Flexible Flow Shop Scheduling Research Articles

Production Scheduling Methodology, Taking into Account the Influence of the Selection of Production Resources

The overwhelming majority of methodologies for the flexible flow shop scheduling problem proposed so far have a common feature, which is the assumption of constant time and cost for the execution of individual technological operations (ignoring an optimal selecting combination of individual employees and tools). Even if the existence of the influence of the selection of production resources on the course of operations is signaled in the available works, the research so far has not focused on the measurable effect of such a solution that takes into account this phenomenon in scheduling. The proposed production scheduling methodology, including the influence of employees and tools, turned out to be more effective in terms of minimizing the maximum completion time and the cost of the production process compared to existing solutions. The efficiency of the new proposed scheduling methodology was assessed using examples of four technological processes. The research was carried out on the basis of a dedicated adaptation of the Monte Carlo optimization algorithm in order to determine the actual effect of the new solution. The algorithm itself is not an integral part of the proposed solution, and the universal methodology developed will ensure significant profit for any optimization algorithm correctly implemented.

Bilevel learning for large-scale flexible flow shop scheduling

Many industrial practitioners are facing the challenge of solving large-scale scheduling problems within a limited time. In this paper, we propose a novel bilevel scheduler based on constraint Markov Decision Process to solve large-scale flexible flow shop scheduling problems (FFSP). There are many intelligent algorithms proposed to solve FFSP, but they take quite long time to execute or are even not working for large-scale problems. Our scheduler is able to decide the sequence of a large number of jobs in a limited time with the objective to minimize makespans. The upper level is designed to explore an initial global sequence, whereas the lower level aims to look for partial sequence refinements. In the implementation, Double Deep Q Network (DDQN) is used in the upper level and Graph Pointer Network (GPN) lies within the lower level. The two levels are connected by a sliding-window sampling mechanism. Based on datasets from public benchmarks and real-world industrial scenarios with over 5000 jobs, experiments show that our bilevel scheduler significantly outperforms seven baseline algorithms, including three state-of-the-art heuristics, three deep learning based algorithms, and another bilevel model, in terms of makespans and computational time. In particular, it only takes less than 200 s to get solutions of large-scale problems with up to 5000 jobs and matches the performance of the state-of-the-art heuristics.

Grid-Based Hybrid Genetic Approach to Relaxed Flexible Flow Shop with Sequence-Dependent Setup Times

In this paper, a hybrid genetic algorithm implemented in a grid environment to solve hard instances of the flexible flow shop scheduling problem with sequence-dependent setup times is introduced. The genetic algorithm takes advantage of the distributed computing power on the grid to apply a hybrid local search to each individual in the population and reach a near optimal solution in a reduced number of generations. Ant colony systems and simulated annealing are used to apply a combination of iterative and cooperative local searches, respectively. This algorithm is implemented using a master–slave scheme, where the master process distributes the population on the slave process and coordinates the communication on the computational grid elements. The experimental results point out that the proposed scheme obtains the upper bound in a broad set of test instances. Also, an efficiency analysis of the proposed algorithm indicates its competitive use of the computational resources of the grid.

Application of GATS, a hybrid mega-heuristic model,and DOE, to solve flexible flow shop scheduling problems:a case study

Flexible flow shop scheduling (FFSS) is an NP-hard combinatorial optimization problem. Solving this problem using mathematical modeling approaches is very difficult. Mega-heuristic algorithms, such as the genetic algorithm (GA) and tabu search (TS), are powerful tools for finding near-optimal solutions to problems of this type. This paper develops a GATS model by combining GA and TS for solving FFSS problems. In the model, GA is used as the platform for global search, and TS is used to support GA in local search. This paper also uses the design of experiments (DOE) to optimize the parameters of the GATS model. The performance of the models, GATS and GATS with DOE, is compared with traditional heuristics being used. The result indicates that the models are good approaches for FFSS problems.

