Solving Flow Shop Scheduling Problem Research Articles

Integration of MILP and discrete-event simulation for flow shop scheduling using Benders cuts

Optimization-based scheduling in the chemical industry is highly beneficial but also highly difficult due to its combinatorial complexity. Different modeling and optimization techniques exist, each with individual strengths. We propose Benders decomposition to integrate mixed-integer linear programming (MILP) and discrete-event simulation (DES) to solve flow shop scheduling problems with makespan minimization objective. The basic idea is to generate valid Benders cuts based on sensitivity information of the DES sub problem, which can be found in the critical paths of DES solutions. For scaled literature flow shops, our approach requires at least an order of magnitude fewer iterations than a genetic algorithm and provides optimality gap information. For a real-world case study, our approach finds good solutions very quickly, making it a powerful alternative to established methods. We conclude that the Benders-DES algorithm is a promising approach to combine rigorous MILP optimization capabilities with high-fidelity DES modeling capabilities.

Q-Learning-Based Priority Dispatching Rule Preference Model for Non-Permutation Flow Shop

Non-permutation flow shop scheduling (NPFS) is an extension of the traditional permutation flow shop scheduling, with a broader solution space. The effectiveness of reinforcement learning in solving flow shop scheduling problems has been demonstrated through its powerful combinatorial optimization capabilities. However, the design and training of the end-to-end policy network is complex, leading to long online training time and limited adaptability of offline training. To overcome these problems, we introduced a NPFS dynamic decision-making process and then proposed a novel NPFS method that combines the Q-learning algorithm with the priority dispatching rule (PDR) set. The NPFS dynamic decision-making process involves decomposing the entire process into multiple sub-job queues for scheduling. The PDR demonstrates better scheduling performance when applied to smaller job queues. By utilizing the Q-learning algorithm, PDRs with superior performance are assigned to sub-scheduling queues based on the generation process of sub-job sequences, resulting in an optimized NPFS strategy. The limited number of PDRs in the PDR set and the small number of sub-job queues in the NPFS process contribute to the efficiency of Q-learning in solving NPFS problem. Finally, we demonstrate the superiority of the proposed NPFS method by a series of numerical experiments using the machine-based assignment PDR method and NSGA-II algorithms as performance benchmarks.

The Effectiveness of Genetic Algorithm, And the CDS Method In Solving Flowshop Scheduling Problems

Flow shop scheduling problem is considered NP-hard for m machines and n jobs. For such NP-hard combinatorial optimization problems, heuristics play a major role in searching for near-optimal solutions. In this paper we used Genetic Algorithm, and the CDS method for solving flow shop scheduling problem with makespan as the criteria. The objective of this model is to obtain a sequence of jobs and the minimization of the total completion time (makespan). To test the effectiveness of the method, a dataset of case studies is used to compare the makespan values obtained for each method.

Optimizing production scheduling with the spotted hyena algorithm: A novel approach to the flow shop problem

The spotted hyena optimization algorithm (SHOA) is a novel approach for solving the flow shop-scheduling problem in manufacturing and production settings. The motivation behind SHOA is to simulate the social dynamics and problem-solving behaviors of spotted hyena packs in order to identify and implement optimal schedules for jobs in a flow shop environment. This approach is unique compared to other optimization algorithms such as WOA, GWO, and BA. Through extensive experimentation, SHOA has been shown to outperform traditional algorithms in terms of solution quality and convergence speed. The purpose of this study is to present the details of the SHOA algorithm, demonstrate its effectiveness, and compare its performance with other optimization approaches. The method used in this study includes extensive experimentation and comparison with other algorithms. The findings of this study show that SHOA is a promising tool for optimizing production processes and increasing efficiency. The implications of this study are that SHOA can be used as an effective tool for solving flow shop-scheduling problems in manufacturing and production settings.

