Flexible Flow Shop Research Articles

Flexible Flow Shop Scheduling Method with Public Buffer

Actual manufacturing enterprises usually solve the production blockage problem by increasing the public buffer. However, the increase of the public buffer makes the flexible flow shop scheduling rather challenging. In order to solve the flexible flow shop scheduling problem with public buffer (FFSP–PB), this study proposes a novel method combining the simulated annealing algorithm-based Hopfield neural network algorithm (SAA–HNN) and local scheduling rules. The SAA–HNN algorithm is used as the global optimization method, and constructs the energy function of FFSP–PB to apply its asymptotically stable characteristic. Due to the limitations, such as small search range and high probability of falling into local extremum, this algorithm introduces the simulated annealing algorithm idea such that the algorithm is able to accept poor fitness solution and further expand its search scope during asymptotic convergence. In the process of local scheduling, considering the transferring time of workpieces moving into and out of public buffer and the manufacturing state of workpieces in the production process, this study designed serval local scheduling rules to control the moving process of the workpieces between the public buffer and the limited buffer between the stages. These local scheduling rules can also be used to reduce the production blockage and improve the efficiency of the workpiece transfer. Evaluated by the groups of simulation schemes with the actual production data of one bus manufacturing enterprise, the proposed method outperforms other methods in terms of searching efficiency and optimization target.

Approximation algorithms for two-stage flexible flow shop scheduling

This paper considers a two-stage flexible flow shop scheduling problem, where there are a single machine at the first stage and m parallel machines at the second stage. Each task can be processed by multiple parallel machines at the second stage. The objective is to minimize the makespan. Under some special conditions there is a 3-approximation algorithm for this problem. We propose a new ($$2+\epsilon $$)-approximation algorithm without any condition. For the case where all parallel machines assigned to a task at the second stage must have contiguous addresses, we propose two polynomial time approximation algorithms with approximate ratio less than or equal to 3 by using the existing parallel machine scheduling and strip packing results. Meanwhile two special cases are discussed when the machines number of the second stage is 2 and 3 respectively. Two approximation algorithms with approximation ratios of 2.5 and 2.67 under linear time complexity are proposed. Finally a new lower bound of the model is provided according to the classical Johnson algorithm which improves the previous result.

Flexible flow shop scheduling problem to minimize makespan with renewable resources

This paper deals with a flexible flow shop (FFS) scheduling problem with unrelated parallel machines and renewable resource shared among the stages. The FFS scheduling problem is one of the most common manufacturing environment in which there is more than a machine in at least one production stage. In such a system, to decrease the processing times, additional renewable resources are assigned to the jobs or machines, and it can lead to decrease the total completion time. For this purpose, a mixed integer linear programming (MILP) model is proposed to minimize the maximum completion time (makespan) in an FFS environment. The proposed model is computationally intractable. Therefore, a particle swarm optimization (PSO) algorithm as well as a hybrid PSO and simulated annealing (SA) algorithm named SA-PSO, are developed to solve the model. Through numerical experiments on randomly generated test problems, the authors demonstrate that the hybrid SA-PSO algorithm outperforms the PSO, especially for large size test problems.

Energy-efficient flexible flow shop scheduling with worker flexibility

The classical flexible flow shop scheduling problem (FFSP) only considers machine flexibility. Thus far, the relevant literature has not studied FFSPs with worker flexibility, which is widely seen in practical manufacturing systems. Worker flexibility may greatly affect production efficiency and productivity. Furthermore, with the increase of environmental pollution and energy consumption, manufacturers require innovative methods to improve energy efficiency. In this paper, we propose an energy-efficient FFSP with worker flexibility (EFFSPW), in which the flexibility of machines and workers as well as the processing time, energy consumption and worker cost related factors are considered simultaneously. A hybrid evolutionary algorithm (HEA) is then presented to solve the proposed EFFSPW, where some effective operators and a new variable neighborhood search approach are designed. Comprehensive experiments including 54 benchmark instances of the EFFSPW are carried out, and Taguchi analysis is used to determine the best combination of key parameters for the HEA. Experimental results show that the proposed HEA can obtain better solutions for most of these benchmark instances compared to two other well-known algorithms, demonstrating its superior performance in terms of both solution quality and computational efficiency.

Research on Simulation Decision of Logistics in Flexible Factory

Aiming at problems that the flexible scheduling capability of the production line in the existing factory is poor due to islanding effect and existing scheduling methods ignore non-cutting time and dynamic change of time when solve the minimum completion time, this paper studies the optimization of multi-variety and small batch workflow scheduling, and establishes an optimal job flow allocation model based on dynamic time parameters. Taking a flexible flow shop as an example, the model is applied to the implementation, and the EM-PLANT simulation software is used to make digital decision to realize the scientific scheduling of workpiece flow in cyber environment of production line. The simulation results show that the optimal allocation model can reduce the average completion time of workflow and improve production line efficiency.