Scheduling Flexible Flow Shop in Labeling Companies to Minimize the Makespan

In the competitive global marketplace, production scheduling plays a vital role in planning in manufacturing. Scheduling deals directly with the time to output products quickly and with a low production cost. This research examines case study of a Radio-Frequency Identification labeling department at Avery Dennison. The main objective of the company is to have a method that allows for the sequencing and scheduling of a set of jobs so it can be completed on or before the customer’s due date to minimize the number of late orders. This study analyzes the flexible flow shop scheduling problem with a sequence dependent setup by modifying the processing time and setup time to minimize the makespan on multiple machines. Based on the defined mathematical model, this study includes an alternative approach and application of heuristic algorithm with the input being big data. Both optimization programs are used in this study and compared to determine which method can better solve the company’s problems. The proposed algorithm is able to improve machine utilization with large-scale problems.

Auxiliary resource planning in a flexible flow shop scheduling problem considering stage skipping

This paper investigates a flexible flow shop scheduling problem wherein there are some unrelated parallel machines with different technology levels in the first stage. Some of these machines are multifunctional that can do several processes on jobs. Therefore, the jobs assigned to these machines do not require processing in some of the next stages. Although the majority of the traditional scheduling problems deal with machines as the only resource, there are usually unavailability constraints to auxiliary resources such as labor, tools, pallets, industrial robots, and so on. This challenge with inspiration from a spring manufacturing plant is tackled in the considered problem with machine eligibility and sequence-dependent setup times. This problem is described with a numeric example, and its parameters and decision variables are defined. Then, to formulate the problem, a mixed-integer linear programming model is developed to minimize the makespan and determine the number of required auxiliary resources. Then the genetic algorithm is calibrated for all aforementioned features of the problem at hand as the main solution approach. Furthermore, two other well-known metaheuristics i.e., simulated annealing and enhanced particle swarm optimization are modified and employed for computational comparisons. The result shows that the proposed algorithm provides accurate results regarding the number of required auxiliary resources to achieve the minimum makespan. Moreover, supplementary analysis is presented considering practical constraints such as budget and desired efficiency of machines. The result indicates that the solution approach could provide proper alternatives for managers in various conditions.

An effective hybrid meta-heuristic for flexible flow shop scheduling with limited buffers and step-deteriorating jobs

This paper addresses a flexible flow shop scheduling problem considering limited buffers and step-deteriorating jobs, where there are multiple non-identical parallel machines. A mixed integer programming model is proposed, with the criterion of minimizing the makespan and total tardiness simultaneously. To handle this problem, an effective hybrid meta-heuristic algorithm, named GVNSA, is developed based on genetic algorithm (GA), variable neighborhood search (VNS) and simulated annealing (SA). In the algorithm, with a two-dimensional matrix encoding scheme, the NEH (Nawaz–Enscore–Ham) heuristic and bottleneck elimination method are implemented to determine the initial population. A three-level rolling translation approach is designed for decoding. To balance the exploration and exploitation abilities, three effective steps are executed: 1) partial matching crossover and mutation strategy based on multiple neighborhood search structures are imposed on the GA operators; 2) a VNS with SA is introduced to re-optimize some individuals from GA, where four neighborhood structures are constructed; 3) a modified CDS (Campbell–Dudek–Smith) heuristic is embedded to disturb population in the mid-iteration. Numerical experiments are carried out on test problems with different scales. Computational results demonstrate that the proposed GVNSA can obtain higher quality solutions in comparison with other heuristics and meta-heuristics existing in literature.

RETRACTED ARTICLE: Preventive maintenance for the flexible flowshop scheduling under uncertainty: a waste-to-energy system.

Nowadays, an efficient and robust plan for maintenance activities can reduce the total cost significantly in the equipment-driven industry. Maintenance activities are directly associated with the impact on the plant output, production quality, production cost, safety, and the environmental performance. To address this challenge more broadly, this paper presents an optimization model for the problem of flexible flowshop scheduling in a series-parallel waste-to-energy (WTE) system. To this end, a preventive maintenance (PM) policy is proposed to find an optimal sequence for processing tasks and minimize the delays. To deal with the uncertainty of the flexible flowshop scheduling of waste-to-energy in practice, the work processing time is modeled to be uncertain in this study. Therefore, a robust optimization model is applied to address the proposed problem. Due to the computational complexity of this model, a novel scenario-based genetic algorithm is proposed to solve it. The applicability of this research is shown by a real-life case study for a WTE system in Iran. The proposed algorithm is compared against an exact optimization method and a canonical genetic algorithm. The findings confirm a competitive performance of the proposed method in terms of time savings that will ultimately save the cost of the proposed PM policy.