A Hybrid Discrete Memetic Algorithm for Solving Flow-Shop Scheduling Problems

Flow-shop scheduling problems are classic examples of multi-resource and multi-operation scheduling problems where the objective is to minimize the makespan. Because of the high complexity and intractability of the problem, apart from some exceptional cases, there are no explicit algorithms for finding the optimal permutation in multi-machine environments. Therefore, different heuristic approaches, including evolutionary and memetic algorithms, are used to obtain the solution—or at least, a close enough approximation of the optimum. This paper proposes a novel approach: a novel combination of two rather efficient such heuristics, the discrete bacterial memetic evolutionary algorithm (DBMEA) proposed earlier by our group, and a conveniently modified heuristics, the Monte Carlo tree method. By their nested combination a new algorithm was obtained: the hybrid discrete bacterial memetic evolutionary algorithm (HDBMEA), which was extensively tested on the Taillard benchmark data set. Our results have been compared against all important other approaches published in the literature, and we found that this novel compound method produces good results overall and, in some cases, even better approximations of the optimum than any of the so far proposed solutions.

A bi-objective hybrid vibration damping optimization model for synchronous flow shop scheduling problems

Flow shop scheduling deals with the determination of the optimal sequence of jobs processing on machines in a fixed order with the main objective consisting of minimizing the completion time of all jobs (makespan). This type of scheduling problem appears in many industrial and production planning applications. This study proposes a new bi-objective mixed-integer programming model for solving the synchronous flow shop scheduling problems with completion time. The objective functions are the total makespan and the sum of tardiness and earliness cost of blocks. At the same time, jobs are moved among machines through a synchronous transportation system with synchronized processing cycles. In each cycle, the existing jobs begin simultaneously, each on one of the machines, and after completion, wait until the last job is completed. Subsequently, all the jobs are moved concurrently to the next machine. Four algorithms, including non-dominated sorting genetic algorithm (NSGA II), multi-objective simulated annealing (MOSA), multi-objective particle swarm optimization (MOPSO), and multi-objective hybrid vibration-damping optimization (MOHVDO), are used to find a near-optimal solution for this NP-hard problem. In particular, the proposed hybrid VDO algorithm is based on the imperialist competitive algorithm (ICA) and the integration of a neighborhood creation technique. MOHVDO and MOSA show the best performance among the other algorithms regarding objective functions and CPU Time, respectively. Thus, the results from running small-scale and medium-scale problems in MOHVDO and MOSA are compared with the solutions obtained from the epsilon-constraint method. In particular, the error percentage of MOHVDO’s objective functions is less than 2% compared to the epsilon-constraint method for all solved problems. Besides the specific results obtained in terms of performance and, hence, practical applicability, the proposed approach fills a considerable gap in the literature. Indeed, even though variants of the aforementioned meta-heuristic algorithms have been largely introduced in multi-objective environments, a simultaneous implementation of these algorithms as well as a compared study of their performance when solving flow shop scheduling problems has been so far overlooked.

Nash equilibrium inspired greedy search for solving flow shop scheduling problems

Nash equilibrium inspired greedy search for solving flow shop scheduling problems

Solving flow shop scheduling problem based on improved non-dominated genetic algorithm

Aiming at the multi-objective problem of flow workshop problem, a multi-objective optimization model was constructed and an improved non-dominated sorting genetic algorithm was proposed. Firstly, aiming at these problems, this paper proposes a two-stage chromosome coding method to adapt to the new production scenarios. Secondly, a new adaptive method is proposed to improve the convergence speed and the superiority of Pareto solution set. Finally, simulation results show that the optimality of the improved non-dominated sorting genetic algorithm is improved greatly.

Solving flow shop scheduling problems with the objective of minimizing TCT when tie occurs

Scheduling process arises naturally upon availability of resources through a systematic approach in which prior planning and decisions should be made. Two machine flow shop scheduling problem (FSSP) was solved by Johnson in the mid of 1954 with makespan minimization as objective. Earlier we proposed two algorithms for the makespan objective; in this paper we intend to investigate the same algorithms for the objective of Total Completion Time of all the jobs (TCT). Experimental results had shown that one of our algorithms gives better results than the other two when the machine order is reversed.

A parameter tuned hybrid algorithm for solving flow shop scheduling problems with parallel assembly stages

In this paper, we study the scheduling problem for a customized production system consisting of a flow shop production line with a parallel assembly stage that produces various products in two stages. In the first stage of the production line, parts are produced using a flow shop production line, and in the second stage, products are assembled on one of the parallel assembly lines. The objective is to minimize the time required to complete all goods (makespan) using efficient scheduling. A mathematical model is developed; however, the model is NP-hard and cannot be solved in a reasonable amount of time. To solve this NP-hard problem, we propose two well-known metaheuristics and a hybrid algorithm. To calibrate and improve the performance of our algorithms, we employ the Taguchi method. We evaluate the performance of our hybrid algorithm with the two well-known methods of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) and demonstrate that our hybrid algorithm outperforms both the GA and PSO approaches in terms of efficiency.

