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Comparison of lot streaming division methodologies for multi-objective hybrid flowshop scheduling problem by considering limited waiting time
Abstract
In this paper, a multi-objective hybrid flowshop scheduling problem (HFSP) with limited waiting time and machine capability constraints is addressed. Given its importance, the implementation of lot streaming division methodologies with the problem is investigated through a design of experiment (DoE) setting based on real data extracted from a leading tire manufacturer in Gebze, Turkey. By doing so, specific characteristics of the addressed HFSP can be further explored to provide insights into its complexity and suggest recommendations for improving the operational efficiency of such systems resembling it. Based on the problem specifications and constraints, a novel generic multi-objective optimization model with objectives including the makespan, the average flow time, and the total workload imbalance is formulated. Since the studied problem is NP-hard in the strong sense, several algorithms based on the non-dominated sorting genetic algorithm-II (NSGA-II) are proposed according to the division methodologies, i.e., consistent sublots and equal sublots. Since the main aim of this problem is to further analyze the implementation of lot streaming on the HFSP problem, the developed algorithms are compared with each other to gain remarkable insights into the problem. Four different comparison metrics are employed to assess the solution quality of the proposed algorithms in terms of intensification and diversification aspects. Computational results demonstrate that employing the consistent sublot methodology leads to significant improvements in all metrics compared to the equal sublot methodology.
... The study also showed a 12% reduction in idle time, 38% decrease in workload imbalance, and a 23% increase in production volume. Recently, the authors of Ref. 34 based on the problem specifications and constraints, a novel generic multi-objective optimization model with objectives including the makespan, the average flow time, and the total workload imbalance is formulated. Use non-dominated sorting genetic algorithm-II (NSGA-II) to solve this problem. ...
The total cost of assembly is a critical factor in robotic assembly line balancing, as it encompasses all the costs associated with the assembly line, including initial costs, setup, maintenance, and energy cost. This study introduces a different approach to the robotic assembly line balancing problem, with a dual focus on minimizing both cycle time and overall assembly costs. The effectiveness of the proposed approach is validated through three case study problems taken from the literature and results are compared to traditional assembly allocation methods. For case study 1, 89.4% (42 out of 47) of the solutions achieved a lower total cost, and 34% (16 out of 47) of the solutions utilized fewer workstations; and for case study 2, 96.4% (108 out of 112) of the solutions achieved a lower total cost, and 58.9% (66 out of 112) of the solutions utilized fewer workstations for the same cycle time. These results demonstrate a significant savings in cost and a notable improvement in workstation efficiency for a substantial portion of the solutions. This comprehensive approach allows an effective resource allocation, reduces inefficiencies, and enhances the overall cost-effectiveness and performance of the robotic assembly line. It also supports decision-makers in selecting more sustainable and economically viable assembly line solutions that optimize both productivity and energy efficiency.
... For the steelmaking-continuous-casting dynamic scheduling problem under equipment failure, Long et al. [4] proposed a two-phase robust dynamic production scheduling method based on release time-series prediction for the scenario of uncertain tasks. The authors of [5] based on the problem specifications and constraints, a novel generic multi-objective optimization model with objectives including the makespan, the average flow time, and the total workload imbalance is formulated. Use non-dominated sorting genetic algorithm-II (NSGA-II) to solve this problem. ...
The challenge of distributing molten iron involves the optimal allocation of blast furnace output to various steelmaking furnaces, considering the blast furnace’s production capacity and the steelmaking converter’s consumption capacity. The primary objective is to prioritize the distribution from the blast furnace to achieve a balance between iron and steel production while ensuring that the volume of hot metal within the system remains within a safe range. To address this, a constrained multi-objective nonlinear programming model is abstracted. A linear weighting method combines multiple objectives into a single objective function, while the Lagrange multiplier method addresses constraints. The proposed hybrid Archimedes optimization algorithm effectively solves this problem, demonstrating significant improvements in time efficiency and precision compared to existing methods.
Heijunka is the central concept of the Toyota Production System which aims to maintain both flexibility and stability of the production system by producing the same quantity of products every time interval (a day, a shift, an hour, etc.). This study is a systematic literature review whose objective is to give an idea about the most important research areas regarding this concept and to propose an agenda for further research. A total of 60 articles were reviewed using specified inclusion and exclusion criteria. The review showed that heijunka received little attention in the academic literature and disclosed the existence of three main research topics, namely: Implementation of heijunka and its benefits, Heijunka-related problem-solving using optimization, and Heijunka and Industry 4.0 technologies. This review could have some limitations related to the number of reviewed articles. It is possible that, unintentionally, some important articles haven’t been included.
This study investigates a flow shop scheduling problem with queue time limits and skipping jobs, which are common scheduling requirements for semiconductor and printed circuit board manufacturing systems. These manufacturing systems involve the most complex processes, which are strictly controlled and constrained to manufacture high-quality products and satisfy dynamic customer orders. Further, queue times between consecutive stages are limited. Given that the queue times are limited, jobs must begin the next step within the maximum queue time after the jobs in the previous step are completed. In the considered flow shop, several jobs can skip the first step, referred to as skipping jobs. Skipping jobs exist because of multiple types of products processed in the same flow shop. For the considered flow shop, this paper proposes a mathematical programming formulation and a genetic algorithm to minimize the makespan. The GA demonstrated its strengths through comprehensive computational experiments, demonstrating its effectiveness and efficiency. As the problem size increased, the GA's performance improved noticeably, while maintaining acceptable computation times for real-world fab facilities. We also validated its performance in various scenarios involving queue time limits and skipping jobs, to further emphasize its capabilities.
Many organizations today are interesting to implementing lean manufacturing principles that should enable them to eliminating the wastes to reducing a manufacturing lead time. This paper concentrates on increasing the competitive level of the company in globalization markets and improving of the productivity by reducing the manufacturing lead time. This will be by using the main tool of lean manufacturing which is value stream mapping (VSM) to identifying all the activities of manufacturing process (value and non-value added activities) to reducing elimination of wastes (non-value added activities) by converting a manufacturing system to pull instead of push by applying some of pull system strategies as kanban and first on first out lane (FIFO). ARENA software is used to simulate the current and future state. This work is executed in the state company for electrical industries in Baghdad. The obtained results of the application showed that implementation of lean principles helped on reducing of a manufacturing lead time by 33%.
