Permutation Flow Shop Scheduling Research Articles

Improved biogeography-based optimization algorithm for lean production scheduling of prefabricated components

PurposeFor prefabricated building construction, improper handling of the production scheduling for prefabricated components is one of the main reasons that affect project performance, which causes overspending, schedule overdue and quality issues. Prior research on prefabricated components production schedule has shown that optimizing the flow shop scheduling problem (FSSP) is the basis for solving this issue. However, some key resources and the behavior of the participants in the context of actual prefabricated components production are not considered comprehensively.Design/methodology/approachThis paper characterizes the production scheduling of the prefabricated components problem into a permutation flow shop scheduling problem (PFSSP) with multi-optimization objectives, and limitation on mold and buffers size. The lean construction principles of value-based management (VBM) and just-in-time (JIT) are incorporated into the production process of precast components. Furthermore, this paper applies biogeography-based optimization (BBO) to the production scheduling problem of prefabricated components combined with some improvement measures.FindingsThis paper focuses on two specific scenarios: production planning and production rescheduling. In the production planning stage, based on the production factor, this study establishes a multi-constrained and multi-objective prefabricated component production scheduling mathematical model and uses the improved BBO for prefabricated component production scheduling. In the production rescheduling stage, the proposed model allows real-time production plan adjustments based on uncertain events. An actual case has been used to verify the effectiveness of the proposed model and the improved BBO.Research limitations/implicationsWith respect to limitations, only linear weighted transformations are used for objective optimization. In regards to research implications, this paper considers the production of prefabricated components in an environment where all parties in the supply chain of prefabricated components participate to solve the production scheduling problem. In addition, this paper creatively applies the improved BBO to the production scheduling problem of prefabricated components. Compared to other algorithms, the results show that the improved BBO show optimized result.Practical implicationsThe proposed approach helps prefabricated component manufacturers consider complex requirements which could be used to formulate a more scientific and reasonable production plan. The proposed plan could ensure the construction project schedule and balance the reasonable requirements of all parties. In addition, improving the ability of prefabricated component production enterprises to deal with uncertain events. According to actual production conditions (such as the occupation of mold resources and storage resources of completed components), prefabricated component manufacturers could adjust production plans to reduce the cost and improve the efficiency of the whole prefabricated construction project.Originality/valueThe value of this article is to provide details of the procedures and resource constraints from the perspective of the precast components supply chain, which is closer to the actual production process of prefabricated components. In addition, developing the production scheduling for lean production will be in line with the concept of sustainable development. The proposed lean production scheduling could establish relationships between prefabricated component factory manufacturers, transportation companies, on-site contractors and production workers to reduce the adverse effects of emergencies on the prefabricated component production process, and promote the smooth and efficient operation of construction projects.

An efficiency and robustness analysis of warm-start mathematical models for idle and waiting times optimization in the flow shop

This paper aims to address current manufacturing problems such as high buffers and energy waste by considering a novel performance measure, the sum of the core and front idle time of each machine and the core waiting time of each job, within the permutation flow shop scheduling optimization. Four new mixed-integer linear programming (MILP) models and three warm-start procedures were implemented in 240 instances of a widely used benchmark. The results of computational experiments were evaluated using performance profiles, considering computing times and optimality gaps. Among the models, the solver achieved better results with the position-based models than with the sequence-based models, achieving 25% more optimal solutions, being more efficient and robust. Regarding the warm-start strategies, we highlight the procedure with the longest processing time (LPT) heuristic as the best method among the seven studied.

Distributed assembly permutation flow-shop scheduling problem with non-identical factories and considering budget constraints