Solving a flow shop scheduling problem with missing operations in an Industry 4.0 production environment

Industry 4.0 is a modern approach that aims at enhancing the connectivity between the different stages of the production process and the requirements of consumers. This paper addresses a relevant problem for both Industry 4.0 and flow shop literature: the missing operations flow shop scheduling problem. In general, in order to reduce the computational effort required to solve flow shop scheduling problems only permutation schedules (PFS) are considered, i.e., the same job sequence is used for all the machines involved. However, considering only PFS is not a constraint that is based on the real-world conditions of the industrial environments, and it is only a simplification strategy used frequently in the literature. Moreover, non-permutation (NPFS) orderings may be used for most of the real flow shop systems, i.e., different job schedules can be used for different machines in the production line, since NPFS solutions usually outperform the PFS ones. In this work, a novel mathematical formulation to minimize total tardiness and a resolution method, which considers both PFS and (the more computationally expensive) NPFS solutions, are presented to solve the flow shop scheduling problem with missing operations. The solution approach has two stages. First, a Genetic Algorithm, which only considers PFS solutions, is applied to solve the scheduling problem. The resulting solution is then improved in the second stage by means of a Simulated Annealing algorithm that expands the search space by considering NPFS solutions. The experimental tests were performed on a set of instances considering varying proportions of missing operations, as it is usual in the Industry 4.0 production environment. The results show that NPFS solutions clearly outperform PFS solutions for this problem.

A new heuristic for flowshop scheduling problems minimizing system utilization time subject to minimum makespan

This paper presents a heuristic algorithm to solve flow shop scheduling problems (FSSP) with the criterion to minimise the system utilisation time with minimum of maximum completion time (makespan)...

African Buffalo Optimization for Solving Flow Shop Scheduling Problem to Minimize Makespan

In this paper, African Buffalo Optimization is proposed to solve the flow-shop Scheduling Problem (FSP). The FSP involves n-job that was processed in m-machine. The aim is to reduce the makespan of the whole process. In this study, we also compare the African Buffalo Optimization with an exact solution and other meta-heuristic methods, such as Particle Swarm Optimization (PSO), Hybrid Genetics Algorithm, and also Crow-search Algorithm (CSA) to know the performance of the methods in solution quality and computational time. Friedman test showing African Buffalo Optimization gives an optimal solution in solution quality, the same result with the exact solution, PSO, and hybrid GA.

Multi-Objective Artificial Bee Colony Algorithms and Chaotic-TOPSIS Method for Solving Flowshop Scheduling Problem and Decision Making

Retrieval of optimal solution(s) for a permutation flowshop scheduling problem within a reasonable computational timeframe has been a challenge till yet. The problem includes optimization of various criterions like makespan, total flowtime, earliness, tardiness, etc and obtaining a Pareto solution for final decision making. This paper remodels a discrete artificial bee colony algorithm for permutation flowshop scheduling problem executed through three different scenarios raised the analysis of time complexity measure. To enhance the search procedure, we have explored the alternative and combined use of two local search algorithms named as: iterated greedy search algorithm and iterated local search algorithm in our discrete artificial bee colony algorithm and the results are summarized with respect to completion time, mean weighted tardiness, and mean weighted earliness. The two algorithms are prioritised on insertion and swap of neighbourhood structures which will intensify the local optima in the search space. Further the performance of the algorithm is compared with the test results of multi-objective artificial bee colony algorithm. The result of our optimization process concludes with a set of non-dominated solutions lead to different Pareto fronts. Finally, we propose a chaotic based technique for order of preference by similarity to ideal solution (chaotic-TOPSIS) using a suitable chaotic map for criteria adaptation in order to enhance the decision accuracy in the multi-objective problem domain.