Integration Design of Sortie Scheduling for Carrier Aircrafts Based on Hybrid Flexible Flowshop

Previous studies focused on deck-disposed and trajectory planning problem separately, and there was no systematic study from the whole process. This paper studied sortie scheduling for carrier aircrafts from the perspective of the whole scheduling and dispatch process. According to the process of sortie on flight deck, the sortie task was abstracted into six virtual stages, namely, deck-disposed, taxiing to preparing spot, taxiing from preparing spot to catapult, preparation on the catapult, takeoff, and cooling and recovery for the jet blast deflectors, and, the corresponding machines were also defined, respectively. The constraints were expressed, and the sortie scheduling model was build based on hybrid flexible flowshop scheduling. In addition, the one-sided symplectic pseudospectral method and the proposed collision avoidance strategy based on priority principle were combined to realize the collaborative trajectories planning of taxiing for multiple aircrafts. To obtain the optimal or near optimal solution, the double-layer genetic algorithm was proposed. Finally, the experiments were carried out based on the Nimitz-class aircraft carrier; the sortie task of 8 aircrafts under unknown conditions of deck-disposed and 13 aircrafts with fixed deck-disposed were studied, respectively. Experimental results show that the established model can well describe the sortie of aircraft, and it meets all constraints and actual requirements, which shows that the proposed method and the model can be used for sortie task effectively.

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.

Blockchain-oriented dynamic modelling of smart contract design and execution in the supply chain

Recently, the applications of Blockchain technology have begun to revolutionise different aspects of supply chain (SC) management. Among others, Blockchain is a platform to execute the smart contracts in the SC as transactions. We develop and test a new model for smart contract design in the SC with multiple logistics service providers and show that this problem can be presented as a multi-processor flexible flow shop scheduling. A distinctive feature of our approach is that the execution of physical operations is modelled inside the start and completion of cyber information services. We name this modelling concept ‘virtual operation’. The constructed model and the developed experimental environment constitute an event-driven dynamic approach to task and service composition when designing the smart contract. Our approach is also of value when considering the contract execution stage. The use of state control variables in our model allows for operations status updates in the Blockchain that in turn, feeds automated information feedbacks, disruption detection and control of contract execution. The latter launches the re-scheduling procedure, comprehensively combining planning and adaptation decisions within a unified methodological framework of dynamic control theory. The modelling complex developed can be used to design and control smart contracts in the SC.

A Simultaneous Worker Assignment and Scheduling Problem to Minimize Makespan in Flexible Flow Shop via Metaheuristic Approaches

A Simultaneous Worker Assignment and Scheduling Problem to Minimize Makespan in Flexible Flow Shop via Metaheuristic Approaches

An Improved Compact Genetic Algorithm for Scheduling Problems in a Flexible Flow Shop with a Multi-Queue Buffer

Flow shop scheduling optimization is one important topic of applying artificial intelligence to modern bus manufacture. The scheduling method is essential for the production efficiency and thus the economic profit. In this paper, we investigate the scheduling problems in a flexible flow shop with setup times. Particularly, the practical constraints of the multi-queue limited buffer are considered in the proposed model. To solve the complex optimization problem, we propose an improved compact genetic algorithm (ICGA) with local dispatching rules. The global optimization adopts the ICGA, and the capability of the algorithm evaluation is improved by mapping the probability model of the compact genetic algorithm to a new one through the probability density function of the Gaussian distribution. In addition, multiple heuristic rules are used to guide the assignment process. Specifically, the rules include max queue buffer capacity remaining (MQBCR) and shortest setup time (SST), which can improve the local dispatching process for the multi-queue limited buffer. We evaluate our method through the real data from a bus manufacture production line. The results show that the proposed ICGA with local dispatching rules and is very efficient and outperforms other existing methods.

Discrete and continuous-time formulations for dealing with break periods: Preemptive and non-preemptive scheduling

This paper presents new mixed-integer linear programming (MILP) approaches for handling preemption both in discrete and continuous-time scheduling formulations. Preemption refers to the capability of interrupting the execution of a task when encountering a pre-defined break period, assuming that the task continues immediately after the end of such time window. We rely on Generalized Disjunctive Programming to derive the constraints for the continuous-time formulations and on a compact convex hull reformulation to make them computationally efficient. We investigate both the general precedence and multiple time grids representation concepts. Generalization of the discrete-time formulation is simpler, involving a change in the model parameters. Validation and comparison of the mathematical formulations is done through the solution of sixteen benchmark problems, involving instances with one to four sets of breaks. The results show that the general precedence formulation is computationally more effective for flexible flowshops, being outperformed by the discrete-time approach when considering common rather than machine-dependent breaks. For single stage plants with parallel units, the continuous multiple time grid formulation prevails.

