Flow Shop Scheduling Model Research Articles

Multi-machine flow shop scheduling problems with rejection using genetic algorithm

This work is a study on scheduling problem with rejection on a set of multi-machine in a flow-shop scheduling system. This paper will attempt to indicate development of a multi-machine flow-shop scheduling model considering rejection (this problem is NP-hard due to the NP-hardness of the same problem variation on a two-machine). We analyse the quality of a solution with two criteria: one is the make span and the one is the total rejection cost. The aim of this study is to present an approximation algorithm and three heuristic algorithms and a genetic algorithm (GA) and successfully applied to Multi-machine flow-shop scheduling model considering rejection to minimise the make span plus total rejection cost. Several tests problems were carried out to assess the performance of the proposed algorithms. We can conclude here that the GA is the most functional algorithm, followed by the approximation algorithm.

Dominance rule and opposition-based particle swarm optimization for two-stage assembly scheduling with time cumulated learning effect

This paper introduces a two-stage assembly flowshop scheduling model with time cumulated learning effect, which exists in many realistic scheduling settings. By the time cumulated learning effect, we mean that the actual job processing time of a job depends on its scheduled position as well as the processing times of the jobs already processed. The first stage consists of two independently working machines where each machine produces its own component. The second stage consists of a single assembly machine. The objective is to identify a schedule that minimizes the total completion time of all jobs. With analysis on the discussed problem, some dominance rules are developed to optimize the solving procedure. Incorporating with the developed dominance rules, a dominance rule and opposition-based particle swarm optimization algorithm (DR-OPSO) and branch-and-bound are devised. Computational experiments have been conducted to compare the performances of the proposed DR-OPSO and branch-and-bound through comparing with the standard O-PSO and PSO. The results fully demonstrate the efficiency and effectiveness of the proposed DR-OPSO algorithm, providing references to the relevant decision-makers in practice.

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.

Discrete particle swarm optimization to solve multi-objective limited-wait hybrid flow shop scheduling problem

This paper proposes a discrete Particle Swam Optimization (PSO) to solve limited-wait hybrid flowshop scheduing problem with multi objectives. Flow shop schedulimg represents the condition when several machines are arranged in series and each job must be processed at each machine with same sequence. The objective functions are minimizing completion time (makespan), total tardiness time, and total machine idle time. Flow shop scheduling model always grows to cope with the real production system accurately. Since flow shop scheduling is a NP-Hard problem then the most suitable method to solve is metaheuristics. One of metaheuristics algorithm is Particle Swarm Optimization (PSO), an algorithm which is based on the behavior of a swarm. Originally, PSO was intended to solve continuous optimization problems. Since flow shop scheduling is a discrete optimization problem, then, we need to modify PSO to fit the problem. The modification is done by using probability transition matrix mechanism. While to handle multi objectives problem, we use Pareto Optimal (MPSO). The results of MPSO is better than the PSO because the MPSO solution set produced higher probability to find the optimal solution. Besides the MPSO solution set is closer to the optimal solution

Three-stage flow-shop scheduling model with batch processing machine and discrete processing machine

This study discusses the model development of three-stage flow-shop scheduling involving Batch Processing Machine (BPM) and Discrete Processing Machine (DPM). Each job passes several stages of the production process from the first stage in DPM-a, the second stage in BPM, to the third stage in DPM-b. Each job is sequentially processed in DPM-a and DPM-b. in BPM; every job is handled simultaneously at the same time. The maximum weight determines the capacity of BPM. This study uses mathematic modeling approach. The result model produced in this study is Mixed Integer Linear Programming (MILP) Model. Purpose function model is minimizing total completion time. Model testing is done by using numerical examples with several data scenarios. The results showed that the model produced was the optimum model and provided a unique schedule pattern. In the future research can be formulated the heuristic model.

