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

Deterministic Assembly Scheduling Problems: A Review and Classification of Concurrent-Type Scheduling Models and Solution Procedures

Many activities in industry and services require the scheduling of tasks that can be concurrently executed, the most clear example being perhaps the assembly of products carried out in manufacturing. Although numerous scientific contributions have been produced on this area over the last decades, the wide extension of the problems covered and the lack of a unified approach have lead to a situation where the state of the art in the field is unclear, which in turn hinders new research and makes translating the scientific knowledge into practice difficult. In this paper we propose a unified notation for assembly scheduling models that encompass all concurrent-type scheduling problems. Using this notation, the existing contributions are reviewed and classified into a single framework, so a comprehensive, unified picture of the field is obtained. In addition, a number of conclusions regarding the state of the art in the topic are presented, as well as some opportunities for future research.Ministerio de Ciencia e Innovación español DPI2016-80750-

Progress in Material Handling Research: 2010

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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

New Solution Approaches for Scheduling Problems in Production and Logistics

The current cumulative PhD thesis consists of six papers published in/submitted to scientific journals. The focus of the thesis is to develop new solution approaches for scheduling problems encountering in manufacturing as well as in logistics. The thesis is divided into two parts: “ma-chine scheduling in production” and “scheduling problems in logistics” each of them consisting three papers. To have most comprehensive overview of the topic of machine scheduling, the first part of the thesis starts with two systematic review papers, which were conducted on tertiary level (i.e., re-viewing literature reviews). Both of these papers analyze a sample of around 130 literature re-views on machine scheduling problems. The first paper use a subjective quantitative approach to evaluate the sample, while the second papers uses content analysis which is an objective quanti-tative approach to extract meaningful information from massive data. Based on the analysis, main attributes of scheduling problems in production are identified and are classified into sever-al categories. Although the focus of both these papers are set to review scheduling problems in manufacturing, the results are not restricted to machine scheduling problem and the results can be extended to the second part of the thesis. General drawbacks of literature reviews are identi-fied and several suggestions for future researches are also provided in both papers. The third paper in the first part of the thesis presents the results of 105 new heuristic algorithms developed to minimize total flow time of a set of jobs in a flowshop manufacturing environ-ment. The computational experiments confirm that the best heuristic proposed in this paper im-proves the average error of best existing algorithm by around 25 percent. The first paper in second part is focused on minimizing number of electric tow-trains responsi-ble to deliver spare parts from warehouse to the production lines. Together with minimizing number of these electric vehicles the paper is also focused to maximize the work load balance among the drivers of the vehicles. For this problem, after analyzing the complexity of the prob-lem, an opening heuristic, a mixed integer linear programing (MILP) model and a taboo-search neighborhood search approach are proposed. Several managerial insights, such as the effect of battery capacity on the number of required vehicles, are also discussed. The second paper of the second part addresses the problem of preparing unit loaded devices (ULDs) at air cargos to be loaded latter on in planes. The objective of this problem is to mini-mize number of workers required in a way that all existing flight departure times are met and number of available places for building ULDs is not violated. For this problem, first, a MILP model is proposed and then it is boosted with a couple of heuristics which enabled the model to find near optimum solutions in a matter of 10 seconds. The paper also investigates the inherent tradeoff between labor and space utilization as well as the uncertainty about the volume of cargo to be processed. The last paper of the second part proposes an integrated model to improve both ergonomic and economic performance of manual order picking process by rotating pallets in the warehouse. For the problem under consideration in this paper, we first present and MILP model and then pro-pose a neighborhood search based on simulated annealing. The results of numerical experiment indicate that selectively rotating pallets may reduce both order picking time as well as the load on order picker, which leads to a quicker and less risky order picking process

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

Aproximações heurísticas para um problema de escalonamento do tipo flexible job-shop

Mestrado em Engenharia e Gestão IndustrialEste trabalho aborda um novo tipo de problema de escalonamento que pode ser encontrado em várias aplicações do mundo-real, principalmente na indústria transformadora. Em relação à configuração do shop floor, o problema pode ser classificado como flexible job-shop, onde os trabalhos podem ter diferentes rotas ao longo dos recursos e as suas operações têm um conjunto de recursos onde podem ser realizadas. Outras características de processamento abordadas são: datas possíveis de início, restrições de precedência (entre operações de um mesmo trabalho ou entre diferentes trabalhos), capacidade dos recursos (incluindo paragens, alterações na capacidade e capacidade infinita) e tempos de setup (que podem ser dependentes ou independentes da sequência). O objetivo é minimizar o número total de trabalhos atrasados. Para resolver o novo problema de escalonamento proposto um modelo de programação linear inteira mista é apresentado e novas abordagens heurísticas são propostas. Duas heurísticas construtivas, cinco heurísticas de melhoramento e duas metaheurísticas são propostas. As heurísticas construtivas são baseadas em regras de ordenação simples, onde as principais diferenças entre elas dizem respeito às regras de ordenação utilizadas e à forma de atribuir os recursos às operações. Os métodos são designados de job-by-job (JBJ), operation-by-operation (OBO) e resource-by-resource (RBR). Dentro das heurísticas de melhoramento, a reassign e a external exchange visam alterar a atribuição dos recursos, a internal exchange e a swap pretendem alterar a sequência de operações e a reinsert-reassign é focada em mudar, simultaneamente, ambas as partes. Algumas das heurísticas propostas são usadas em metaheurísticas, nomeadamente a greedy randomized adaptive search procedure (GRASP) e a iterated local search (ILS). Para avaliar estas abordagens, é proposto um novo conjunto de instâncias adaptadas de problemas de escalonamento gerais do tipo flexible job-shop. De todos os métodos, o que apresenta os melhores resultados é o ILS-OBO obtendo melhores valores médios de gaps em tempos médios inferiores a 3 minutos.This work addresses a new type of scheduling problem which can be found in several real-world applications, mostly in manufacturing. Regarding shop floor configuration, the problem can be classified as flexible job-shop, where jobs can have different routes passing through resources and their operations have a set of eligible resources in which they can be performed. The processing characteristics addressed are release dates, precedence constraints (either between operations of the same job or between different jobs), resources capacity (including downtimes, changes in capacity, and infinite capacity), and setup times, which can be sequence-dependent or sequence-independent. The objective is to minimise the total number of tardy jobs. To tackle the newly proposed flexible job-shop scheduling problem (FJSP), a mixed integer linear programming model (MILP) is presented and new heuristic approaches are put forward. Three constructive heuristics, five improvement heuristics, and two metaheuristics are proposed. The constructive heuristics are based on simple dispatching rules, where the main differences among them concern the used dispatching rules and the way resources are assigned. The methods are named job-by-job (JBJ), operation-by-operation (OBO) and resource-by-resource (RBR). Within improvement heuristics, reassign and external exchange aim to change the resources assignment, internal exchange and swap intend changing the operations sequence, and reinsert-reassign is focused in simultaneously changing both parts. Some of the proposed heuristics are used within metaheuristic frameworks, namely greedy randomized adaptive search procedure (GRASP) and iterative local search (ILS). In order to evaluate these approaches, a new set of benchmark instances adapted from the general FJSP is proposed. Out of all methods, the one which shows the best average results is ILS-OBO obtaining the best average gap values in average times lower than 3 minutes