A parallel genetic algorithm for multi-objective flexible flowshop scheduling in pasta manufacturing

Among the potential road maps to sustainable production, efficient manufacturing scheduling is a promising direction. This paper addresses the lack of knowledge in the scheduling theory by introducing a generalized flexible flow shop model with unrelated parallel machines in each stage. A mixed-integer programming formulation is proposed for such model, solved by a two-phase genetic algorithm (GA), tackling job sequencing and machine allocation in each phase. The algorithm is parallelized with a specialized island model, where the evaluated chromosomes of all generations are preserved to provide the final Pareto-Optimal solutions. The feasibility of our method is demonstrated with a small example from literature, followed with the investigation of the premature convergence issue. Afterwards, the algorithm is applied to a real-sized instance from a Belgium pasta manufacturer. We illustrate how the algorithm converges over iterations to trade-off near-optimal solutions (with 8.50% shorter makespan, 5.24% cheaper energy cost and 6.02% lower labor cost), and how the evaluated candidates distribute in the objective space. A comparison with a NSGA-II implementation is further performed using hypothesis testing, having 5.43%, 0.95% and 2.07% improvement in three sub-objectives mentioned above. Although this paper focuses on scheduling issues, the proposed GA can serve as an efficient method for other multi-objective optimization problems.

Effective constructive heuristics for distributed no-wait flexible flow shop scheduling problem

The distributed shop scheduling has gained a great deal of attention due to its high-efficient collaboration and production. This paper studies a distributed no-wait flexible flow shop scheduling problem (DNWFFSP) with the makespan criterion, where each factory includes an identical flexible flow shop with no-wait constraint that requires each job to be processed without any waiting time between consecutive stages. A mixed-integer linear programming model for the DNWFFSP is presented. A machine selection method based on the first earliest available machine rule is presented. Three greedy factory assignment rules incorporating NEH (Nawaz-Enscore-Ham) heuristic are developed to allocate jobs into factories. Fourteen dispatch rules involving simple sorting and decomposition method are developed to construct a priority sequence of jobs. Thus, several constructive heuristics are obtained by combining dispatch rules and factory assignment rules. Furthermore, a constructive heuristic version of variable neighborhood descend is designed to address the DNWFFSP. One of constructive heuristics is selected to generate an initial solution, and five neighborhood search methods are used as the local search procedure. A comprehensive numerical comparison and statistical analysis are carried out to investigate the performance of the proposed approaches. The distributed NEH2 with smallest largest-medium rule obtains better results than other constructive heuristics for large-size instances.

Scheduling on flexible flow shop with cost-related objective function considering outsourcing options

This study considers outsourcing decisions in a flexible flow shop scheduling problem, in which each job can be processed by either an in-house production line or outsourced. The selected objective function aims to minimize the weighted sum of tardiness costs, in-house production costs, and outsourcing costs with respect to the jobs due date. The purpose of the problem is to select the jobs that must be processed in-house, schedule processing of the jobs in-house, and finally select and assign other jobs to the subcontractors. We develop a mixed-integer linear programming (MILP) model for the research problem. Regarding the complexity of the research problem, the MILP model cannot be used for large-scale problems. Therefore, four metaheuristic algorithms, including SA, GA, PSO, hybrid PSO-SA, are proposed to solve the problem. Furthermore, some random test problems with different sizes are generated to evaluate the effectiveness of the proposed MILP model and solution approaches. The obtained results demonstrate that the GA can obtain better solutions in comparison to the other algorithms.

