the clients to the warehouse and assignment to docking bays. The goal is to solve the scheduling and assignment problem, to improve both company’s service levels and the efficiency of its resources. After the real problem analysis, it was possible to conclude that it could be solved as a batching machine scheduling problem, where the jobs are the clients to be schedule, and the machine is the warehouse. The problem can be described as max 1 | rj,s-batch | Cmax . A Mixed Integer Linear Programming (MILP) model was proposed. However, as the number of jobs increased it started having computational difficulties. To overcome the problems of the MILP model two heuristics were proposed. The first one is a Constructive Algorithm (CA) that creates a first solution for the problem. The second heuristic is a metaheuristic algorithm, based on Simulated Annealing procedures, that starts with the initial solution of the CA and through three possible moves starts constructing the neighboring solutions space. After constructing the neighboring solutions space, it returns the best solution found. The computational tests proved that both the MILP model and the heuristics can ensure both feasible and optimum solutions. However, the MILP model consumes more computational resources. For some larger instances and giving a maximum limit of computational time of 8 hours, the MILP model cannot reach the optimality, nor the good results obtained by the heuristics, for those larger instances. The machine scheduling is a good approach for scheduling the trucks to the warehouse. Since it is also an innovative approach for the problem, considering the literature studied, maybe this work will inspire others to work on this idea or, at least, serve as a basis for future researches.Este trabalho tem como cenário a Indústria Cimenteira no processo de agendamento de clientes para atendimento no armazém e atribuição de pontos de carga. O objetivo é resolver o problema de agendamento visando otimizar tanto os níveis de serviço da empresa bem como a eficiência dos seus recursos. Depois da análise detalhada do problema real foi possível concluir que este podia ser resolvido como um problema de processamento em lotes em máquina única, onde as tarefas a agendar seriam os clientes e a máquina o armazém. O problema pode então ser descrito como 1 | rj,s-batch | Cmax . Um modelo de Programação Linear Inteira Mista (PLIM) foi proposto. Contudo, à medida que o número de tarefas aumentava, o modelo começava a ter dificuldades computacionais na obtenção de solução ótima. Para ultrapassar essas dificuldades, foram desenhadas e propostas duas heurísticas. A primeira é um Algoritmo Construtivo (AC) capaz de retornar uma solução inicial. A segunda, uma meta-heurística, baseada na abordagem do Simulated Annealing, que trabalha a solução inicial gerada pelo AC, através de três movimentos possíveis, e gera uma vizinhança de soluções. Depois, procura e retorna a melhor solução possível dessa vizinhança. Os testes computacionais provaram que tanto o modelo de PLIM como as heurísticas são capazes de retornar tanto soluções possíveis como ótimas. Contudo, o modelo de PLIM consome muitos mais recursos computacionais do que as heurísticas. Para instâncias de tamanho superior, dado um tempo de computação máximo de 8 horas, o PLIM, não conseguindo atingir a solução ótima, nem sequer consegue atingir soluções tão boas como as das heurísticas. A abordagem de agendamento em máquinas, utilizada neste trabalho, mostrou-se ser uma boa abordagem para o agendamento de clientes no armazém. Para além disso, esta é uma abordagem inovadora, tendo em conta a literatura estudada, e, talvez possa inspirar outros autores a trabalhar nesta ideia ou então servir de base para pesquisas futuras