Flexible Flow Shop Scheduling Problem Research Articles

Memetic algorithm for solving flexible flow-shop scheduling problems with dynamic transport waiting times

Flexible flow-shop scheduling with dynamic transport waiting times (FFSPDW) is a typical flow shop scheduling problem in smart manufacturing system. In this problem, jobs need to be transported by transporters like AGV (Automated Guided Vehicle) to next stage after processing. During transportation, waiting time dynamically occurs for both jobs and transporters, and finally contributes to makespan. The waiting times are conditioned by buffer capacity, machine allocations and production sequence. In order to minimize makespan with consideration of dynamic waiting times, we proposed a waiting time calculation approach to evaluate waiting time and makespan. This approach considers two situations: infinite buffer capacity and zero buffer capacity. Further, we developed a memetic algorithm integrated with waiting time calculation approach to solve FFSPDW. Finally, we verified the algorithm parameters via analysis of variance. Computational results show that the proposed memetic algorithm is able to reach high quality solutions with short computation time. Consequently, the proposed approach is suitable for solving industrial FFSPDW problems.

Three Hybrid Metaheuristic Algorithms for Stochastic Flexible Flow Shop Scheduling Problem with Preventive Maintenance and Budget Constraint

Stochastic flexible flow shop scheduling problem (SFFSSP) is one the main focus of researchers due to the complexity arises from inherent uncertainties and also the difficulty of solving such NP-hard problems. Conventionally, in such problems each machine’s job process time may encounter uncertainty due to their relevant random behaviour. In order to examine such problems more realistically, fixed interval preventive maintenance (PM) and budget constraint are considered.PM activity is a crucial task to reduce the production efficiency. In the current research we focused on a scheduling problem which a job is processed at the upstream stage and all the downstream machines get busy or alternatively PM cost is significant, consequently the job waits inside the buffers and increases the associated holding cost. This paper proposes a new more realistic mathematical model which considers both the PM and holding cost of jobs inside the buffers in the stochastic flexible flow shop scheduling problem. The holding cost is controlled in the model via the budget constraint. In order to solve the proposedmodel, three hybrid metaheuristic algorithms are introduced. They include a couple of well-known metaheuristic algorithms which have efficient quality solutions in the literature. The two algorithms of them constructed byincorporationof the particle swarm optimization algorithm (PSO) and parallel simulated annealing (PSA) methods under different random generation policies. The third one enriched based on genetic algorithm (GA) with PSA. To evaluate the performance of the proposed algorithms, different numerical examples are presented. Computational experiments revealed that the proposed algorithms embedboth desirable accuracy and CPU time. Among them, the PSO-PSAП outperforms than other algorithms in terms of makespan and CPU time especially for large size problems.

A Dual Heterogeneous Island Genetic Algorithm for Solving Large Size Flexible Flow Shop Scheduling Problems on Hybrid Multicore CPU and GPU Platforms

The flexible flow shop scheduling problem is an NP-hard problem and it requires significant resolution time to find optimal or even adequate solutions when dealing with large size instances. Thus, this paper proposes a dual island genetic algorithm consisting of a parallel cellular model and a parallel pseudo-model. This is a two-level parallelization highly consistent with the underlying architectures and is well suited for parallelizing inside or between GPUs and a multicore CPU. At the higher level, the efficiency of the island GA is improved by exploring new regions within the search space utilizing different methods. In the meantime, the cellular model keeps the population diversity by decentralization and the pseudo-model enhances the search ability by the complementary parent strategy at the lower level. To encourage the information sharing between islands, a penetration inspired migration policy is designed which sets the topology, the rate, the interval, and the strategy adaptively. Finally, the proposed method is tested on some large size flexible flow shop scheduling instances in comparison with other parallel algorithms. The computational results show that it not only can obtain competitive results but also reduces execution time.

Research on limited buffer scheduling problems in flexible flow shops with setup times

In order to solve the limited buffer scheduling problems in flexible flow shops with setup times, this paper proposes an improved whale optimization algorithm (IWOA) as a global optimization algorithm. Firstly, this paper presents a mathematic programming model for limited buffer in flexible flow shops with setup times, and applies the IWOA algorithm as the global optimization algorithm. Based on the whale optimization algorithm (WOA), the improved algorithm uses Levy flight, opposition-based learning strategy and simulated annealing to expand the search range, enhance the ability for jumping out of local extremum, and improve the continuous evolution of the algorithm. To verify the improvement of the proposed algorithm on the optimization ability of the standard WOA algorithm, the IWOA algorithm is tested by verification examples of small-scale and large-scale flexible flow shop scheduling problems, and the imperialist competitive algorithm (ICA), bat algorithm (BA), and whale optimization algorithm (WOA) are used for comparision. Based on the instance data of bus manufacturer, simulation tests are made on the four algorithms under variouis of practical evalucation scenarios. The simulation results show that the IWOA algorithm can better solve this type of limited buffer scheduling problem in flexible flow shops with setup times compared with the state of the art algorithms.