Flexible Flow Shop Scheduling and Energy Saving Optimization Strategy under Low Carbon Target

In order to reduce the carbon emissions of the flow shop which consists of unrelated parallel machine, a kind of scheduling mathematical mode with low carbon emission target is built by analyzing the carbon emissions of the machine tools under different running conditions. Not only the carbon emissions produced in the handling process which is rarely discussed in the previous studies, but also the carbon emissions produced during the start-up and shutdown process of the selected machine tools are considered in the model. Based on this model, a multi-state alternation energy saving optimization strategy is proposed to reduce carbon emissions during the idle waiting period of machine tools. An improved genetic algorithm is employed to solve this optimization problem. In the end, the t cases are studied to validate the strategy.

Minimizing the operational costs in a flexible flow shop scheduling problem with unrelated parallel machines

This paper investigates a flexible flow shop scheduling problem with the aim of minimizing the operational costs as a new objective function. In this production system, there are some unrelated parallel machines with different performances and different technology levels in the first stage and each other stage consists of a single machine. Setup times are assumed as sequence-dependent and are need when a machine starts to process a new job. Some of the parallel machines in the first stage are multifunctional and can do several processes on jobs. So, the jobs that are assigned to these machines do not need to be processed in some next stages. This problem is described with an example, and its parameters and decision variables are defined. Then a mathematical model based on mixed-integer linear programming (MIP) is developed to solve the problem in small-sized scales. As this problem is discussed in an Np-hard environment, the Genetic Algorithm (GA) is applied to solve the considered problem on practical-sized scales. Due to the result, the operational costs conflict with makespan as a common objective function in scheduling problems. Therefore, the supplementary analysis has been presented considering a restriction on the makespan.

An efficiency improvement of flexible flow shop scheduling in automotive part company

Flexible flow shop is becoming more interested and applied in industries due to its impact from higher workloads. Flexible flow shop scheduling problem is focused to minimize the makespan. A metaheuristic model based on Hybrid Tabu Search is developed to overcome this problem. Firstly, Hybrid Tabu Search is modelled based on the factory data. The Earliest Due Date rule is used as the scheduling method for the current status. FlexSim simulation software is used to evaluate the Hybrid Tabu Search model. The outcome is validated with two different basic heuristic solutions; Campbell, Dudek and Smith’s and Gupta’s heuristics. It is found that the proposed model can improve the job sequence based on makespan criteria.

Multi-objective permutation and non-permutation flow shop scheduling problems with no-wait: a systematic literature review

Flow shop scheduling is a type of scheduling where sequence follows for each job on a set of machines for processing. In practice, jobs in flow shops can arrive at irregular times, and the no-wait constraint allows the changes in the job order to flexibly manage such irregularity. The flexible flow shop scheduling problems with no-wait have mainly addressed for flow optimization on the shop floor in manufacturing, processing, and allied industries. The scope of this paper is to identify the literature available on permutation and non-permutation flow shop scheduling with no-wait constraint. This paper organizes scheduling problems based on performance measures of variability and shop environments. The extended summary of two/three-machine and m-machine problems has been compiled, including their objectives, algorithms, parametric considerations, and their findings. A systematic appearance of both conceptual and analytical results summarizes various advances of the no-wait constraint. The paper includes independently investigated problems and suggestions for future research directions.

Solving multi-objective flexible flow-shop scheduling problem using teaching-learning-based optimization embedded with maximum deviation theory

Solving multi-objective flexible flow-shop scheduling problem using teaching-learning-based optimization embedded with maximum deviation theory

Flexible flow shop scheduling with interval grey processing time

Purposepurpose of this paper is providing a solution for flexible flow shop scheduling problem with uncertain processing time in aeronautical composite lay-up workshop.Design/methodology/approachA flexible flow scheduling model and algorithm with interval grey processing time is established. First, according to actual needs of composite laminate shop scheduling process, interval grey number is used to represent uncertain processing time, and interval grey processing time measurement method, grey number calculation and comparison rules, grey Gantt chart, and other methods are further applied. Then a flexible flow shop scheduling model with interval grey processing time (G-FFSP) is established, and an artificial bee colony algorithm based on an adaptive neighbourhood search strategy is designed to solve the model. Finally, six examples are generated for simulation scheduling, and the efficiency and performance of the model and algorithm are evaluated by comparing the results.FindingsResults show that flexible flow shop scheduling model and algorithm with interval grey processing time can provide an optimal solution for composite lay-up shop scheduling problems and other similar flow shop scheduling problems.Social implicationsUncertain processing time is common in flexible workshop manufacturing, and manual scheduling greatly restricts the production efficiency of workshop. In this paper, combined with grey system theory, an intelligent algorithm is used to solve flexible flow shop scheduling problem to promote intelligent and efficient production of enterprises.Originality/valueThis paper applies and perfects interval grey processing time measurement method, grey number calculation and comparison rules, grey Gantt chart and other methods. A flexible flow shop scheduling model with interval grey processing time is established, and an artificial bee colony algorithm with an adaptive domain search strategy is designed. It provides a comprehensive solution for flexible flow shop scheduling with uncertain processing time.