A fitness assignment strategy based on the grey and entropy parallel analysis and its application to MOEA

In this paper, grey and entropy parallel analysis (GEPA) is presented as a new fitness-assignment strategy for solving multi-objective optimization problems. An evolutionary algorithm based on GEPA is proposed, and the grey and entropy parallel relational grade (GEPRG) is used as the fitness value to guide the development of the evolutionary algorithm. Under the analysis of the existing research work, the multi-objective flow shop scheduling problem is chosen as the application object and a flow shop scheduling model with five objectives is established. GEPA_GA, the GA based on GEPA, is described. To verify the performance of the proposed algorithm, GEPA_GA, together with the GA based on the random weighting method (RW_GA), NSGA-II and the GA based on g-dominance (g_GA), are used to optimize the multi-objective flow shop scheduling problem. The experimental data are analyzed by the statistical analysis method, the Kruskal–Wallis test, and three evaluation metrics. The influences of the five grey relational operators and the distinguishing coefficient on the algorithm performance are also studied. Experiments shows that the results obtained by GEPA_GA are better than those of RW_GA, NSGA-II and g_GA even under the situation that the combination of operator and distinguishing coefficient is not the best. It is proven that GEPA_GA works well in solving the multi-objective flow shop scheduling optimization problem, and GEPA is a promising strategy for solving multi-objective optimization problems.

Permutation flow shop scheduling problem to minimize nonlinear objective function with release dates

In a dynamic flow shop scheduling model, each released job has to be executed on a set of machines in series following the identical route. The criterion of optimality, total k-power completion time (k≥2) is addressed for this problem. Given its NP-hardness, a branch and bound (B&B) algorithm is designed to obtain the optimal solutions for small-scale problems. On the basis of an initial population generated by the upper bounds of the B&B algorithm, a discrete differential evolution algorithm is introduced to solve medium-scale problems. As the by-product of the B&B algorithm, a sequence-independent lower bound with performance guarantee is presented as a substitute of the optimal solution for large-scale problems. Moreover, the worst-case ratio of the shortest-processing-time-based rule under a consistency condition is provided for the problem. The numerical experiments demonstrate the effectiveness of the proposed algorithms and the new lower bound.

Permutation flow-shop scheduling problem to optimize a quadratic objective function

ABSTRACTA flow-shop scheduling model enables appropriate sequencing for each job and for processing on a set of machines in compliance with identical processing orders. The objective is to achieve a feasible schedule for optimizing a given criterion. Permutation is a special setting of the model in which the processing order of the jobs on the machines is identical for each subsequent step of processing. This article addresses the permutation flow-shop scheduling problem to minimize the criterion of total weighted quadratic completion time. With a probability hypothesis, the asymptotic optimality of the weighted shortest processing time schedule under a consistency condition (WSPT-CC) is proven for sufficiently large-scale problems. However, the worst case performance ratio of the WSPT-CC schedule is the square of the number of machines in certain situations. A discrete differential evolution algorithm, where a new crossover method with multiple-point insertion is used to improve the final outcome, is presented to obtain high-quality solutions for moderate-scale problems. A sequence-independent lower bound is designed for pruning in a branch-and-bound algorithm for small-scale problems. A set of random experiments demonstrates the performance of the lower bound and the effectiveness of the proposed algorithms.

Optimized flowshop scheduling of multiple production lines for precast production

The current approach in practice to produce the flowshop schedules of precast production is the dispatching rule technique, which does not guarantee optimal schedules. Some researchers have developed models for a single production line to optimize the scheduling, in which Genetic Algorithm (GA) is used to obtain the solution. However the models cannot be used for multiple production lines. Moreover, some optimization constraints and objectives were missing in the models, such as avoiding frequent type change of precast components during production. Both issues hinder their work to be applied to real precast plants. To overcome the problem, this paper proposes a Flowshop Scheduling Model of Multiple production lines for Precast production (MP-FSM) and develops a corresponding optimization approach to facilitate optimized scheduling by using GA. The approach was validated preliminarily by comparing with traditional scheduling approaches. The results demonstrated that optimized schedules can be obtained by using the proposed approach.