PurposeThis paper aims to address a distributed assembly permutation flow-shop scheduling problem (DAPFSP) considering budget constraints and factory eligibility. The first stage of the considered production system is composed of several non-identical factories with different technology levels and so the factories' performance is different in terms of processing time and cost. The second stage is an assembly stage wherein there are some parallel work stations to assemble the ready parts into the products. The objective function is to minimize the maximum completion time of products (makespan).Design/methodology/approachFirst, the problem is formulated as mixed-integer linear programing (MIP) model. In view of the nondeterministic polynomial (NP)-hard nature, three approximate algorithms are adopted based on variable neighborhood search (VNS) and the Johnsons' rule to solve the problem on the practical scales. The proposed algorithms are applied to solve some test instances in different sizes.FindingsComparison result to mathematical model validates the performance accuracy and efficiency of three proposed methods. In addition, the result demonstrated that the proposed two-level self-adaptive variable neighborhood search (TLSAVNS) algorithm outperforms the other two proposed methods. Moreover, the proposed model highlighted the effects of budget constraints and factory eligibility on the makespan. Supplementary analysis was presented by adjusting different amounts of the budget for controlling the makespan and total expected costs. The proposed solution approach can provide proper alternatives for managers to make a trade-off in different various situations.Originality/valueThe problem of distributed assembly permutation flow-shop scheduling is traditionally studied considering identical factories. However, processing factories as an important element in the supply chain use different technology levels in the real world. The current paper is the first study that investigates that problem under non-identical factories condition. In addition, the impact of different technology levels is investigated in terms of operational costs, quality levels and processing times.

Discrete differential evolution metaheuristics for permutation flow shop scheduling problems

Scheduling problems (SP) in the permutation flow shop (PFS) environment are present in many intermittent production industries, consisting of to determinate the processing order of n jobs in m sequential machines, with the purpose to optimize some performance criterion. In this paper, three optimization algorithms based on discrete differential evolution (DE) metaheuristics are applied to PFS scheduling problems, to minimize the makespan, are proposed, that are Discrete Differential Evolution, and Discrete Self-Adaptive Differential Evolution for SP in PFS named DDE-PFS, DSADE-PFS1 and DSADE-PFS2, respectively. The Carlier (CB), Heller (HB), Reeves (RB), and Taillard (TB) numerical benchmarks were adopted to test the proposed optimization algorithms. The performance of the optimization algorithms was evaluated regarding relative percentage error (RPE) criterion, convergence, standard deviation (Std), statistical tests of Friedman and post hoc Nemenyi. For TB, the DSADE-PFS1 algorithm presented a better performance in terms of RPE and Std measures. For CB and HB, the DSADE-PFS1 and DSADE-PFS2 algorithms presented a better performance in RPE, and the DSADE-PFS2 algorithm in terms of Std. For RB, the DSADE-PFS2 algorithm presented a better performance in RPE, while the DSADE-PFS1 algorithm was achieved in Std. Considering the processing time for each algorithm the DSADE-PFS2 approach achieved better results than CB, HB, and RB. Overall the results have shown that the optimization approaches proposed in this paper are promising for the SP in PFS, with highly competitive results in terms of average performance values.

A matrix cube-based estimation of distribution algorithm for the energy-efficient distributed assembly permutation flow-shop scheduling problem

In this paper, a matrix-cube-based estimation of distribution algorithm (MCEDA) is proposed to solve the energy-efficient distributed assembly permutation flow-shop scheduling problem (EE_DAPFSP) that minimizes both the maximum completion time (Cmax) and the total carbon emission (TCE) simultaneously. Firstly, a high-quality and diverse initial population is constructed via a hybrid initialization method. Secondly, a matrix-cube-based probabilistic model and its update mechanism are designed to appropriately accumulate the valuable pattern information from superior solutions. Thirdly, a suitable sampling strategy is developed to sample the probabilistic model to generate a new population per generation, so as to guide the search direction toward promising regions in solution space. Fourthly, a problem-dependent neighborhood search based on critical path is provided to perform an in-depth local search around the promising regions found by the global search. Fifthly, two types of speed adjustment strategies based on problem properties are also embedded to further improve the quality of the obtained solutions. Sixthly, the influence of the parameters is investigated based on the multi-factor analysis of variance of Design-of-Experiments. Finally, extensive experiments and comprehensive comparisons with several recent state-of-the-art multi-objective algorithms are carried out based on the well-known benchmark instances, and the statistical results demonstrate the efficiency and effectiveness of the proposed MCEDA in addressing the EE_DAPFSP.