Organ transplantation is a crucial task in the healthcare supply chain, which organizes the supply and demand for various vital organs. In this regard, dealing with uncertainty is one of the main challengings in designing an organ transplant supply chain. To address this gap, in the present research, a mathematical formulation and solution method is proposed to optimize the organ transplants supply chain under shipment time uncertainty. A possibilistic programming model and simulation-based solution method are developed for organ transplant center location, allocation, and distribution. The proposed mathematical model optimizes the overall cost by considering the fuzzy uncertainty of organ demands and transportation time. Moreover, a novel simulation-based optimization is applied using the credibility theory to deal with the uncertainty in the optimization of this mathematical model. In addition, the proposed model and solution method are evaluated by implementing different test problems. The numerical results demonstrate that the optimal credibility level is between 0.2 and 0.6 in all tested cases. Moreover, the patient’s satisfaction rate is higher than the viability rate in the designed organ supply chain.
Since the last decade, transportation and distribution systems have experienced significant growth and development. Designing distribution systems utilizing electric vehicles is one of the main issues in this field. Accordingly, this research provides a novel solution method for a two-echelon distribution system using electric vehicles. At the first level, the required products are sent from a central depot to satellite stations. At the second level, these products are distributed among different customers. In routing electric vehicles, battery capacity and visiting charging stations are taken into consideration. In this regard, a mathematical model is developed for the electric vehicle routing at both levels. To solve the model, a newly developed meta-heuristic algorithm is proposed as Improved Moth-Flame Optimization (IMFO) Algorithm. The evaluation of IMFO indicates that, in small and medium-scale test problems, this algorithm has errors of about 1.2%. It also performs better than the classic moth-flame algorithm as well as the genetic algorithm on large-scale test problems. Moreover, the sensitivity analysis of the demand and time window parameters shows that a rise in demand leads to a sharp increase in the cost of the distribution system, but the opening of the time window can help to reduce costs.
In this paper, a new problem of job sequences in a workshop is presented, taking into account non-unit demands for the jobs and whose objective is to minimize the total completion time for all the jobs (Cmax) satisfying a set of restrictions imposed on the problem to preserve the production mix. Two procedures are proposed to solve the new problem: Mixed Integer Linear Programming and a Metaheuristic based on Multistart and Local Search. The two proposed procedures are tested using instance set Nissan-9Eng.I, in both cases giving rise to highly satisfactory performance both in quality of solutions obtained and in the CPU times required. Through a case study of the Nissan engine manufacturing plant in Barcelona, our economic-productive analysis reveals that it is possible to save an average of € 1162.83 per day, manufacturing 270 engines, when we transform the current assembly line into a Heijunka-Flow Shop.
We consider a single-job model lot streaming problem in two-machine flow shops with speed scaling, in which the job can be splitted into n consistent sublots, and each sublot can be processed at varying continuous speeds on each machine. The aim is to find an optimal schedule that determines both the sizes and the processing speeds of sublots so that the job can be finished before a given deadline and the total energy consumption is minimized. To solve this problem, we investigate the structural properties of the optimal schedules and show that it can be obtained within a no-wait environment. Then, we show that the problem is in fact a convex optimization problem, and can be solved by existing convex programming techniques.
This paper explores the flowshop cell design in the cellular manufacturing system to minimize the number of machines, considering shifting the bottleneck machine and the annual demand. In a flowshop cell, products are processed through a series of production stages. Based on the number of machines per stage, the cell can be classified as either a production line (flowshop) or flexible flowshop. Two steps are followed in this study to design flexible flowshop cell. First, the un-capacitated mathematical model distributes the products into families and their corresponding machines into cells (product family formulation). Second, two non-linear mathematical models are proposed to design flexible flowshop. The first non-linear mathematical model is developed to build a flexible flowshop cell based on production rates. In this context, the number of machines in the system is determined, considering the machine duplication possibilities per stage for all products simultaneously, based on minimizing the total mean capacity required. The minimum number of machines per system is determined using a second non-linear mathematical model, with the objective to minimize the number of machines in the cell. In the two proposed nonlinear mathematical models, there is a limitation for the number of machine types. The results show that, as machine duplication is allowed, the number of machines per cell increases. Therefore, flexible flowshop design contributes to minimize the total number of machines in the system. In this way, the number of cells is reduced while production rates increase, and the total number of machines and total mean capacity required decrease.
As the product life cycles have continuously decreased, disassembly system design has been regarded to be important for manufacturing enterprises. Effective design of a disassembly system enables the enterprises to recycle the end of life products with low cost and high utilization of labors. This study focuses on the line segmentation problem of disassembly system where the worker assignment and segment determination decisions are made simultaneously. To do so, higher utilization of worker resources is achieved and disassembly operations are carried out by effective worker teams since the worker timetabling and disassembly line segmentation problems taken into consideration concurrently. To represent the problem mathematically, an integer programming model is developed. Besides, two different heuristic procedures, namely SSGWA and CSGWA, are presented to solve the problem in a reasonable amount of time. According to the computational results, SSGWA heuristic superior to CSGWA heuristic consistently because it takes both line segmentation and worker assignment decisions into account simultaneously.
Nowadays, scheduling problems under different disruptions are a key to become competitive in the global market of this century. Permutation flow shop scheduling problems are very important as they consider one of the important types of scheduling problems. In this paper, we consider a challenging scheduling problem of a permutation flow shop in the presence of different types of real-time events such as new job arrival and machine breakdown. A multi-objective optimisation model that takes into account multiple performance measures in order to minimise the effect of different real-time events is used in this paper. To solve this problem, we apply the proposed multi-objective model and adapt a predictive-reactive based Biased Randomised Iterated Greedy approach for the problem, which is hybridised a Biased Randomisation process and the Iterated Greedy algorithm. Furthermore, the proposed approach is compared against the predictive-reactive based Particle Swarm Optimisation method for the same problem. Additionally, to show the efficiency of the proposed model, we compare this model by testing the predictive-reactive based Biased Randomised Iterated Greedy approach to two other models: the bi-objective model that consider only two objectives and the classical single-objective model of minimising the makespan. Further statistical analysis is performed in this study by using an Analysis of Variance measure. The extensive experiments and statistical analysis demonstrate that the proposed multi-objective model is better than the other models in reducing the relative percentage deviation. Additionally, despite their simplicity, the Biased Randomised Iterated Greedy algorithm is shown to be State-of-the-art method that outperform the Particle Swarm Optimisation algorithm.