The economic lot scheduling problem in limited-buffer flexible flow shops: Mathematical models and a discrete fruit fly algorithm

This paper considers the lot scheduling problem in the flexible flow shop with limited intermediate buffers to minimize total cost which includes the inventory holding and setup costs. The single available mathematical model by Akrami et al. (2006) for this problem suffers from not only being non-linear but also high size-complexity. In this paper, two new mixed integer linear programming models are developed for the problem. Moreover, a fruit fly optimization algorithm is developed to effectively solve the large problems. For model’s evaluation, this paper experimentally compares the proposed models with the available model. Moreover, the proposed algorithm is also evaluated by comparing with two well-known algorithms (tabu search and genetic algorithm) in the literature and adaption of three recent algorithms for the flexible flow shop problem. All the results and analyses show the high performance of the proposed mathematical models as well as fruit fly optimization algorithm.

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.

Multi‐level, multi‐stage lot‐sizing and scheduling in the flexible flow shop with demand information updating

AbstractMotivated by a real‐world problem in an automobile manufacturing firm, we study the multi‐level, multi‐stage lot‐sizing and scheduling problem with demand information updating. The objective is to determine the quantities and sequences of production on different production stages to minimize the total costs of production and inventory. We employ the martingale model for forecast evolution to model the evolving demand over time and build a mixed‐integer programing (MIP) model for the problem using a hybrid period approach (i.e., combining micro‐ and macro‐periods). To solve this NP‐hard problem, we propose three heuristic algorithms based on the idea of “relax‐and‐fix” within the rolling horizon framework. We conduct computational experiments to test the performance of the heuristic algorithms as well as compare the performance of the proposed heuristics with the benchmark procedure (truncated procedure for MIP) for both small‐ and large‐scale problem instances. The computational results show that Heuristic 1 performs the best among the three heuristic algorithms.

A multi-item multi-packaging model to minimise cost of lost units, unpacking cost and CO2 emissions

This paper presents two multi-objective models that integrate packaging size and production scheduling problems for a flexible flow shop system. The main objective is to find the packaging size of finished product per item and the production schedule that would minimise cost of lost units, unpacking cost, inventory cost, earliness/tardiness penalties and kilograms of carbon dioxide emitted by resources operation. Since the complexity of the proposed models, a Pareto-based hybrid genetic algorithm (HGA) is also developed. A case study was developed to analyse the performance of both models using different instances. Numerical results indicate that the outperformance of one model over the other depends on the demand and the packaging size.

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.

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.

Flexible Flowshop Design in Cellular Manufacturing Systems

This paper explores the flowshop cell design in the cellular manufacturing system to minimize the number of machines, considering shifting the bottleneck machine and the annual demand. In a flowshop cell, products are processed through a series of production stages. Based on the number of machines per stage, the cell can be classified as either a production line (flowshop) or flexible flowshop. Two steps are followed in this study to design flexible flowshop cell. First, the un-capacitated mathematical model distributes the products into families and their corresponding machines into cells (product family formulation). Second, two non-linear mathematical models are proposed to design flexible flowshop. The first non-linear mathematical model is developed to build a flexible flowshop cell based on production rates. In this context, the number of machines in the system is determined, considering the machine duplication possibilities per stage for all products simultaneously, based on minimizing the total mean capacity required. The minimum number of machines per system is determined using a second non-linear mathematical model, with the objective to minimize the number of machines in the cell. In the two proposed nonlinear mathematical models, there is a limitation for the number of machine types. The results show that, as machine duplication is allowed, the number of machines per cell increases. Therefore, flexible flowshop design contributes to minimize the total number of machines in the system. In this way, the number of cells is reduced while production rates increase, and the total number of machines and total mean capacity required decrease.

Optimization for energy-efficient flexible flow shop scheduling under time of use electricity tariffs

With the development of society and economy, the global energy problem has become increasingly critical. Methods for time of use electricity tariffs have been introduced to balance the demand for resource and increase the energy efficiency in manufacturing industry. The scheduling problem for flexible flow shop in the environment of TOU is studied in this paper. An energy consumption model of machine tools is established which involves the processing energy, standby energy and set-up energy for a detailed description of electricity cost in shop-floor. The Improved Strength Pareto Evolutionary Algorithm is employed in which a novel gene encoding considering processing sequence, machine tool and processing time simultaneously is proposed to obtain the Pareto Front of the makespan and electricity cost. A case study is presented and the result shows that the proposed method is applicable for trade-off of electricity cost and delivery time for the purpose of enhanced energy efficiency.

Multi-queue Limited Buffer Scheduling Problems in Flexible Flow Shop with Setup Times

Multi-queue Limited Buffer Scheduling Problems in Flexible Flow Shop with Setup Times