A multi-objective teaching−learning-based optimization algorithm to scheduling in turning processes for minimizing makespan and carbon footprint

Industry is responsible for nearly half of the global energy consumption. Recent studies on sustainable manufacturing focused on energy saving to reduce the unit production cost and environmental impacts. Besides energy consumption, certain manufacturing activities in machine shops, such as the use of cutting fluids, disposal of worn tools, and material consumption, also cause other environmental impacts. Since all these activities lead to carbon footprint directly or indirectly, carbon footprint can be employed as a new and overall environment criterion in manufacturing. In this study, an integrated model for processing parameter optimization and flow-shop scheduling was developed. Objectives to minimize both makespan and carbon footprint were considered simultaneously, which was solved by a multi-objective teaching−learning-based optimization algorithm. Furthermore, three carbon-footprint-reduction strategies were employed to optimize the scheduling results: (i) postponing strategy, (ii) setup strategy, and (iii) processing parameter preliminary optimization strategy. In the theoretical aspect, the strategies greatly improved the performance of the optimization results through reducing machine idle time and cutting down the search space. From the perspective of practical applications, these strategies greatly help elevate production efficiency and reduce environmental impacts.

A bi-objective integrated procurement, production, and distribution problem of a multi-echelon supply chain network design: A new tuned MOEA

Efficient management of supply chain (SC) requires systematic considerations of miscellaneous issues in its comprehensive version. In this paper, a multi-periodic structure is developed for a supply chain network design (SCND) involving suppliers, factories, distribution centers (DCs), and retailers. The nature of the logistic decisions is tactical that encompasses procurement of raw materials from suppliers, production of finished product at factories, distribution of finished product to retailers via DCs, and the storage of raw materials and end product at factories and DCs. Besides, to make the structure more comprehensive, a flow-shop scheduling model in manufacturing part of the SC is integrated in order to obtain optimal delivery time of the product that consists of the makespan and the ship time of the product to DCs via factories. Moreover, to make the model more realistic, shortage in the form of backorder can occur in each period. The two objectives are minimizing the total SC costs as well as minimizing the average tardiness of product to DCs. The obtained model is a bi-objective mixed-integer non-linear programming (MINLP) model that is shown to belong to NP-Hard class of the optimization problems. Thus, a novel algorithm, called multi-objective biogeography based optimization (MOBBO) with tuned parameters is presented to find a near-optimum solution. As there is no benchmark available in the literature, the parameter-tuned multi-objective simulated annealing algorithm (MOSA) and the popular non-dominated sorting genetic algorithm (NSGA-II) are developed to validate the results obtained and to evaluate the performance of MOBBO using randomly generated test instances.

A cooperative co-evolutionary particle swarm optimiser based on a niche sharing scheme for the flow shop scheduling problem under uncertainty

The flow shop scheduling problem based on ideal and precise conditions has been a focus of considerable research since the first easy scheduling problem was formulated. In reality, some uncertain factors always restrict the scheduling optimisation problem. In this paper, taking uncertain processing time as an example, we use generalised rough sets theory to transform the rough flow shop scheduling model into the precise scheduling model. We adopt a cooperative co-evolutionary particle swarm optimisation algorithm based on a niche sharing scheme (NCPSO) to minimise the makespan in comparison with the particle swarm optimiser (PSO) and co-evolution particle swarm optimiser (CPSO) algorithms. The new algorithm is characterised by a strengthening of the ability to reserve excellent particles and searching the optimal solution. Experimental results show that the new algorithm is more effective and efficient than the others.

A memetic algorithm for the re-entrant permutation flowshop scheduling problem to minimize the makespan

A common assumption in the classical permutation flowshop scheduling model is that each job is processed on each machine at most once. However, this assumption does not hold for a re-entrant flowshop in which a job may be operated by one or more machines many times. Given that the re-entrant permutation flowshop scheduling problem to minimize the makespan is very complex, we adopt the CPLEX solver and develop a memetic algorithm (MA) to tackle the problem. We conduct computational experiments to test the effectiveness of the proposed algorithm and compare it with two existing heuristics. The results show that CPLEX can solve mid-size problem instances in a reasonable computing time, and the proposed MA is effective in treating the problem and outperforms the two existing heuristics.