Hybrid flow shop scheduling problems are encountered in many real-world manufacturing operations such as computer assembly, TFT-LCD module assembly, and solar cell manufacturing. Most research considers the scheduling problem in regard to time requirements and the steps needed to improve production efficiency. However, the increasing amount of carbon emissions worldwide is contributing to the worsening global warming problem. Many countries and international organizations have started to pay attention to this problem, even creating mechanisms to reduce carbon emissions. Furthermore, manufacturing enterprises are showing growing interest in realizing energy savings. Thus, the present research study focuses on reducing energy costs and completion time at the manufacturing-system level. This paper proposed a multi-objective mixed-integer programming for energy-efficient hybrid flow shop scheduling with lot streaming in order to minimize both the production makespan and electric power consumption. Due to a trade-off between these objectives and the computational complexity of the proposed multi-objective mixed-integer program, this study adopts the genetic algorithm (GA) to obtain approximate Pareto solutions more efficiently. In addition, a multi-objective energy efficiency scheduling algorithm is also developed to calculate the fitness values of each chromosome in GA. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Under a mass individualisation paradigm, the individualised design of manufacturing systems is difficult as it involves adaptive integrating both new and legacy machines for the formation of part families with uncertainty. A systematic virtual model mirroring the real world of manufacturing system is essential to bridge the gap between its design and operation. This paper presents a digital twin-driven methodology for rapid individualised designing of the automated flow-shop manufacturing system. The digital twin merges physics-based system modelling and distributed semi-physical simulation to provide engineering solution analysis capabilities and generates an authoritative digital design of the system at pre-production phase. An effective feedbacking of collected decision-support information from the intelligent multi-objective optimisation of the dynamic execution is presented to boost the applicability of the digital twin vision in the designing of AFMS. Finally, a bi-level iterative coordination mechanism is proposed to achieve optimal design performance for required functions of AFMS. A case study is conducted to prove the feasibility and effectiveness of the proposed methodology.
Purpose
Lean manufacturing (LM) concepts have been widely adopted in diverse industrial sectors. However, no literature review focusing on case studies describing LM implementation is available. Case studies represent the actual implementation and provide secondary data for further analysis. This study aims to review the same to understand the pathways of LM implementation. In addition, it aims to analyse other related review questions, such as how implementing LM impacts manufacturing capabilities and the maturity level of manufacturing organisations that implemented LM, to name a few.
Design/methodology/approach
A literature review of case studies that discuss the implementation of LM during the last decade (from 2010 to 2020) is carried out. These studies were synthesised, and content analyses were performed to reveal critical insights.
Findings
The implementation pattern of LM significantly varies across manufacturing organisations. The findings show simultaneous improvement in manufacturing capabilities. Towards the end of the last decade, organisations implemented LM with radio frequency identification, e-kanban, simulation, etc.
Originality/value
Reviewing the case studies documenting LM implementation to comprehend the various nuances is a novel attempt. Furthermore, potential future research directions are identified for advancing the research in the domain of LM.
An actual hybrid flow shop scheduling (HFSS) problem with operation skipping is investigated from the steelmaking continuous casting (SCC) process, which plays a vital role in the productive processing of a slab in iron and steel enterprises. Firstly, a mixed integer mathematical model is explored for this problem based on the previous survey. Secondly, a block heuristic method based on double-layer right shift is presented on the basis of the problem-specific characteristics, which can generate the better initial solution for the problem. Thirdly, an improved memetic algorithm (IMA) with double-vector-representation based on attribution feature is proposed for dealing with the problem, which includes the block heuristic for initialization, the novel mutation structure on the basis of the problem-specific characteristics, and the enhanced local research to improve the exploitation ability. Finally, to test the performance of the IMA, a large number of instances from a steel plant are adopted. By statistical analysis, the results of experiment evaluation indicate that the proposed IMA has highly effective performance and obvious advantages comparing with other well-known algorithms.
Note to Practitioners
—Due to the change of order and the technology requirements of SCC process, partial charges must be further refined to eliminate the impurities or heat molten steel. This study models a novel hybrid flow shop scheduling problem with operation skipping, in which all charges undergo the primary refining stage, and partial ones undergo the double or triple refining stage. The average sojourn time, the total earliness and the total tardiness are taken as the objective functions, and the constraint for operation skipping is added. We develop an IMA based on the attribution feature of charge, in which double-vector-representation is designed, and a novel mutation structure on the basis of the problem-specific characteristics is presented, and an enhanced local research is proposed to improve the exploitation ability. Furthermore, a block heuristic method with double-layer right shift is presented to generate good initial individuals. The performance of IMA is analyzed by comparing with six modern meta-heuristics algorithms, the results show that the IMA is more superior than others. Because of the complex of scheduling problem in SCC, some dynamic influence, such as machine breakdowns, the influence of transportation tools, should be considered. The paper’s work can be extended to the above actual dynamic problem. Moreover, the presented IMA can also be developed to other hybrid flow shop scheduling problem with operation skipping.
Inspired by a real-world textile packing process, this paper investigates a novel hybrid flowshop scheduling problem with batch processing machines to minimize the makespan. Geometry sizes of textile products, non-identical capacities of packing machines, and the capacity of the needle detector are addressed in parallel-batching modes. To make batching and sequencing decisions simultaneously, a mixed integer linear programming model (MILP) is formulated. Then, a matheuristic method, Tabu Search with Fixing and Optimization (TSFO), is developed. Using tabu search to determine which variables to be fixed, the MILP is solved through a fix-and-optimize process. The results of extensive computational experiments show that the TSFO yields better solutions within much less computation time than solving the model directly in a commercial solver. Furthermore, the TSFO also outperforms an existing method in a special case from literature.
