Flexible Flow Shop Scheduling Research Articles

Multiple rules with game theoretic analysis for flexible flow shop scheduling problem with component altering times

This paper studies the flexible flow shop scheduling problem with component altering times (FFSP-CAT), which is a specific form of the flexible flow shop scheduling problem with sequence dependent setup times in the practical scenario. Dealing with FFSP-CAT includes the jobs' machine assignment determination and the globe optimisation. We develop six rules for jobs' machine assignment, and since these rules will easily conflict with one another if they are used with the same priorities, we construct a repeated cooperative model and provide a game theoretical analysis, then derive a Nash equilibrium machine assignment scheme (NEMAS) to effectively manage these rules for jobs' machines assignment at each stage. Furthermore, to achieve the global optimum, we design an advanced compact genetic algorithm (ACGA). By combining NEMAS and ACGA, an approach named advanced compact genetic algorithm with Nash equilibrium machine assignment scheme (ACGA-NEMAS) is used for minimising the makespan of FFSP-CAT. Through extensive comparison experiments with different scales of instances, we show that the algorithm with NEMAS acquires 56.85% improvement over the algorithm without NEMAS, and ACGA-NEMAS performs 80.28% better than genetic algorithm.

Two meta-heuristic algorithms for flexible flow shop scheduling problem with robotic transportation and release time

In this research, flexible flow shop scheduling with unrelated parallel machines at each stage are considered. The number of stages and machines vary at each stage and each machine can process specific operations. In other words, machines have eligibility and parts have different release times. In addition, the blocking restriction is considered for the problem. Parts should pass each stage and process on only one machine at each stage. In the proposed problem, transportation of parts, loading and unloading parts are done by robots and the objective function is finding an optimal sequence of processing parts and robots movements to minimize the makespan and finding the closest number to the optimal number of robots. The main contribution of this study is to present the mixed integer linear programming model for the problem which considers release times for parts in scheduling area, loading and unloading times of parts which transferred by robots. New methodologies are investigated for solving the proposed model. Ant Colony Optimization (ACO) with double pheromone and genetic algorithm (GA) are proposed. Finally, two meta-heuristic algorithms are compared to each other, computational results show that the GA performs better than ACO and the near optimal numbers of robots are determined.

Discrete Particle Swarm Optimization Algorithm in Flexible Hybrid Flow Shop Scheduling

Traditional flexible flow shop scheduling cannot adapt to the work processes with existence of parallel machines, and blocks or limits the processes with no-wait constraints. Firstly, according to the problem in NWBFFSSP, which minimizes the maximum time used in the flow shop, an optimal solving model has been designed to realize the flexible flow shop scheduling with multi constraints; besides, for the distribution of machinery is improved, Finally, in the solving process, a real-time release priority strategy has been proposed to determine processing machine for each work piece. Furthermore, a methodology to detect work piece conflicts has been introduced while the conflicts are then eliminated by a kind of right moving strategy based on the maximum difference. The experimental results verify the effectiveness and feasibility of the proposed algorithm.

Energy-efficient dynamic scheduling for a flexible flow shop using an improved particle swarm optimization

Due to increasing energy requirements and associated environmental impacts, nowadays manufacturing companies are facing the emergent challenges to meet the demand of sustainable manufacturing. Most existing research on reducing energy consumption in production scheduling problems has focused on static scheduling models. However, there exist many unexpected disruptions like new job arrivals and machine breakdown in a real-world production scheduling. In this paper, it is proposed an approach to address the dynamic scheduling problem reducing energy consumption and makespan for a flexible flow shop scheduling. Since the problem is strongly NP-hard, a novel algorithm based on an improved particle swarm optimization is adopted to search for the Pareto optimal solution in dynamic flexible flow shop scheduling problems. Finally, numerical experiments are carried out to evaluate the performance and efficiency of the proposed approach.

Application of Ontology in Event-Driven Job-Shop Scheduling Problems

Aiming at the flexible flow-shop scheduling problem of cloud manufacturing, this paper introduces event driven concept and apply ontologies to Job-Shop scheduling problem FT46. The inference of ontology models allows the system to gain the dynamic information of workshop, and then rule engine is used to match event patterns to optimize the job shop scheduling problem.