Security based bi-objective flow shop scheduling model and its hybrid genetic algorithm

In this paper, we considered the flow shop scheduling problem with respect to the both objectives of the makespan and the mean continuous running time, proposed a security based bi-objective flow shop scheduling model. To solve the proposed model more effectively, we presented a hybrid genetic algorithm (HGA), which used some tailor made genetic operators and a local search operator in order to improve the local search ability of GA. The proposed algorithm is tested with some well-known problems in literature. The computational results demonstrated the effectiveness of the proposed algorithm.

Scheduling of Discrete Manufacturing Process for Energy Saving

Rotor machining is a traditional discrete manufacturing process, among which large amount of non-essential energy is being wasted. The machining process belongs to pipeline production, so a flow-shop scheduling model is built to optimize it. But when there are over three machines, this will be an NP-hard problem. We introduce an improved ant-colony algorithm to find the best solution and then use the real machining data to test it. The total energy consumption is reduced by over 10% and this shows the model and intelligent algorithm work well.

Time-window-based combined objective DE algorithm for hybrid flow-shop

In this paper, a time-window-based hybrid flow-shop scheduling model is presented for manufacturing enterprise for solving production scheduling optimisation problem in the rolling production process. Time window deviation sum and the earliness/tardiness (E/T) penalty sum’s optimisation goal are modelled, and differential evolution (DE) global optimisation algorithm is used to conduct the global optimisation. The assigned tasks to determine a job’s machining path in the time window frame can be finished in each stage. The hybrid flow-shop scheduling optimisation method based on time window can improve the equipment utilisation and reduce scheduling conflict situations. Our time-window-based hybrid flow-shop scheduling optimisation method is evaluated by multiple sets of programs’ numerical analysis, and the results show that the proposed approach can meet the requirement of business rolling production scheduling very well.

Nonpermutation flow line scheduling by ant colony optimization

AbstractA flow line is a conventional manufacturing system where all jobs must be processed on all machines with the same operation sequence. Line buffers allow nonpermutation flowshop scheduling and job sequences to be changed on different machines. A mixed-integer linear programming model for nonpermutation flowshop scheduling and the buffer requirement along with manufacturing implication is proposed. Ant colony optimization based heuristic is evaluated against Taillard's (1993) well-known flowshop benchmark instances, with 20 to 500 jobs to be processed on 5 to 20 machines (stages). Computation experiments show that the proposed algorithm is incumbent to the state-of-the-art ant colony optimization for flowshop with higher job to machine ratios, using the makespan as the optimization criterion.

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.

A hybrid flowshop scheduling model considering dedicated machines and lot-splitting for the solar cell industry

This paper studies a solar cell industry scheduling problem, which is similar to traditional hybrid flowshop scheduling (HFS). In a typical HFS problem, the allocation of machine resources for each order should be scheduled in advance. However, the challenge in solar cell manufacturing is the number of machines that can be adjusted dynamically to complete the job. An optimal production scheduling model is developed to explore these issues, considering the practical characteristics, such as hybrid flowshop, parallel machine system, dedicated machines, sequence independent job setup times and sequence dependent job setup times. The objective of this model is to minimise the makespan and to decide the processing sequence of the orders/lots in each stage, lot-splitting decisions for the orders and the number of machines used to satisfy the demands in each stage. From the experimental results, lot-splitting has significant effect on shortening the makespan, and the improvement effect is influenced by the processing time and the setup time of orders. Therefore, the threshold point to improve the makespan can be identified. In addition, the model also indicates that more lot-splitting approaches, that is, the flexibility of allocating orders/lots to machines is larger, will result in a better scheduling performance.

Inventory Based Bi-Objective Flow Shop Scheduling Model and Its Hybrid Genetic Algorithm

Flow shop scheduling problem is a typical NP-hard problem, and the researchers have established many different multi-objective models for this problem, but none of these models have taken the inventory capacity into account. In this paper, an inventory based bi-objective flow shop scheduling model was proposed, in which both the total completion time and the inventory capacity were as objectives to be optimized simultaneously. To solve the proposed model more effectively, we used a tailor-made crossover operator, and mutation operator, and designed a new local search operator, which can improve the local search ability of GA greatly. Based on all these, a hybrid genetic algorithm was proposed. The computer simulations were made on a set of benchmark problems, and the results indicated the effectiveness of the proposed algorithm.