Flow shop scheduling with variable processing times based on differential shuffled frog leaping algorithm

In the problem of flexible flow shop scheduling with variable processing times, the change of processing speed often affects product quality and causes fluctuations in capacity, which makes it difficult to solve the scheduling problem. In the light of the flexible flow-shop scheduling problem with variable processing times (FFSP-VPT), the FFSP-VPT mathematical model is established. The improved differential shuffled frog leaping algorithm (DSFLA) serves as the global optimisation algorithm. It overcomes the shortcomings of the adaptive shuffled frog leaping algorithm which easily falls into local optimum and converges slowly. The two-stage coding method is used to determine the online sequence of the job and processing speed of the stage with variable processing times. The simulation experiments confirm the improvement of the shuffled frog leaping algorithm in global search ability and its effectiveness in solving the flexible flow shop scheduling problem with variable processing times.

Research on limited buffer scheduling problems in flexible flow shops with setup times

In order to solve the limited buffer scheduling problems in flexible flow shops with setup times, this paper proposes an improved whale optimization algorithm (IWOA) as a global optimization algorithm. Firstly, this paper presents a mathematic programming model for limited buffer in flexible flow shops with setup times, and applies the IWOA algorithm as the global optimization algorithm. Based on the whale optimization algorithm (WOA), the improved algorithm uses Levy flight, opposition-based learning strategy and simulated annealing to expand the search range, enhance the ability for jumping out of local extremum, and improve the continuous evolution of the algorithm. To verify the improvement of the proposed algorithm on the optimization ability of the standard WOA algorithm, the IWOA algorithm is tested by verification examples of small-scale and large-scale flexible flow shop scheduling problems, and the imperialist competitive algorithm (ICA), bat algorithm (BA), and whale optimization algorithm (WOA) are used for comparision. Based on the instance data of bus manufacturer, simulation tests are made on the four algorithms under variouis of practical evalucation scenarios. The simulation results show that the IWOA algorithm can better solve this type of limited buffer scheduling problem in flexible flow shops with setup times compared with the state of the art algorithms.

Stochastic flexible flow shop scheduling problem with limited buffers and fixed interval preventive maintenance: a hybrid approach of simulation and metaheuristic algorithms

This study focused on the uncertain flexible flow shop scheduling problem with limited buffers when preventive maintenance is applied at fixed intervals. This issue has not been addressed in spite of widespread applications, due to complexity arising in solving such a stochastic decision making problem. To this aim, a novel optimization model is presented along with two types of solving methods using metaheuristic algorithms with and without a computer simulation model. The proposed hybrid method, named HSIM-META, integrates the computer simulation model along with the three most common metaheuristic algorithms, i.e., genetic algorithm (GA), simulated annealing (SA) algorithm, and particle swarm optimization (PSO), which offer better solution quality according to the literature. For this purpose, the simulation outputs are applied as an initial population for the tuned metaheuristic parameters to look for the next improved solution by investigating different approaches. Different numerical examples are discussed to examine the performance of the proposed method. The computational results of the proposed method, including hybrid simulation with GA (HSIM-GA), SA (HSIM-SA), and PSO (HSIM-PSO), are compared with the just applying GA, SA, and PSO. The results reveal that the suggested method acts more efficiently in terms of accuracy and speed in solving the problem.

Mathematical models and an elephant herding optimization for multiprocessor-task flexible flow shop scheduling problems in the manufacturing resource planning (MRPII) system

Shop floor control (SFC) is one of the main concepts in manufacturing resource planning (MRPII) and production scheduling is a key element in SFC. This paper studies the hybrid flow shop scheduling problem where jobs are multiprocessor. The objective is to minimize total completion time. Although there are several papers considering hybrid flow-shop scheduling problem with multiprocessor tasks, but none propose a mathematical model for this problem. At first, the two problems (fixed and selective cases) are mathematically formulated by mixed integer linear programming models. Using commercial software, the model is used to solve the small instances of the problems. Moreover, an elephant herding optimization is developed to solve large instances of the problems. To numerically evaluate the proposed algorithm, it is compared with two available algorithms in the literature, simulated annealing and shuffled frog-leaping algorithm in the literature.