Scheduling of multi-component products in a two-stage flexible flow shop

In this research, the problem of scheduling and sequencing of two-stage assembly-type flexible flow shop with dedicated assembly lines, which produce different products according to requested demand during the planning horizon with the aim of minimizing maximum completion time of products is investigated. The first stage consists of several parallel machines in site I with different speeds in processing components and one machine in site II, and the second stage consists of two dedicated assembly lines. Each product requires several kinds of components with different sizes. Each component has its own structure which leading to difference processing times to assemble. Products composed of only single-process components are assigned to the first assembly line and products composed of at least a two-process component are assigned to the second assembly line. Components are placed on the related dedicated assembly line in the second phase after being completed on the assigned machines in the first phase and final products will be produced by assembling the components. The main contribution of our work is development of a new mathematical model in flexible flow shop scheduling problem and presentation of a new methodology for solving the proposed model. Flexible flow shop problems being an NP-hard problem, therefore we proposed a hybrid meta-heuristic method as a combination of simulated annealing (SA) and imperialist competitive algorithms (ICA). We implement our obtained algorithm and the ones obtained by the LINGO9 software package. Various parameters and operators of the proposed Meta-heuristic algorithm are discussed and calibrated by means of Taguchi statistical technique.

A dynamic co-evolution compact genetic algorithm for E/T problem

In this paper, a dynamic co-evolution compact genetic algorithm (DCCGA) is proposed for flexible flow shop scheduling problem (FFSP) to minimize the total earliness and tardiness (E/T) penalties. In this new algorithm, a dynamic co-evolution mechanism containing two probabilistic models and a best individual inheritance strategy are integrated into the compact genetic algorithm (CGA). For improving the stability of the evolutionary trend in the evolution processes, the diversity of evolution trend and the convergence speed. Lastly, the experimental results show that, DCCGA outperforms CGA by 11.74% on the problem we study.

Hybrid-particle Interaction Particle Swarm Optimization Algorithm

To overcome the searching shortages of the existing particle swarm optimization algorithms only considered a single kind of attraction and repulsion rules, different attraction and repulsion rules should be considered in different searching stages, later-stage attraction-enhanced hybrid attraction and repulsion particle swarm optimization algorithm(LAPSO algorithm) is proposed: At the early stage, the diversity of particles are maintained by the rules of attraction and repulsion in artificial physics, to improve the global searching ability; When the particles move to the global optimal solution area, enhanced the effect of attraction and reduced the effect of repulsion, using the attractions of other particles with better fitness values and the global optimal solution particle to improve the local searching ability. In order to further improve the optimal performance of LAPSO algorithm, hybrid-particle interaction particle swarm optimization algorithm(HIPSO algorithm) is proposed by combining LAPSO algorithm and hybrid fully connected-ring topology. The test results of six Benchmark functions show that the proposed LAPSO algorithm and HIPSO algorithm have better population diversity, better optimization precision, convergence rate and optimal solution searching ability than the existing extended-particle swarm optimization algorithm, micro-particle swarm optimization algorithm and median-oriented particle swarm optimization algorithm. The optimal solution searching ability of HIPSO algorithm is verified by the discrete optimization example of flexible flow-shop scheduling in the reference [7] and continuous optimization example of ultrasonic vibration process parameters in the reference [20].

Approximation algorithms for the three-stage flexible flow shop problem with mid group constraint

This paper considers a three-stage flexible flow shop scheduling problem, where the jobs have the group constraint at the second stage and the three stages consist of unrelated parallel machines. Because of the complexity of this problem, approximation algorithms are more appropriate to solve it. Firstly, we propose ten heuristic algorithms based on the idea of combined algorithms proposed by Soewandi and Elmaghraby (2001) and give their time complexities. Secondly, since there is no reference on the worst-case performance ratios of RDM, SP.H1 and SP.H2 algorithms for the unrelated parallel machines, we provide the worst-case performance ratios of these three algorithms and then give the worst-case performance ratios of the nine algorithms proposed in this paper. Finally, to evaluate the performance of the ten algorithms, four lower bounds of this problem are proposed in Appendix A and a computational experiment is designed, where lots of instances are generated and each algorithm is run with every instance. Experimental results indicate that the performances of ten heuristic algorithms are contingent on different configurations and SP.JH-MJ algorithm generally outperforms the others with respect to the three-stage flexible flow shop scheduling problem addressed in this paper.

A hybrid NSGA-II and VNS for solving a bi-objective no-wait flexible flowshop scheduling problem

We address the no-wait k-stage flexible flowshop scheduling problem where there are m identical machines at each stage. The objectives are to schedule the available n jobs so that makespan and mean tardiness of n jobs are minimized. Sequence-dependent setup times are treated in this problem as one of the prominent practical assumptions. This problem is NP-hard, and therefore we present a new multiobjective approach for solving the mentioned problem. The proposed meta-heuristic is evaluated based on randomly generated data in comparison with two well-known multiobjective algorithm including NSGA-II and SPEA-II. Due to sensitivity of our proposed algorithm to parameter values, a new approach for tackling of this issue was designed. Our proposed method includes Taguchi method (TM) and multiobjective decision making (MODM). We have chosen six measures into two groups. Qualitative metrics including number of Pareto solutions (NPS), diversity metric (DM) as well as the spread of non-dominance solution (SNS) and quantitative metrics including the rate of achievement to two objectives simultaneously (RAS), mean ideal distance (MID) and quality metric (QM) to evaluate the performance of our proposed algorithms. Computational experiments and comparisons show that the proposed NSGA-II + VNS algorithm generates better or competitive results than the existing NSGA-II and SPEA-II for the no-wait flexible flow shop scheduling problem with sequence-dependent setup times to simultaneous minimizing the makespan and mean tardiness criterion.