Product portfolio design is one of the important and effective factors in the financial and physical flows of various supply chains, especially dairy products. Accordingly, the financial and physical flows of the portfolio should be taken into consideration during the supply chain design. In this study, a closed-loop supply chain (CLSC) network is designed for dairy products aiming at maximizing the net cash flow from assets and maximizing the amounts paid to shareholders simultaneously. To find the optimal policy, an accelerated Benders decomposition (ABD) algorithm is implemented to tackle the complexity of the model. Moreover, three multi-objective optimization solution approaches of the weighted sum method (WSM), augmented ε-constraint (AEC), and fuzzy multi-objective programming (FMOP) are implemented to tackle the bi-objectiveness of the model. Next, a real case study in Iran is investigated to reveal the applicability of the developed methodology. Numerical results reveal that the ABD method reduces CPU time by about 10.8%. Moreover, the results of the case study demonstrate that by integrating financial and physical flows, an improvement of 4.8478% in the net cash flow from assets and a 2.3% improvement in the amounts paid to shareholders compared to the current situation.
More enterprises are facing rapid and changing market demand and small but frequent orders, and they extend the production capability of manufacturing systems to respond to these changes. This paper studies a distributed heterogeneous hybrid flow shop lot-streaming scheduling problem (DHHFLSP) with the minimization of makespan. In the DHHFLSP, the processing capacity of each factory is different and each job can be split into several sub-lots. These sub-lots are assigned to several non-identical factories. The mixed-integer linear programming model (MILP) of DHHFLSP is established. To solve the DHHFLSP, eighteen constructive heuristics and an iterated local search algorithm (ILS) are designed. In constructive heuristics, the jobs are sorted according to several time-based heuristic rules or they are divided into several groups according to bottleneck stages, and then these jobs are assigned into factories through two NEH-based job assignment rules. In the ILS, the NEH-based heuristic (NEHafter) plus Largest medium rule is used to generate an initial solution. Two greedy insertion operators with or without critical factories are adopted to generate the perturbation solutions. Four greedy local search operators are designed to make a deep search. The influence of the parameters and main components are investigated by a comprehensive analysis. The comparisons with several related algorithms on extensive testing instances demonstrate the effectiveness and efficiency of the ILS algorithm.
This study investigates the optimization of non-permutation flow-shop scheduling problems and lot-sizing simultaneously. Contrary to previous works, we first study the energy awareness of non-permutation flow-shop scheduling and lot-sizing using modified novel meta-heuristic algorithms. In this regard, first, a mixed-integer linear mathematical model is proposed. This model aimed to determine the size of each sub-category and determine each machine's speed within each sub-category to minimize makespan and total consumed energy simultaneously. In order to optimize this model, Multi-objective Ant Lion Optimizer (MOALO), Multi-objective Keshtel Algorithm (MOKA), and Multi-objective Keshtel and Social Engineering Optimizer (MOKSEA) are proposed. First, the validation of the mathematical model is evaluated by implementing it in a real case of the food industry using GAMS software. Next, the Taguchi design of the experiment is applied to adjust the meta-heuristic algorithms' parameters. Then the efficiency of these meta-heuristic algorithms is evaluated by comparing with Epsilon-constraint (EPC), Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Particle Swarm Optimization (MOPSO) using several test problems. The results demonstrated that the MOALO, MOKA, and MOKSEO algorithms could find optimal solutions that can be viewed as a set of Pareto solutions, which means the used algorithm has the necessary validity. Moreover, the proposed hybrid algorithm can provide Pareto solutions in a shorter time than EPC and higher quality than NSGA-II and MOPSO. Finally, the model's key parameters were the subject of sensitivity analysis; the results showed a linear relationship between the processing time and the first and second objective functions.
In this study, lot streaming in hybrid flowshop scheduling problem under machine capability and limited waiting time (lwt) constraints is investigated. The HFSP plays a vital role in the effective management of a multi-stage manufacturing system. To the best knowledge of the authors, the problem with its distinctive characteristics is addressed for the first time in the literature. A novel generic optimization model with the makespan objective is formulated to represent the problem mathematically. Structural properties and a lower bound formulation are presented to further explore the problem. Since the problem belongs to the NP-hard class, the genetic algorithm (GA) based approaches are employed to solve the problem by emphasizing the strategic and tactical level decisions. Furthermore, a design of experiment setting is constructed based on a practical case study to obtain remarkable insights regarding the HFSP problem with the lwt constraint. By doing so, the combinations of the lot streaming methodologies along with the sublot assignment methods are compared to each other through the employed algorithms. The computational results demonstrate that regardless of the employed crossover operator, the random-based sublot assignment with consistent sublots methodology leads to higher-quality solutions by up to 60% compared to the combination of the production leveling-based sublot assignment with equal sublots methodology. The results of the experiments provide remarkable insights regarding the factors and their levels as well. In this manner, the number of sublots and the number of machines have a significant impact on the quality of the solutions. Therefore, it is suggested to implement an order release mechanism for the multi-stage manufacturing system with the hybrid flowshop setting.
Lot streaming is the most widely used technique to facilitate the overlap of successive operations. Considering the consistent sublots and machine breakdown, this study investigates the multi-objective hybrid flowshop rescheduling problem with consistent sublots (MOHFRP_CS), which aims at optimising the total completion time, starting time deviations of operations, and average adjustment of sublot sizes simultaneously. By introducing the decomposition strategy and effective migrating birds optimisation framework, this paper develops a multi-objective migrating birds optimisation algorithm based on decomposition (MMBO/D). In MMBO/D, the problem is decomposed into a series of sub-problems, and its solutions are initialised by the Glover operator and further optimised by the variable neighbourhood descent strategy. The weights assigned to the sub-problems are adapted dynamically according to a variable weight strategy, and a global update strategy is employed to update the solutions. A novel sharing and benefiting mechanism is proposed to implement coevolution among different sub-problems. Competitive mechanisms are modified by considering similar sub-problems to improve population quality. A criterion is designed to check whether a subproblem is stuck in the local optima. The comprehensive computational results demonstrate that MMBO/D outperforms other state-of-the-art multi-objective evolutionary algorithms (MOEAs) for the addressed problem.