A bi-objective MILP model for blocking hybrid flexible flow shop scheduling problem: robust possibilistic programming approach

ABSTRACTOne of the important issues in scheduling due to the frequent use of it in manufacturing industries and factories is the hybrid flow shop (HFS) scheduling problem. In this paper, a bi-objective mixed integer linear programming (MILP) model for the problem is presented in which blocking constraint is also considered. The first objective function tries to minimize the makespan and the second one tries to minimize the total costs of machine allocation at each stage. In fact, in this model, the number and the type of machines at each stage are determined by the model according to the processing and setup times and cost of machines. Because most issues in the real world are uncertain, in this study, processing times, sequence-dependent setup times, and costs are considered as uncertain parameters. The robust possibilistic programming (RPP) approach is used to cope with the uncertainty. In this paper, the realistic and the hard worst-case robust approaches are used. The realistic and the soft worst-case robust models became the same because we are only concerned about the robustness of the makespan. Comparing the results between fuzzy and robust fuzzy models shows that the realistic model is more suitable than fuzzy and hard worst-case models in terms of mean and standard deviation.

GPU based parallel genetic algorithm for solving an energy efficient dynamic flexible flow shop scheduling problem

Due to new government legislation, customers’ environmental concerns and continuously rising cost of energy, energy efficiency is becoming an essential parameter of industrial manufacturing processes in recent years. Most efforts considering energy issues in scheduling problems have focused on static scheduling. But in fact, scheduling problems are dynamic in the real world with uncertain new arrival jobs after the execution time. This paper proposes an energy efficient dynamic flexible flow shop scheduling model using the peak power value with consideration of new arrival jobs. As the problem is strongly NP-hard, a priority based hybrid parallel Genetic Algorithm with a predictive reactive complete rescheduling strategy is developed. In order to achieve a speedup to meet the short response in the dynamic environment, the proposed method is designed to be highly consistent with the NVIDIA CUDA software model. Finally, numerical experiments are conducted and show that our approach can not only solve the problem flexibly, but also gain competitive results and reduce time requirements dramatically.

A control method to save machine energy in production

Nowadays, energy saving is one of the most talked about issues in our life, it is also increasingly important in the manufacturing industry. This research considers the dynamic flexible flow shop scheduling (DFFS) problem, which is an extended version of the classical flow-shop scheduling problem. A flexible flow shop has multiple stages with multiple machines at each stage for processing multiple products. Previous research on DFFS aimed to achieve just-in-time production, or reducing difference between the actual completion time and the due date of each job. However, little research has been made on energy saving of machines in production. To address such a need, this paper proposes a method that dynamically turns on and off machines so as to reduce energy consumption while achieving JIT production. The proposed method has been tested on different environments, and the results show that it is high performing for both JIT production and energy saving.

Multi-Objective Flexible Flow Shop Scheduling Problem Considering Variable Processing Time due to Renewable Energy

Renewable energy is an alternative to non-renewable energy to reduce the carbon footprint of manufacturing systems. Finding out how to make an alternative energy-efficient scheduling solution when renewable and non-renewable energy drives production is of great importance. In this paper, a multi-objective flexible flow shop scheduling problem that considers variable processing time due to renewable energy (MFFSP-VPTRE) is studied. First, the optimization model of the MFFSP-VPTRE is formulated considering the periodicity of renewable energy and the limitations of energy storage capacity. Then, a hybrid non-dominated sorting genetic algorithm with variable local search (HNSGA-II) is proposed to solve the MFFSP-VPTRE. An operation and machine-based encoding method is employed. A low-carbon scheduling algorithm is presented. Besides the crossover and mutation, a variable local search is used to improve the offspring’s Pareto set. The offspring and the parents are combined and those that dominate more are selected to continue evolving. Finally, two groups of experiments are carried out. The results show that the low-carbon scheduling algorithm can effectively reduce the carbon footprint under the premise of makespan optimization and the HNSGA-II outperforms the traditional NSGA-II and can solve the MFFSP-VPTRE effectively and efficiently.