A Metaheuristic approach for Batch Sizing and Scheduling Problem in Flexible Flow Shop with Unrelated Parallel Machines

This article considers a makespan minimization batch sizing and scheduling problem in a flexible flow shop scheduling problem with unrelated parallel machines and sequence dependent setup time. Because of NP-completeness of this problem, it is necessary to use the heuristics method. Therefore, this article presents a new mixed simulated-genetic algorithm (MSGA) to tackle this problem. In the comparison, this research reports optimality gaps which are calculated with respect to MSGA method and optimal solution for small instances and the average objective function for large instances. Computational studies indicate that the MSGA is computationally efficient and effective even for small and large instances.

A note on “A mathematical model and extension algorithm for assembly flexible flow shop scheduling problem”

In a recent paper by Fattahi et al. (Int J Adv Manuf Technol 65:787–802, 2013), a mathematical model is presented for a two-stage assembly scheduling problem containing a hybrid flow shop and an assembly stage. Some constraints in the model are not valid. This note shows that some new constraints are proposed for the mathematical model. An example is proposed to present and prove this new model by executing mathematical software.

An intelligent hybrid meta-heuristic for solving a case of no-wait two-stage flexible flow shop scheduling problem with unrelated parallel machines

This paper addresses the problem of no-wait two-stage flexible flow shop scheduling problem (NWTSFFSSP) considering unrelated parallel machines, sequence-dependent setup times, probable reworks and different ready times to actualize the problem. The performance measure used in this study is minimizing maximum completion time (makespan). Because of the complexity of addressed problem, we propose a novel intelligent hybrid algorithm [called hybrid algorithm (HA)] based on imperialist competitive algorithm (ICA) which are combined with simulated annealing (SA), variable neighborhood search (VNS) and genetic algorithm (GA) for solving the mentioned problem. The hybridization is carried out to overcome some existing drawbacks of each of these three algorithms and also for increasing the capability of ICA. To achieve reliable results, Taguchi approach is used to define robust parameters' values for our proposed algorithm. A simulation model is developed to study the performance of our proposed algorithm against ICA, SA, VNS, GA and ant colony optimization (ACO). The results of the study reveal the relative superiority of HA studied. In addition, potential areas for further researches are highlighted.

A holonic approach to flexible flow shop scheduling under stochastic processing times

Flexible flow shop scheduling problems are NP-hard and tend to become more complex when stochastic uncertainties are taken into consideration. This paper presents a novel decomposition-based holonic approach (DBHA) for minimising the makespan of a flexible flow shop (FFS) with stochastic processing times. The proposed DBHA employs autonomous and cooperative holons to construct solutions. When jobs are released to an FFS, the machines of the FFS are firstly grouped by a neighbouring K-means clustering algorithm into an appropriate number of cluster holons, based on their stochastic nature. A scheduling policy, determined by the back propagation networks (BPNs), is then assigned to each cluster holon for schedule generation. For cluster holons of a low stochastic nature, the Genetic Algorithm Control (GAC) is adopted to generate local schedules in a centralised manner; on the other hand, for cluster holons of a high stochastic nature, the Shortest Processing Time Based Contract Net Protocol (SPT-CNP) is applied to conduct negotiations for scheduling in a decentralised manner. The combination of these two scheduling policies enables the DBHA to achieve globally good solutions, with considerable adaptability in dynamic environments. Computation results indicate that the DBHA outperforms either GAC or SPT-CNP alone for FFS scheduling with stochastic processing times.

Scheduling rules for two-stage flexible flow shop scheduling problem subject to tail group constraint

This paper considers a two-stage flexible flow shop scheduling problem with task tail group constraint, where the two stages are made up of unrelated parallel machines. The objective is to find a schedule to minimize the total tardiness of jobs. For this problem, a mathematical model is formulated. Through analyzing this kind of problem, it is proved to be NP-hard and an advantage scheduling rule is proposed. According to the advantage scheduling rule, a new heuristic method called EL algorithm, is designed to solve this problem. From the theoretical analysis of EL algorithm, we provide EL algorithm with the time complexity and worst-case analysis. To test the performance of EL algorithm, a computational experiment is designed. In the computational experiment, both the twelve dispatching rules based on the literatures and EL algorithm are applied to the benchmark instances. Simulation results indicate that LPT–CDS, SPT–Pal, SPT–CDS and EL algorithms are effective and EL algorithm outperforms the other twelve dispatching rules with respect to the two-stage flexible flow shop scheduling problem proposed in this paper.