Due to its practicality, hybrid flowshop scheduling problem (HFSP) with productivity objective has been extensively explored. However, studies on HFSP considering green objective in distributed production environment are quite limited. Moreover, the current manufacturing mode is gradually evolving toward distributed co-production mode. Thus, this paper investigated a distributed hybrid flowshop scheduling problem (DHFSP) with objectives of minimization the makespan and total energy consumption (TEC). To address this problem, this paper designed a Pareto-based multi-objective hybrid iterated greedy algorithm (MOHIG) by integrating the merits of genetic operator and iterated greedy heuristic. In this MOHIG, firstly, one cooperative initialization strategy is proposed to boost initial solutions’ quality based on the previous experience and rules. Secondly, one knowledge-based multi-objective local search method is invented to enhance the exploitation capability according to characteristics of problem. Thirdly, an energy-saving technique is developed to decrease the idle energy consumption of machine tools. Furthermore, the effectiveness of each improvement component of MOHIG is assessed by three common indicators. Finally, the proposed MOHIG algorithm is compared with other multi-objective optimization algorithms, including SPEA2, MOEA/D, and NSGAII. Experimental results indicate that the proposed MOHIG outperforms its compared algorithms in solving this problem. In addition, this research can better guide practical production in some certain environments.
Distributed factory processing has attracted the attention and application of many companies because of the low cost and high flexibility. In the present study, the self-adaptive artificial bee colony algorithm (SABC) is presented to solve the distributed resource-constrained hybrid flowshop scheduling (DRCHFS) problems aiming to minimize the makespan. In the proposed algorithm, the two-dimensional vector solution representation is employed. Then, resource constraint in the decoding process is considered. In addition, a self-adaptive perturbation structure and local search strategy based on the critical factory are investigated to enhance searching abilities. The proposed algorithm is tested based on a randomly generated set of the real shop scheduling system, and then numerically analyze and compare the proposed algorithm with the existing heuristic algorithms to verify its effectiveness.
As regards distributed hybrid flow shop scheduling with sequence-dependent setup times (DHFSP-SDST), three novel mixed-integer linear programming (MILP) models and a constraint programming (CP) model are formulated for the same-factory and different-factory environments. The three novel MILP models are based on two different modeling ideas. The existing MILP model and the three proposed MILP models are compared in detail from several aspects, such as binary decision variables, continuous decision variables, constraints, solution performance and solution time. By solving the benchmarks in existing studies, the effectiveness and superiority of the proposed MILP and CP models are proved. Experimental results show that the MILP model of sequence-based modeling idea performs best, the MILP model of adjacent sequence-based modeling idea takes the second place and the existing MILP model of position-based modeling idea performs worst. The CP model is more efficient and effective than MILP models. In addition, compared with the existing meta-heuristic algorithms (e.g., DABC and IABC), the proposed MILP models prove the optimal solutions of 37 instances and improve 17 current best solutions. The CP model solves all the 45 instances to optimality and improves 19 current best solutions for benchmarks in the existing studies
Lot streaming is the most widely used technique to facilitate overlapping of successive operations. Inspired by real-world scenarios, this paper studies a multi-objective hybrid flowshop scheduling problem with consistent sublots, aiming to simultaneously optimize two conflicting objectives: the makespan and total number of sublots. Considering the setup and transportation operations, a multi-objective mixed integer programming model is developed and the trade-off between the two objectives is evaluated. Because of the NP-hard property of the addressed problem, metaheuristics are suggested. It is well known that the performance of metaheuristics is highly dependent on the setting of algorithmic parameters, referred to as numerical and categorical parameters. However, the traditional design process might be biased by previous experience. To eliminate these issues, an automated algorithm design (AAD) methodology is introduced to conceive a multi-objective evolutionary algorithm (MOEA) in a promising framework. The AAD enables designing the algorithm by automatically determining parameters and their combinations with minimal user intervention. With regard to the problem-specific characteristics and the employed algorithm framework, for the categorical parameters, including decomposition, solution encoding and decoding, solution initialization and neighborhood structures, several operators are designed specifically. Along with the numerical parameters, these categorical parameters are determined and combined using the designed iterated racing procedure. Comprehensive computational results demonstrate that the automated MOEA outperforms other state-of-the-art MOEAs for the addressed problem.
Energy-efficient scheduling of distributed production systems has become a common practice among large companies with the advancement of economic globalization and green manufacturing. Nevertheless, energy-efficient scheduling of distributed permutation flow-shop problem with limited buffers (DPFSP-LB) does not receive adequate attention in the relevant literature. This paper is therefore the first attempt to study this DPFSP-LB with objectives of minimizing makespan and total energy consumption (TEC). To solve this energy-efficient DPFSP-LB, a Pareto-based collaborative multi-objective optimization algorithm (CMOA) is proposed. In the proposed CMOA, first, the speed scaling strategy based on problem property is designed to reduce TEC. Second, a collaborative initialization strategy is presented to generate a high-quality initial population. Third, three properties of DPFSP-LB are utilized to develop a collaborative search operator and a knowledge-based local search operator. Finally, we verify the effectiveness of each improvement component of CMOA and compare it against other well-known multi-objective optimization algorithms on instances. Experiment results demonstrate the effectiveness of CMOA in solving this energy-efficient DPFSP-LB. Especially, the CMOA is able to obtain excellent results on all problems regarding the comprehensive metric, and is also competitive to its rivals regarding the convergence metric.
The classical flexible flowshop (FFc) environment consists of c-stages in series with m-machines in parallel at each stage, where each job has to undergo a particular series of actions. In this paper we consider a similar, yet different, and still a challenging real-life setting, that, to the best of our knowledge, has not been studied to date. We assume that there are ℓ-sets in parallel in which each of the sets is an m-machine proportionate flowshop. In this new setting, each job can be processed on each one of the sets, but once a set is chosen, the job must be processed on all of its machines, in first-in-first-out method. We study several fundamental scheduling measures such as makespan, maximum tardiness with common due-date, total tardiness with common due-date, and total load. Moreover, we consider optional job-rejection and focus on minimising the total completion time. All problems are shown to be NP-hard, and pseudo-polynomial dynamic programming (DP) solution algorithms and Simulated Annealing (SA) metaheuristics are provided. The efficiency of all our proposed algorithms is validated through an extensive numerical study.