Integrated stochastic bicriteria flow shop scheduling problem with preventive maintenance

In this paper, the concept of flexible and multiple preventive maintenance activities is introduced by reformulating classical bicriteria permutation flow shop scheduling problem into stochastic scheduling with objective to minimise system utilisation time with minimum makespan. The mathematical model is formulated to handle the uncertainties in job processing time and the time interval for machine maintenance. The problem of stochastic flow shop scheduling environment with maintenance activities, is NP-hard. Therefore, the advanced metaheuristic is implemented to solve large scale instances of referred problem. Extensive computational analysis is carried out to depict the superiority of proposed metaheuristic in terms of effectiveness and efficacy.

Mixed Integer Linear Programming formulations for the permutation flow shop scheduling problem with preventive maintenance activities

Mixed Integer Linear Programming formulations for the permutation flow shop scheduling problem with preventive maintenance activities

Application of dendrogram-directed design space exploration to bi-objective permutation flow-shop scheduling problem

Application of dendrogram-directed design space exploration to bi-objective permutation flow-shop scheduling problem

A New Priority Rule for Initial Ordering of Jobs in Permutation Flowshop Scheduling Problems

Scheduling in a permutation flowshop refers to processing of jobs in a set of available machines in the same order. Among the several possible performance characteristics of a flowshop, makespan remains one of the highest preferred metrics by researchers in the past six decades. The constructive heuristic proposed by Nawaz-Enscore-Ham (NEH) is one of the best for makespan minimization. The performance essentially depends on the initial ordering jobs according to a particular priority rule (PR). The popular priority rules are non-increasing order of the jobs' total processing time, the sum of average processing time and standard deviation and, the sum of average processing time, standard deviation and absolute skewness among others. The objective of this paper is to propose and analyse a new job priority rule for the permutation flowshop. The popular priority rules available in the literature are studied and, one of the best priority rules; the sum of average processing time and standard deviation is slightly modified, by replacing the standard deviation by mean absolute deviation (MAD). To assess the performance of the new rule, four benchmark datasets are used. The computational results and statistical analyses demonstrate the better performance of the new rule.

Artificial bee colony algorithm for solving multi-objective distributed fuzzy permutation flow shop problem

The distributed permutation flow shop scheduling (DPFSS) is a permutation flow shop scheduling problem including the multi-factory environment. The processing times of the jobs in a real life scheduling problem cannot be precisely know because of the human factor. In this study, the process times and due dates of the jobs are considered triangular and trapezoidal fuzzy numbers for DPFSS environment. An artificial bee colony (ABC) algorithm is developed to solve the multi-objective distributed fuzzy permutation flow shop (DFPFS) problem. First, the proposed ABC algorithm is calibrated with the well-known DPFSS instances in the literature. Then, the DPFSS instances are fuzzified and solved with the algorithm. According to the results, the proposed ABC algorithm performs well to solve the DFPFS problems.

Distributed no-wait flow shop problem with sequence dependent setup time: Optimization of makespan and maximum tardiness

This paper investigates a multi-objective optimization distributed no-wait permutation flow shop scheduling problem under the constraint of sequence dependent setup time. Our optimization case is minimizing the makespan and maximum tardiness criteria. Therefore, our main objective will be to find the optimal jobs sequence that minimizes a function representing the two criteria of makespan and maximum tardiness. This function will be linearly dependent of these two criteria via a weighting parameter for each criterion. To solve this industrial problem, we propose the mixed integer linear programming (MILP) and a set of efficient metaheuristics solving different size instances. To this end, we suggest three inspired nature metaheuristics: The genetic algorithm (GA), the artificial bee colony (ABC) algorithm and migratory bird optimization (MBO) algorithm. We suggest a total of six new algorithms based on nature-inspired metaheuristics. Also, two constructive heuristics are used, the greedy randomized adaptive search procedure (GRASP) and Nawaz–Enscore–Ham (NEH) algorithms. It was revealed that GA algorithm with NEH initialization gives the best results comparing to the other metaheuristics.