Two NEH Heuristic Improvements for Flowshop Scheduling Problem with Makespan Criterion

Since its creation by Nawaz, Enscore, and Ham in 1983, NEH remains the best heuristic method to solve flowshop scheduling problems. In the large body of literature dealing with the application of this heuristic, it can be clearly noted that results differ from one paper to another. In this paper, two methods are proposed to improve the original NEH, based on the two points in the method where choices must be made, in case of equivalence between two job orders or partial sequences. When an equality occurs in a sorting method, two results are equivalent, but can lead to different final results. In order to propose the first improvement to NEH, the factorial basis decomposition method is introduced, which makes a number computationally correspond to a permutation. This method is very helpful for the first improvement, and allows testing of all the sequencing possibilities for problems counting up to 50 jobs. The second improvement is located where NEH keeps the best partial sequence. Similarly, a list of equivalent partial sequences is kept, rather than only one, to provide the global method a chance of better performance. The results obtained with the successive use of the two methods of improvement present an average improvement of 19% over the already effective results of the original NEH method.

A two-phase simulated annealing algorithm to minimise the completion time variance of jobs in flowshops

In this paper, simulated annealing (SA) algorithm is employed to solve the flowshop scheduling problem with the objective of minimising the completion time variance (CTV) of jobs. Four variants of the two-phase SA algorithm (SA-I to SA-IV) are proposed to solve flowshop scheduling problem with the objective of minimising the CTV of jobs without considering the right shifting of completion time of jobs on the last machine. The proposed SA algorithms have been tested on 90 benchmark flowshop scheduling problems. The solutions yielded by the proposed SA variants are compared with the best CTV of jobs reported in the literature, and the proposed SA-III is found to perform well in minimising the chosen performance measure (CTV) particularly in medium and large size problems.

A new approach for solving flow shop scheduling problems with generalized intuitionistic fuzzy numbers

A new approach for solving flow shop scheduling problems with generalized intuitionistic fuzzy numbers

Flowshop scheduling with artificial neural networks

For effective modelling of flowshop scheduling problems, artificial neural networks (ANNs), due to their robustness, parallelism and predictive ability have been successfully used by researchers. These studies reveal that the ANNs trained with conventional back propagation (CBP) algorithm utilising the gradient descent method are commonly applied to model and solve flowshop scheduling problems. However, the existing scheduling literature has not explored the suitability of some improved neural network training algorithms, such as gradient descent with adaptive learning (GDAL), Boyden, Fletcher, Goldfarb and Shanno updated Quasi-Newton (UQ-N), and Levenberg-Marquardt (L-M) algorithms to solve the flowshop scheduling problem. In this article, we investigate the use of these training algorithms as competitive neural network learning tools to minimise makepsan in a flowshop. Based on training and testing measures, overall results from extensive computational experiments demonstrate that, in terms of the solution quality and computational effort required, the L-M algorithm performs the best followed by the UQ-N algorithm, GDAL algorithm, and the CBP algorithm. These computational results also reveal that the average percent deviation of the makespan from its best solution obtained by using the ANN trained with the L-M algorithm is the least among all examined approaches for the benchmark problem instances.

An improvement heuristic for permutation flow shop scheduling

An improvement heuristic algorithm is proposed in this paper for solving flow shop scheduling problem (Fm / prmu / Cmax). To test its efficiency, firstly the performance of the proposed algorithm is done against the six heuristics existing in the literature including the best NEH heuristic on 120 Taillard benchmarks. Further, this set of 120 Taillard instances is increased to 266 benchmark problem instances which include Carlier's, some Reeves and some new hard VRF instances from Vallada et al. (2015). On these instances, the performance of the proposed algorithm is tested against the best NEH and the famous CDS heuristic with the best known upper bounds. Further, a brief analysis of the other heuristics and metaheuristics existing in literature is done on Taillard problem instances. The proposed heuristic outperforms all the heuristics reported in this paper.

An improvement heuristic for permutation flow shop scheduling

An improvement heuristic algorithm is proposed in this paper for solving flow shop scheduling problem (Fm / prmu / Cmax). To test its efficiency, firstly the performance of the proposed algorithm is done against the six heuristics existing in the literature including the best NEH heuristic on 120 Taillard benchmarks. Further, this set of 120 Taillard instances is increased to 266 benchmark problem instances which include Carlier's, some Reeves and some new hard VRF instances from Vallada et al. (2015). On these instances, the performance of the proposed algorithm is tested against the best NEH and the famous CDS heuristic with the best known upper bounds. Further, a brief analysis of the other heuristics and metaheuristics existing in literature is done on Taillard problem instances. The proposed heuristic outperforms all the heuristics reported in this paper.