Lot streaming is the most widely used technique of supporting the overlap of consecutive operations. Inspired by the real-world scenarios, this paper introduces this issue into the hybrid flowshop scheduling problem with consistent sublots (HFSP_CS). The innovations of this paper lie in developing a mixed integer linear programming (MILP) model, and in developing a collaborative variable neighborhood descent algorithm (CVND). The CVND evolves with a primary solution and an archive set comprising of promising solutions found in the progress, and contains four processes including the VND process, collaborative process, archive set and primary solution restart processes. Accordingly, the primary solution conducts the VND process with the defined neighborhood structures to implement the local exploitation. The archive set executes the collaborative process to learn from the historical information to implement the global search. The archive set restart is triggered when it is stuck into the local optima. The primary solution restart aims to conduct a large perturbation on the primary solution for the following loop of VND process. Regarding the problem-specific characteristics, the solution encoding and decoding are designed and an improvement strategy is developed to further improve the solution quality. To validate the CVND, two sets of instances are collected. Through comparing with the CPLEX solver, a heuristic and five state-of-the-art metaheuristics on small instances, the CVND shows the most suitable performance in terms of the objective values and algorithm efficiency. Through comparing with the heuristic and metaheuristics on medium–large instances, the CVND performs statistically better in terms of the relative percentage deviation values.
This work studies a two-stage hybrid flowshop problem with secondary resources (workers). The goal is to minimise the average tardiness. The workers are assigned to the workstations by time buckets (work shifts), and the assignment changes during the planning horizon. Two versions of the problem are studied: (i) the case where the average efficiency of the workers determines the time to process jobs; (ii) the case where the efficiency of the slowest worker assigned to a workstation determines the time to process jobs. The problem is NP hard and a set of heuristics are proposed to generate job sequences and worker assignments. Computational experiments are performed on randomly generated test problems. The experiments revealed that the proposed heuristics are able to find a large percentage of the optimal solutions for small sized instances, while on large sized instances the heuristic performance depended on experimental factors.
The classical hybrid flow shop scheduling problem (HFSSP) considers the operation and machine constraints but not the worker constraint. Acknowledging the influence and potential of human factors as a key element in improving production efficiency in a real hybrid flow shop, we consider a new realistic HFSSP with worker constraint (HFSSPW) and construct its mixed integer linear programming model. Seven multi-objective evolutionary algorithms with heuristic decoding (HD) (MOEAHs) are proposed to solve the HFSSPW. According to list scheduling, we first present four HD methods for four MOEAHs, and these methods incorporate four priority rules of machine and worker assignments. The earliest due date (EDD) rule is further introduced into the HD methods for the other three MOEAHs. The developed model is solved using CPLEX based on 20 loose instances under a time limit, and the four proposed MOEAHs are evaluated by comparing them with the results from CPLEX and two best-performing algorithms in the literature. The computational results reveal that the proposed MOEAHs perform excellently in terms of the makespan objective. Additionally, comprehensive experiments, including 150 tight instances, are conducted. In terms of solution quality and efficiency, the computational results show that the proposed MOEAHs demonstrate highly effective performance, and integrating EDD into the HD can substantially enhance algorithm performance. Finally, a real-life problem of the foundry plant is solved by MOEAHs and the scheduling solutions totally meet the delivery requirement.
The hybrid flowshop scheduling problem with unrelated parallel machines exists in many industrial manufacturers, which is an NP-hard combinatorial optimisation problem. To solve this problem more effectively, an improved gravitational search (IGS) algorithm is proposed which combines three strategies: generate new individuals using the mutation strategy of the standard differential evolution (DE) algorithm and preserve the optimal solution via a greedy strategy; substitute the exponential gravitational constant of the standard gravitational search (GS) algorithm with a linear function; improve the velocity update formula of the standard GS algorithm by mixing an adaptive weight and the global search strategy of the standard particle swarm optimisation (PSO) algorithm. Benchmark examples are solved to demonstrate the proposed IGS algorithm is superior to the standard genetic algorithm, DE, GS, DE with local search, estimation of distribution algorithm and artificial bee colony algorithms. Two more examples from a real-world water-meter manufacturing enterprise are effectively solved.
Recent years, the multi-objective evolutionary algorithm based on decomposition (MOEA/D) has been researched and applied for numerous optimization problems. In this study, we propose an improved version of MOEA/D with problem-specific heuristics, named PH-MOEAD, to solve the hybrid flowshop scheduling (HFS) lot-streaming problems, where the variable sub-lots constraint is considered to minimize four objectives, i.e., the penalty caused by the average sojourn time, the energy consumption in the last stage, as well as the earliness and the tardiness values. For solving this complex scheduling problem, each solution is coded by a two-vector-based solution representation, i.e., a sub-lot vector and a scheduling vector. Then, a novel mutation heuristic considering the permutations in the sub-lots is proposed, which can improve the exploitation abilities. Next, a problem-specific crossover heuristic is developed, which considered solutions with different sub-lot size, and therefore can make a solution feasible and enhance the exploration abilities of the algorithm as well. Moreover, several problem-specific lemmas are proposed and a right-shift heuristic based on them is subsequently developed, which can further improve the performance of the algorithm. Lastly, a population initialization mechanism is embedded that can assign a fit reference vector for each solution. Through comprehensive computational comparisons and statistical analysis, the highly effective performance of the proposed algorithm is favorably compared against several presented algorithms, both in solution quality and population diversity.
This paper addresses the multi-stage hybrid flowshop scheduling problem with identical parallel machines at each stage by considering the effect of human factors. The various levels of labours and the effects of their learning and forgetting are studied. The minimization of the weighted sum of the makespan and total flow time is the objective function. Since the problem is NP-hard, an improved version of the particle swarm optimization (PSO) algorithm is presented to solve the problem. A dispatching rule and a constructive heuristic are incorporated to improve the initial solutions of the PSO algorithm. The variable neighbourhood search (VNS) algorithm is also hybridized with the PSO algorithm to attain the optimal solutions consuming less computational time. An industrial scheduling problem of an automobile manufacturing unit is discussed. Moreover, several instances of the random benchmark problem are used to validate the performance of the proposed algorithm. Computational experiments have been performed and the results prove the effectiveness of the proposed approach.