No-wait two stage hybrid flow shop scheduling with genetic and adaptive imperialist competitive algorithms

This article studies a no-wait two-stage flexible flow shop scheduling problem with setup times aiming to minimize the total completion time. The problem is solved using an adaptive imperialist competitive algorithm (AICA) and genetic algorithm (GA). To test the performance of the proposed AICA and GA, the algorithms are compared with ant colony optimisation, known as an effective algorithm in the literature. The performance of the algorithms are evaluated by solving both small and large-scale problems. Their performance is evaluated in terms of relative percentage deviation. Finally the results of the study are discussed and conclusions and potential areas for further study are highlighted.

Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm

Abstract The traditional production scheduling problem considers performance indicators such as processing time, cost, and quality as optimization objectives in manufacturing systems; however, it does not take energy consumption or environmental impacts completely into account. Therefore, this paper proposes an energy-efficient model for flexible flow shop scheduling (FFS). First, a mathematical model for a FFS problem, which is based on an energy-efficient mechanism, is described to solve multi-objective optimization. Since FFS is well known as a NP-hard problem, an improved, genetic-simulated annealing algorithm is adopted to make a significant trade-off between the makespan and the total energy consumption to implement a feasible scheduling. Finally, a case study of a production scheduling problem for a metalworking workshop in a plant is simulated. The experimental results show that the relationship between the makespan and the energy consumption may be apparently conflicting. In addition, an energy-saving decision is performed in a feasible scheduling. Using the decision method, there could be significant potential for minimizing energy consumption.

Bi-objective simulated annealing approaches for no-wait two-stage flexible flow shop scheduling problem

This paper focuses on solving the bi-objective problem of no-wait two-stage flexible flow shop scheduling. The objectives considered in this study are minimum makespan (Cmax), as well as maximum tardiness of jobs (Tmax). This problem is known as NP-hard. Hence, three bi-objective optimization methods based on simulated annealing, called CWSA (classical weighted simulated annealing), NWSA (normalized weighted simulated annealing), and FSA (fuzzy simulated annealing), are developed to solve the problem with the goal of finding approximations of the optimal Pareto front. Due to the fact that meta-heuristic algorithms are very vigilant of parameter values, we proposed a new reliable method, by mixing the Taguchi method and a Multi-Objective Decision Making (MODM) approach, for achieving our purpose. The algorithms are evaluated by solving both small and large scale problems. The performances are evaluated in terms of a relative deviation index. Finally, the result of the study is discussed and concluded, and potential areas of further study are highlighted.

A hybrid water flow algorithm for multi-objective flexible flow shop scheduling problems

In this article, the multi-objective flexible flow shop scheduling problem with limited intermediate buffers is addressed. The objectives considered in this problem consist of minimizing the completion time of jobs and minimizing the total tardiness time of jobs. A hybrid water flow algorithm for solving this problem is proposed. Landscape analysis is performed to determine the weights of objective functions, which guide the exploration of feasible regions and movement towards the optimal Pareto solution set. Local and global neighbourhood structures are integrated in the erosion process of the algorithm, while evaporation and precipitation processes are included to enhance the solution exploitation capability of the algorithm in unexplored neighbouring regions. An improvement process is used to reinforce the final Pareto solution set obtained. The performance of the proposed algorithm is tested with benchmark and randomly generated instances. The computational results and comparisons demonstrate the effectiveness and efficiency of the proposed algorithm.

A heuristic algorithm for two-stage flexible flow shop scheduling with head group constraint

On the background of the shops in the mould manufacturers, in this paper, a two-stage flexible flow shop scheduling problem is first described to minimise the makespan with head group constraint and released time, where the first stage consists of unrelated parallel work centres. Next, this problem is proved to be NP-hard. After that, a constructive heuristic algorithm, named as H′, is proposed and then both its time complexity and worst-case bound are analysed in detail. In addition, three classical heuristics are improved for the solution of this problem and their time complexity is also given. In order to test the efficiency of the H′ algorithm, sets of instances are designed. Compared with the three improved heuristics by means of these sets of examples, the performance of the H′ algorithm is superior. Furthermore, the H′ algorithm can even solve large-size practical problems in a reasonable solution time, which is significant to the application in the shops of mould makers.