Minimizing the total tardiness and the total carbon emissions in the permutation flow shop scheduling problem

In this paper, we consider the permutation flow shop scheduling problem and aim to minimize the total tardiness as well as the total carbon emissions. We present a formulation of the problem through a mixed-integer programming model. To solve the problem, we develop a multi-objective decomposition-based heuristic (MODBH) algorithm, working based on job insertion, as well as a multi-objective VNS algorithm. Furthermore, a multi-objective iterated greedy algorithm is utilized to validate the efficiency of the developed methods. Using extensive computational experiments, we indicate that the MODBH algorithm has a significant superiority to the other developed solution approaches. Furthermore, the multi-objective VNS algorithm shows better performance than the multi-objective iterated greedy algorithm.

A new solution to distributed permutation flow shop scheduling problem based on NASH Q-Learning

Aiming at Distributed Permutation Flow-shop Scheduling Problems (DPFSPs), this study took the minimization of the maximum completion time of the workpieces to be processed in all production tasks as the goal, and took the multi-agent Reinforcement Learning (RL) method as the main frame of the solution model, then, combining with the NASH equilibrium theory and the RL method, it proposed a NASH Q-Learning algorithm for Distributed Flow-shop Scheduling Problem (DFSP) based on Mean Field (MF). In the RL part, this study designed a two-layer online learning mode in which the sample collection and the training improvement proceed alternately, the outer layer collects samples, when the collected samples meet the requirement of batch size, it enters to the inner layer loop, which uses the Q-learning model-free batch processing mode to proceed, and adopts neural network to approximate the value function to adapt to large-scale problems. By comparing the Average Relative Percentage Deviation (ARPD) index of the benchmark test questions, the calculation results of the proposed algorithm outperformed other similar algorithms, which proved the feasibility and efficiency of the proposed algorithm.

Improved Q ‐learning algorithm for solving permutation flow shop scheduling problems

Generally, scheduling problems refer to allocation of available shared resources and the sorting of production tasks, in order to satisfy the specified performance target within a certain time. The fundamental scheduling problem is that all jobs need to be processed on the same route, which is called flow shop scheduling problems (FSSP). The goal of FSSP, proven as an NP-hard problem, is to find a job sequence that minimizes the makespan. In this paper, an improved Q-learning algorithm is proposed for solving the FSSP. Firstly, a problem model based on the basic Q-learning algorithm is constructed. The makespan is used as the feedback signal, and the process of environmental state change is defined as the process of job selection. Q-learning gives the expected utility of taking a given action in a given state. Afterwards, combined with the NEH heuristic, the algorithm efficiency is enhanced by changing the job inserting mode. In order to validate the proposed method, several simulation experiments are carried out on a set of test problems having different scales. The obtained optimization results of the proposed algorithm are compared to the standard Q-learning algorithm and a hybrid algorithm. The discussion and analysis show that the proposed algorithm performs better than the others in solving the permutation FSSP. As a future direction, in order to shorten the running time, further improvements will be studied to increase the performance of the proposed algorithm and make it applicable and efficient for solving multi-objective optimization problems.

Distributed Flow Shop Scheduling with Sequence-Dependent Setup Times Using an Improved Iterated Greedy Algorithm

To meet the multi-cooperation production demand of enterprises, the distributed permutation flow shop scheduling problem (DPFSP) has become the frontier research in the field of manufacturing systems. In this paper, we investigate the DPFSP by minimizing a makespan criterion under the constraint of sequence-dependent setup times. To solve DPFSPs, significant developments of some metaheuristic algorithms are necessary. In this context, a simple and effective improved iterated greedy (NIG) algorithm is proposed to minimize makespan in DPFSPs. According to the features of DPFSPs, a two-stage local search based on single job swapping and job block swapping within the key factory is designed in the proposed algorithm. We compare the proposed algorithm with state-of-the-art algorithms, including the iterative greedy algorithm (2019), iterative greedy proposed by Ruiz and Pan (2019), discrete differential evolution algorithm (2018), discrete artificial bee colony (2018), and artificial chemical reaction optimization (2017). Simulation results show that NIG outperforms the compared algorithms.