In recent years, the interest in seru production system (SPS) has increased to enhance the flexibility of production systems. Because the worker resource in an SPS is critical for adapting to changes in demand, this study focuses on workforce-related operational strategies rarely considered for SPS. To this end, for the first time in the literature, a bi-objective workforce scheduling problem is addressed by considering the interseru worker transfer in SPS. A novel optimisation model is proposed to achieve two objectives, that of minimising makespan and reducing workload imbalance among workers. Because it is proved that the problem falls within a non-deterministic polynomial-time hardness (NP-hard) class, non-dominated sorting genetic algorithm-II (NSGA-II) is employed to solve large-sized problems. For small-sized problems, the second version of the augmented ε-constrained (AUGMECON2) method is implemented and Pareto-optimal solutions are obtained. A set of evaluation metrics is considered to compare two different operational strategies in terms of the desired objectives. The computational results indicate that allowing worker transfer leads to better results for all metrics. The main contribution of the present study is to provide a novel optimisation model for the addressed problem to compare two operational strategies by considering the heterogeneity inherent of workers.
We consider a hybrid flowshop scheduling problem that includes parallel unrelated discrete machines or batch processing machines in different stages of a production system. The problem is motivated by a bottleneck process within the production system of a transformer producer located in the Netherlands. We develop an integer programming model that minimises the total tardiness of jobs over a finite planning horizon. Our model is applicable to a wide range of production systems organised as hybrid flowshops. We strengthen our integer program by exploiting the special properties of some constraints in our formulation. We develop a decision support system (DSS) based on our proposed optimisation model. We compare the results of our initial optimisation model with an improved formulation as well as with a heuristic that was in use at the company before the implementation of our DSS. Our results show that the improved optimisation model significantly outperforms the heuristic and the initial optimisation model in terms of both the solution time and the strength of its linear programming relaxation.
Climate change pushes the operation managers to take account of energy-saving issues in their decision-making of production scheduling and maintenance planning (PSMP). We address a PSMP problem for a single machine system under Time-of-Use electricity tariff. We consider two objectives including the makespan that measures the service level and the total energy cost that measures the energy sustainability. Both objectives are considered in a bi-objective mathematical model that is further solved using a novel heuristic algorithm consisting of two layers based on the problem decomposition. The inner layer problem, which is solved by a branch & bound algorithm, is to optimise the decision variables of preventive maintenance and machine’s setup. The outer layer problem, which is solved by a hybrid NSGA-II algorithm, is to optimise the sequence of jobs and the amount of inserted buffer time. The effectiveness and efficiency of the algorithm are demonstrated by a series of numerical experiments. The Pareto frontier can serve as a tool for managers to consider energy cost explicitly in making decisions. It is observed in some scenarios that reducing energy cost will not increase the makespan.
Energy saving has attracted growing attention due to the advent of sustainable manufacturing. By this motivation, this paper studies a hybrid flowshop green scheduling problem (HFGSP) with variable machine processing speeds. A multi-objective optimization model with the objectives of minimizing the makespan and total energy consumption is developed. To solve this complex problem, a multiobjective discrete artificial bee colony algorithm (MDABC) based on decomposition is suggested. In VND-based employed bee phase, the variable neighborhood descent (VND) with five designed neighborhood is employed to each subproblem to realize their self-evolution. In the collaborative onlooker bee phase, the promising subproblems selected by the order preference technique according to their similarity to an ideal solution (TOPSIS) is evolved by collaborating with the other neighboring subproblems. Particularly, a dynamic neighborhood strategy is developed to define the neighborhood relationship to retain the population diversity. In the solution exchange-based scout bee phase, a solution exchange strategy is developed to enhance the algorithm efficiency and enable the solutions to be exploited in different directions. Moreover, according to the problem-specific characteristics, encoding and decoding methodologies are developed to represent the solution space, and several definitions are proposed to implement objective normalization, and an energy saving procedure is designed to reduce the energy consumption. Through comprehensive computational comparisons and statistical analysis, the developed strategies and MDABC shows highly effective performance.
This paper studies scheduling of hybrid flowshop with sequence-dependent setup times to minimize total weighted earliness and tardiness. Due dates are usually intervals in real life therefore due windows are considered in this paper. Since the considered problem is NP-hard, three population based hybrid metaheuristics are presented, namely: Hybrid squirrel search algorithm (HSSA), opposition based whale optimization algorithm (OBWOA), and discrete grey wolf optimization (DGWO). We utilized some effective and advanced technologies, including variable neighbourhood search, hybrid local search and opposition based learning to enhance the performance of the presented algorithms. The parameters of the presented algorithms are calibrated using design of experiments approach. To evaluate the performance of the presented algorithms, we compare them against five other well-known meta-heuristics on 240 randomly generated problems. The statistically sound results demonstrate that the presented algorithms are very competitive for the considered problem.
The hybrid flowshop scheduling problem (HFSP) has been widely studied in the literature, as it has many real-life applications in industry. Even though many solution approaches have been presented for the HFSP with makespan criterion, studies on HFSP with total flow time minimization have been rather limited. This study presents a mathematical model, four variants of iterated greedy algorithms and a variable block insertion heuristic for the HFSP with total flow time minimization. Based on the well-known NEH heuristic, an efficient constructive heuristic is also proposed, and compared with NEH. A detailed design of experiment is carried out to calibrate the parameters of the proposed algorithms. The HFSP benchmark suite is used for evaluating the performance of the proposed methods. As there are only 10 large instances in the current literature, further 30 large instances are proposed as new benchmarks. The developed model is solved for all instances on CPLEX under a time limit, and the performances of the proposed algorithms are assessed through comparisons with the results from CPLEX and the two best-performing algorithms in literature. Computational results show that the proposed algorithms are very effective in terms of solution time and quality. Additionally, the proposed algorithms are tested on large instances for the makespan criterion, which reveal that they also perform superbly for the makespan objective. Especially for instances with 30 jobs, the proposed algorithms are able to find the current incumbent makespan values reported in literature, and provide three new best solutions.