Solving no-wait two-stage flexible flow shop scheduling problem with unrelated parallel machines and rework time by the adjusted discrete Multi Objective Invasive Weed Optimization and fuzzy dominance approach

Purpose: Adjusted discrete Multi-Objective Invasive Weed Optimization (DMOIWO) algorithm, which uses fuzzy dominant approach for ordering, has been proposed to solve No-wait two-stage flexible flow shop scheduling problem.Design/methodology/approach: No-wait two-stage flexible flow shop scheduling problem by considering sequence-dependent setup times and probable rework in both stations, different ready times for all jobs and rework times for both stations as well as unrelated parallel machines with regards to the simultaneous minimization of maximum job completion time and average latency functions have been investigated in a multi-objective manner. In this study, the parameter setting has been carried out using Taguchi Method based on the quality indicator for beater performance of the algorithm.Findings: The results of this algorithm have been compared with those of conventional, multi-objective algorithms to show the better performance of the proposed algorithm. The results clearly indicated the greater performance of the proposed algorithm.Originality/value: This study provides an efficient method for solving multi objective no-wait two-stage flexible flow shop scheduling problem by considering sequence-dependent setup times, probable rework in both stations, different ready times for all jobs, rework times for both stations and unrelated parallel machines which are the real constraints.

A bi-objective simulation-optimization approach for solving a no-wait two stages flexible flow shop scheduling problem with rework ability

The paper suggests a new rule; called no-wait process. The rule has two stages, and is a flexible flow shop scheduling. The process is the subject to maximize tardiness while minimizing the makespan. This hybrid flow shop problem is known to be NP-hard. Therefore, we come to first, Non-dominated Sorting Genetic Algorithm (NSGA-II), then, Multi-Objective Imperialist Competitive Algorithm (MOICA) and finally, Pareto Archive Evolutionary Strategy (PAES) as three multi-objective Pareto based metaheuristic optimization methods. They are developed to solve the problem to approximately figure out optimal Pareto front. The method is investigated in several problems that differed in size and terms of relative percentage deviation of performance metrics. The conclusion, developed by this method is the most efficient and practicable algorithm at the end.

Improved teaching\u2013learning-based and JAYA optimization algorithms for solving flexible flow shop scheduling problems

Flexible flow shop (or a hybrid flow shop) scheduling problem is an extension of classical flow shop scheduling problem. In a simple flow shop configuration, a job having ‘g’ operations is performed on ‘g’ operation centres (stages) with each stage having only one machine. If any stage contains more than one machine for providing alternate processing facility, then the problem becomes a flexible flow shop problem (FFSP). FFSP which contains all the complexities involved in a simple flow shop and parallel machine scheduling problems is a well-known NP-hard (Non-deterministic polynomial time) problem. Owing to high computational complexity involved in solving these problems, it is not always possible to obtain an optimal solution in a reasonable computation time. To obtain near-optimal solutions in a reasonable computation time, a large variety of meta-heuristics have been proposed in the past. However, tuning algorithm-specific parameters for solving FFSP is rather tricky and time consuming. To address this limitation, teaching–learning-based optimization (TLBO) and JAYA algorithm are chosen for the study because these are not only recent meta-heuristics but they do not require tuning of algorithm-specific parameters. Although these algorithms seem to be elegant, they lose solution diversity after few iterations and get trapped at the local optima. To alleviate such drawback, a new local search procedure is proposed in this paper to improve the solution quality. Further, mutation strategy (inspired from genetic algorithm) is incorporated in the basic algorithm to maintain solution diversity in the population. Computational experiments have been conducted on standard benchmark problems to calculate makespan and computational time. It is found that the rate of convergence of TLBO is superior to JAYA. From the results, it is found that TLBO and JAYA outperform many algorithms reported in the literature and can be treated as efficient methods for solving the FFSP.

A hybrid scheduling approach for a two-stage flexible flow shop with batch processing machines

In this paper, we discuss a flexible flow shop scheduling problem with batch processing machines at each stage and with jobs that have unequal ready times. Scheduling problems of this type can be found in semiconductor wafer fabrication facilities (wafer fabs). We are interested in minimizing the total weighted tardiness of the jobs. We present a mixed integer programming formulation. The batch scheduling problem is NP-hard. Therefore, an iterative stage-based decomposition approach is proposed that is hybridized with neighborhood search techniques. The decomposition scheme provides internal due dates and ready times for the jobs on the first and second stage, respectively. Each of the resulting parallel machine batch scheduling problems is solved by variable neighborhood search in each iteration. Based on the schedules of the subproblems, the internal due dates and ready times are updated. We present the results of designed computational experiments that also consider the number of machines assigned to each stage as a design factor. It turns out that the proposed hybrid approach outperforms an iterative decomposition scheme where a fairly simple heuristic based on time window decomposition and the apparent tardiness cost dispatching rule is used to solve the subproblems. Recommendations for the design of the two stages with respect to the number of parallel machines on each stage are given.