Improved cat swarm optimization for permutation flow shop scheduling problem

To minimize the maximum make span of permutation flow shop scheduling problem, this paper proposed a cat swarm optimization algorithm based on estimation of distribution algorithms. This article Take the cat swarm optimization as the framework, embedded in the Estimation Distribution Algorithm, in the search mode, mining the excellent gene link in the solution sequence by using the probability matrix to combination blocks, speed and position tracking mode using characteristics of cat swarm optimization updates in the cat in order to update the excellent solution sequence generator group. Finally, through the simulation test and result comparison of Carlier and Reeves standard example set, the good robustness and global searching ability of the algorithm are verified.

Iterated Local Search and Other Algorithms for Buffered Two-Machine Permutation Flow Shops with Constant Processing Times on One Machine.

The two-machine permutation flow shop scheduling problem with buffer is studied for the special case that all processing times on one of the two machines are equal to a constant c. This case is interesting because it occurs in various applications, for example, when one machine is a packing machine or when materials have to be transported. Different types of buffers and buffer usage are considered. It is shown that all considered buffer flow shop problems remain NP-hard for the makespan criterion even with the restriction to equal processing times on one machine. However, the special case where the constant c is larger or smaller than all processing times on the other machine is shown to be polynomially solvable by presenting an algorithm (2BF-OPT) that calculates optimal schedules in O(nlogn) steps. Two heuristics for solving the NP-hard flow shop problems are proposed: (i) a modification of the commonly used NEH heuristic (mNEH) and (ii) an Iterated Local Search heuristic (2BF-ILS) that uses the mNEH heuristic for computing its initial solution. It is shown experimentally that the proposed 2BF-ILS heuristic obtains better results than two state-of-the-art algorithms for buffered flow shop problems from the literature and an Ant Colony Optimization algorithm. In addition, it is shown experimentally that 2BF-ILS obtains the same solution quality as the standard NEH heuristic, however, with a smaller number of function evaluations.

Permutation flow shop scheduling with multiple lines and demand plans using reinforcement learning

Existing studies on the permutation flow shop problem (PFSP) commonly assume that jobs are produced on a single line. However, manufacturers may speed up their production by employing multiple lines, where each line produces sub-parts of the final product; which must be assembled by a synchronization machine. This study presents a novel reinforcement learning (RL) approach for the PFSP with multiple lines and demand plans. Our approach differs from existing RL-based scheduling methods as we train the policy to directly generate the sequence in an iterative way, where actions denote the job type to be sequenced next. During cutoff time, we follow a multistart approach that generates sequences with the trained policy, which are subsequently optimized by local search. Our numerical evaluation based on 1050 problem instances with up to three production lines shows that our approach outperforms existing methods on the multi-line problems for short cutoff times, while there is a tie with existing methods for medium and long cutoff times. A further analysis suggests that our approach can also be applied to problems with imbalanced demand plans.

Discrete Jaya with refraction learning and three mutation methods for the permutation flow shop scheduling problem

Discrete Jaya with refraction learning and three mutation methods for the permutation flow shop scheduling problem

A Comparative Analysis of Heuristic Metaheuristic and Exact Approach to Minimize Make Span of Permutation Flow Shop Scheduling

The study of permutation flow shop scheduling issues has proved fascinating. Make span reduction has been explored extensively throughout the years as one of the many factors. If there are more than two machines, finding a schedule that optimizes total completion times for Permutation Flow Shop issues is NP Hard. The well-known Nawaz–Enscore–Ham (NEH) heuristic is acknowledged as the top performing approach for the permutation flow shop scheduling issue till now, according to the make span minimization criteria. For large-scale problems, however, the NEH approach takes a long time to discover an estimated optimum solution. Many researchers have offered heuristics and meta-heuristics as the time it takes to compute grows exponentially in proportion to the size of the problem. For the permutation flow shop scheduling problem, we proposed a genetic algorithm with the criterion of minimizing make span as the criteria. The method's performance is compared to that of the well-known NEH algorithm. Computational experiments on benchmark data sets revealed that the proposed approach produces satisfactory solutions in short computational cycles. Furthermore, it just requires a few user-defined parameters, making it relevant to real-world flow shop scheduling challenges. The findings reveal that, when compared to an exact technique, the proposed genetic algorithm (GA) is capable of rapidly seeking optimal solutions for most small-sized instances. Furthermore, the proposed GA continues to function satisfactorily for medium and large-scale instances and generates solutions in a reasonable period.