We study an integrated economic lot-sizing and sequencing problem (ELSP) in the hybrid flow shop manufacturing setting with unlimited intermediate buffers in a finite planning horizon. The ELSP entails making two simultaneous decisions regarding (i) the manufacturing sequences of products, and (ii) their production quantity. The objective is to minimize the total cost, consisting of inventory holding and set-up costs. To solve this problem, we first develop a novel mixed-integer nonlinear programming (MINLP) model that improves an existing MINLP model in the literature. We then present a novel linearization technique that transforms these two MINLP models into effective mixed-integer linear programming (MILP) models. Additionally, we develop an effective algorithm that hybridizes the iterated local search algorithm with an approximate function. We conduct comprehensive experiments to compare the performance of MILPs+CPLEX with that of MINLPs+BARON. Additionally, our proposed algorithm is compared with four existing metaheuristic algorithms in the literature. Computational results demonstrate that our novel MINLP formulation and its linearized variant significantly improve the solvability and optimality gap of an existing MINLP formulation and its linearized variant. We also show that our new hybrid iterated local search algorithm substantially improves computational performance and optimality gap of the mathematical models and the existing algorithms in the literature, on large-size instances of the problem.
The hybrid flowshop scheduling problem (HFSP) has been widely studied in the past decades. The most commonly used criterion is production efficiency. Green criteria, such as energy consumption and carbon emission, have attracted growing attention with the improvement of the environment protection awareness. Limited attention has been paid to noise pollution. However, noise pollution can lead to health and emotion disorder. Thus, this paper studies a multi-objective HFSP considering noise pollution in addition to production efficiency and energy consumption. First, we formulate a new mixed-integer programming model for this multi-objective HFSP. To realize the green scheduling, one energy conservation/noise reduction strategy is embedded into this model. Then, a novel multi-objective cellular grey wolf optimizer (MOCGWO) is proposed to address this problem. The proposed MOCGWO integrates the merits of cellular automata (CA) for diversification and variable neighborhood search (VNS) for intensification, which balances exploration and exploitation. Finally, to validate the efficiency and effectiveness of the proposed MOCGWO, we compare our proposal with other well-known multi-objective evolutionary algorithms by conducting comparison experiments. The experimental results show that the proposed MOCGWO is significantly better than its competitors on this problem.
This paper proposes an effective new hybrid ant colony algorithm based on crossover and mutation mechanism for no-wait flow shop scheduling with the criterion to minimize the maximum completion time. The no-wait flow shop is known as a typical NP-hard combinational optimization problem. The hybrid ant colony algorithm is applied to the 192 benchmark instances from literature in order to minimize makespan. The performance of the proposed Hybrid Ant Colony algorithm is compared to the Adaptive Learning Approach and Genetic Heuristic algorithm which are used in previous studies to solve the same set of benchmark problems. The computational experiments show that the proposed Hybrid Ant Colony algorithm provides better results relative to the other algorithms.
This paper investigates an energy-conscious hybrid flow shop scheduling problem with unrelated parallel machines (HFSP-UPM) with the energy-saving strategy of turning off and on. We first analyse the energy consumption of HFSP-UPM and formulate five mixed integer linear programming (MILP) models based on two different modelling ideas namely idle time and idle energy. All the models are compared both in size and computational complexities. The results show that MILP models based on different modelling ideas vary dramatically in both size and computational complexities. HFSP-UPM is NP-Hard, thus, an improved genetic algorithm (IGA) is proposed. Specifically, a new energy-conscious decoding method is designed in IGA. To evaluate the proposed IGA, comparative experiments of different-sized instances are conducted. The results demonstrate that the IGA is more effective than the genetic algorithm (GA), simulating annealing algorithm (SA) and migrating birds optimisation algorithm (MBO). Compared with the best MILP model, the IGA can get the solution that is close to an optimal solution with the gap of no more than 2.17% for small-scale instances. For large-scale instances, the IGA can get a better solution than the best MILP model within no more than 10% of the running time of the best MILP model.
We study two-machine hybrid flowshop scheduling with identical jobs. Each job consists of two tasks, namely a flexible task and a fixed task. The flexible task can be processed on either machine, while the fixed task must be processed on the second machine. The fixed task can only be processed after the flexible task is finished. Due to different technological capabilities of the two machines, the flexible task has different processing times on the two machines. Our goal is to find a schedule that minimises the makespan. We consider two variants of the problem, namely no buffer and infinite buffer capacity between the two machines. We present constant-time solution algorithms for both variants. In addition, analysing the relationship between the hybrid benefits and performance difference between the two machines, we find that, for the infinite-buffer case, increasing the technological level of the second machine does not necessarily increase the hybrid benefits.
Problems encountered in real manufacturing environments are complex to solve optimally, and they are expected to fulfill multiple objectives. Such problems are called multi-objective optimization problems(MOPs) involving conflicting objectives. The use of multi-objective evolutionary algorithms (MOEAs) to find solutions for these problems has increased over the last decade. It has been shown that MOEAs are well-suited to search solutions for MOPs having multiple objectives. In this chapter, in addition to comprehensive information, two different MOEAs are implemented to solve a MOP for comparison purposes. One of these algorithms is the non-dominated sorting genetic algorithm (NSGA-II), the effectiveness of which has already been demonstrated in the literature for solving complex MOPs. The other algorithm is fast Pareto genetic algorithm (FastPGA), which has population regulation operator to adapt the population size. These two algorithms are used to solve a scheduling problem in a Hybrid Manufacturing System (HMS). Computational results indicate that FastPGA outperforms NSGA-II.
In this study, the two-stage supply chain scheduling problem with multiple customers and multiple manufacturers is considered. The first stage consists of m manufacturers (suppliers), while the second stage contains q vehicles, each of which distributes the batches from the manufacturers to the customers. Multiple customers and average lead time are two most important issues in practice; however, no study has been carried out so far to investigate these two issues together for the two-stage supply chain scheduling problem. The main contribution of this study is to coordinate production and distribution decisions to obtain an effective scheduling in a two-stage supply chain that contains multiple customers and multiple manufacturers. A mixed integer linear optimization model is developed to formulate the problem with the average lead time objective. Because the problem has been shown to be NP-hard, a hybrid artificial bee colony and simulated annealing (HABCSA) algorithm is introduced and used to solve the problem. In addition, a lower bound (LB) and several structural properties for the problem are presented and different batching mechanisms are developed based on these properties. For the purpose of performance analysis of HABCSA with different batching mechanisms, detailed computational experiments are conducted using random instances which are generated based on real aluminum production data for different capacity levels. The experimental results indicate that the HABCSA heuristic consistently outperforms the Genetic Algorithm (GA) and the Artificial Bee Colony (ABC) algorithm for each capacity level.