Uncertain flexible flow shop scheduling problem subject to breakdowns

Flexible flow shop scheduling problems become more complex when uncertain factors are taken into consideration. Most literature are under the assumption that machines are continuous available. But, a machine can be unavailable for many reasons, such as breakdown and planned preventive maintenance. Once a machine breaks down, then the original schedule can not be executed and we must make the corresponding adjustment according to the actual situation. This paper deals with a flexible flow shop scheduling problem with uncertain processing and repair time subject to breakdowns. Machines are non-continuously available, i.e., they break down at arbitrary time instance not known in advance. The problem with breakdowns is modeled as a series of problems without breakdowns. To solve the problem, approaches including genetic algorithm and particle swarm optimization are used in this paper. A numerical example shows the effectiveness of the proposed approach.

Flexible Flowshop Scheduling Model with Four Stages

Objectives: In this paper, we consider the Flexible Flowshop Scheduling (FFS) problem with parallel machines. The main objective of this paper is to obtain a good schedule of jobs to minimize the makespan of FFS problem. Methods/Statistical analysis: In this study, two heuristic algorithms have been developed of FFS to reduce the makespan. First, we constructed the new heuristic algorithm based on Minimum Processing Time Selective Approach (MPTSA) and Longest Processing Times (LPT) approach to find the optimal or near optimal sequence for minimization of makespan of FFS problem with parallel machines. Next, we developed the heuristic algorithm using PALMER approach. In the PALMER approach we sequence the jobs based on Longest Slope Value (LSV) and obtained the value of objective function. Findings: We compared both the heuristic algorithms with the help of numerical illustrations. We solved the same numerical by both the heuristic algorithm and result show that our constructed heuristic algorithm has resulted in a better industrial production makespan. The percentage improvement of our constructive heuristic algorithm is also calculated. Gantt chart is also generated to verify the effectiveness of constructed heuristic algorithm. Application/Improvements: Our constructed heuristic algorithm is more effective to reduced the makespan of FFS problems as compare to classic heuristic algorithm as Palmer approach and provide an important tool for decision makers in production management.

Stochastic flexible flow shop scheduling problem under quantitative and qualitative decision criteria

This paper addresses a bi-criteria stochastic flexible flow shop (SFFS) scheduling problem in which one criterion is quantitative and the other is qualitative. The quantitative criterion is the total weighted tardiness and the qualitative criterion is the importance of the customer for the company. To solve this problem, the integral analysis method (IAM), which consists of four stages (description of the problem, cardinal analysis, ordinal analysis and integration analysis), was used. The cardinal analysis implements both a mixed integral linear programming (MILP) model and a simulation-optimization approach for the total weighted tardiness solution. The ordinal analysis is performed by stochastic multicriteria acceptability analysis with ordinal data (SMAA-O) in which each alternative is qualified depending on customer importance. Finally, to address the integral analysis, deterministic SMAA is applied to select those alternatives that exhibited the best integral characteristics in terms of minimizing tardiness penalty costs and timely fulfillment of due dates according to customer strategic importance for the company. Results show that IAM enables selection of the alternatives that accomplish in the best way both types of criteria.

Two new meta-heuristics for no-wait flexible flow shop scheduling problem with capacitated machines, mixed make-to-order and make-to-stock policy

This paper focuses on solving no-wait flexible flow shop scheduling problem with capacitated machines and mixed make-to-order and make-to-stock production management policy restrictions. The considered objective function is minimization of the sum of tardiness cost, weighted earliness cost, weighted rejection cost and weighted incomplete cost. Considering the literature, this problem is known as NP-hard. Hence, the cloudy-based simulated annealing (CSA) and artificial immune system are developed to solve the considered problem. Due to the fact that the parameters may influence the meta-heuristic algorithms, the parameters tuning is performed by Taguchi method. Finally, the performances of algorithms are evaluated by solving the randomly generated problems. Computational experiments show that the CSA algorithm obtains higher-quality solutions than another one.