Improved approximation algorithms for two-stage flexible flow shop scheduling

A two-stage flexible flow shop scheduling is a manufacturing infrastructure designed to process a set of jobs, in which a single machine is available at the first stage and m parallel machines are available at the second stage. At the second stage, each task can be processed by multiple parallel machines. The objective is to minimize the maximum job completion time, i.e., the makespan. Sun et al. (J Softw 25:298–313, 2014) presented an $$O(n\log n)$$ -time 3-approximation algorithm for $$F2(1, Pm)~|~size_i~|~C_{\max }$$ under some special conditions. Zhang et al. (J Comb Optim 39:1–14, 2020) presented a 2.5-approximation algorithm for $$F2(1, P2)~|~line_i~|~C_{\max }$$ and a 2.67-approximation algorithm for $$F2(1, P3)~|~line_i~|~C_{\max }$$ , which both run in linear time. In this paper, we achieved following improved results: for $$F2(1, P2)~|~line_i~|~C_{\max }$$ , we present an $$O(n\log n)$$ -time 2.25-approximation algorithm, for $$F2(1, P3)~|~line_i~|~C_{\max }$$ , we present an $$O(n\log n)$$ -time 7/3-approximation algorithm, for $$F2(1, Pm)~|~size_i~|~C_{\max }$$ with the assumption $$ \mathop {\min }_{1 \le i \le n} \left\{ {{p_{1i}}} \right\} \ge \mathop {\max }_{1 \le i \le n} \left\{ {{p_{2i}}} \right\} $$ , we present a linear time optimal algorithm.

A simulation–optimization model for solving flexible flow shop scheduling problems with rework and transportation

We propose an enhanced multi-objective harmony search (EMOHS) algorithm and a Gaussian mutation to solve the flexible flow shop scheduling problems with sequence-based setup time, transportation time, and probable rework. A constructive heuristic is used to generate the initial solution, and clustering is applied to improve the solution. The proposed algorithm uses response surface methodology to minimize both maximum completion time and mean tardiness, concurrently. We evaluate the efficacy of the proposed algorithm using computational experiments based on five measures of diversity metric, simultaneous rate of achievement for two objectives, mean ideal distance, quality metric, and coverage. The experimental results demonstrate the effectiveness of the proposed EMOHS compared with the existing algorithms for solving multi-objective problems.

Hybrid particle swarm optimization and neighborhood strategy search for scheduling machines and equipment and routing of tractors in sugarcane field preparation

This paper presents the Hybrid Particle Swarm Optimization and Neighborhood Strategy Search (HPSO-NS) to solve a tractor scheduling and routing problem with equipment allocation constraint in sugarcane field preparation, to help the growers catch the season and ensure advantageous production of sugar from sugarcane. This problem can be formulated as the flexible flow shop scheduling problem with machine eligibility, time windows, sequence dependent setup time (SDST), blocking, machine restriction and machine grouping (FFS |Ssmt,Mj, Grouping, block, 6-stage, Tool, Tw |∑iNRi). A mixed-integer programming model was developed to solve small-scale problems. The HPSO-NS was developed for large-scale problems, and three neighborhood strategies were added to the PSO procedure and developed. Moreover, two new formulae which were used to select the neighborhood strategy in HPSO-NS are presented in this paper to increase the performance of the proposed method. The computational results show that the HPSO-NS outperforms the original PSO and the lower bound obtained from the optimization software, while using 97% less computational time.