On the two-stage assembly flow shop problem

This paper studies the two-stage assembly flow shop problem (TAFSP) considering aging effects of the machines and preventive maintenance activities. At the first stage, m-1 parallel machines process parts of each jobs, and at the second stage, related parts of the jobs are assembled by one assembly machine. As the machines work on the jobs, their tools get aged. Aging effects on the machines causes that they will not be able to complete the jobs in the same time could as they were new or when they are operating jobs immediately after their preventive maintenance activity. Processing times of the job are related to the positions, in which it is located after the last preventive maintenance. The job that is operated in a position immediately after the preventive maintenance activity on a machine has its standard processing time. However, the processing time of the jobs operated in the further positions increase based on the number of the positions. The machines return to the initial condition after each preventive maintenance activity. The objective is to schedule the jobs on the machines and determine when the preventive maintenance activities get done on them in order to minimize the total weighted tardiness and maintenance costs. An integer mathematical model is presented for the problem and its validation is shown by solving an example in small scale. Since two-stage assembly flow shop problem is NP-hard, in order to solve the problem in medium and large scale two meta-heuristic algorithms, hybrid genetic algorithm (HGA) and hybrid particle swarm optimization (HPSO) are proposed. These algorithms are the hybrid version of genetic algorithm and particle swarm optimization representatively with simulated annealing. The algorithms are tuned by using Taguchi method, and are used to solve many numerical examples. Finally, the statistical analysis illustrates that the performance of HPSO is better than HGA.

This paper investigates integrated two-stage assembly flow shop problem with preventive maintenance (PM) activities under the multi-objective optimisation approaches. Reliability models are employed to carry out the maintenance activities. This paper attempts to find the appropriate sequence of jobs on machines in order to minimise the makespan and determining when to perform the PM activities in order to minimise the system unavailability. As this problem is proven to be NP-hard two multi-objective optimisation methods that are named non-dominated sorting genetic algorithm II (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are employed to find the Pareto-optimal front. The parameters of proposed algorithms are calibrated by artificial neural network (ANN) and the performances of the algorithms on the problem of various sizes are analysed based on four metrics. The computational results reveal NRGA is statistically better than NSGA-II.

This article deals with the two-stage assembly flow shop problem considering preventive maintenance activities and machine breakdowns. The objective is to minimize the makespan. This problem is proven to be NP-hard; thus, we proposed two meta-heuristic algorithms, namely, imperialist competitive algorithm and genetic algorithm, to obtain solutions of the problem. This article describes an approach incorporating simulation with imperialist competitive algorithm for the scheduling purpose having machine breakdowns and preventive maintenance activities. The results obtained are analyzed using Taguchi experimental design, and the parameters of proposed algorithms are calibrated by artificial neural network. The computational results demonstrate that imperialist competitive algorithm is statistically better than genetic algorithm in quality of solution and reaches to better solutions at the same computational time.

Memetic social spider optimization algorithm for scheduling two-stage assembly flowshop in a distributed environment

Mathematical models for multi-stage hybrid assembly flow-shop scheduling with preventive maintenance and release times

To enhance the overall performance of supply chains, coordination among production and distribution stages has recently received an increasing interest. This paper considers the coordinated scheduling of production and transportation in a two-stage assembly flowshop environment. In this problem, product components are first produced and assembled in a two-stage assembly flowshop, and then completed final products are delivered to a customer in batches. Considering the NP-hard nature of this scheduling problem, two fast heuristics (SPT-based heuristic and LPT-based heuristic) and a new hybrid meta-heuristic (HGA-OVNS) are presented to minimise the weighted sum of average arrival time at the customer and total delivery cost. To guide the search process to more promising areas, the proposed HGA-OVNS integrates genetic algorithm with variable neighbourhood search (VNS) to generate the offspring individuals. Furthermore, to enhance the effectiveness of VNS, the opposition-based learning (OBL) is applied to establish some novel opposite neighbourhood structures. The proposed algorithms are validated on a set of randomly generated instances, and the computation results indicate the superiority of HGA-OVNS in quality of solutions.

A novel hybrid discrete differential evolution algorithm for blocking flow shop scheduling problems

This paper considers an assembly scheduling problem which minimizes the total weighted tardiness. The system consists of multiple manufacturing machines in the first stage and an assembly machine in the second stage. A job is composed of multiple components, each component is manufactured on a dedicated machine in the first stage, and the assembly starts on the assembly machine after the completion of all the components’ manufacturing in the first stage. This paper is to try to find effective and efficient schedules to minimize the total weighted tardiness of jobs. This paper analyzes some solution properties to improve search effectiveness and efficiency. Moreover, some lower-bound procedures are derived, and then four constructive heuristics and a branch-and-bound algorithm are suggested. The performances of the derived algorithms are evaluated through numerical experiments. For the problems with no more than 15 jobs, the branch-and-bound algorithm finds the optimal solutions within 20 minutes, and the performance of the four heuristics seems to be similar. However, for problems with more than 30 jobs, HWT shows the best performance among the four heuristics except for two machines.

In simple flow shop problems, each machine operation center includes just one machine. If at least one machine center includes more than one machine, the scheduling problem becomes a flexible flow shop problem (FFSP). Flexible flow shops are thus generalization of simple flow shops. Flexible flow shop scheduling problems have a special structure combining some elements of both the flow shop and the parallel machine scheduling problems. FFSP can be stated as finding a schedule for a general task graph to execute on a multiprocessor system so that the schedule length can be minimized. FFSP is known to be NP-hard. In this study, we present a particle swarm optimization (PSO) algorithm to solve FFSP. PSO is an effective algorithm which gives quality solutions in a reasonable computational time and consists of less numbers parameters as compared to the other evolutionary metaheuristics. Mutation, a commonly used operator in genetic algorithm, has been introduced in PSO so that trapping of solutions at local minima or premature convergence can be avoided. Logistic mapping is used to generate chaotic numbers in this paper. Use of chaotic numbers makes the algorithm converge fast towards near-optimal solution and hence reduce computational efforts further. The performance of schedules is evaluated in terms of total completion time or makespan (Cmax). The results are presented in terms of percentage deviation (PD) of the solution from the lower bound. The results are compared with different versions of genetic algorithm (GA) used for the purpose from open literature. The results indicate that the proposed PSO algorithm is quite effective in reducing makespan because average PD is observed as 2.961, whereas GA results in average percentage deviation of 3.559. Finally, influence of various PSO parameters on solution quality has been investigated.

Flexible flow shop scheduling with uniform parallel machines

In order to solve the flow shop problem efficiently, an immune algorithm is proposed to solve the flow shop scheduling problem. The algorithm is designed according to the immune system mechanism of human or other higher animals, takes the scheduling objectives and constraints as the antigen, takes the solution of the problem as the antibody, encodes the antibody with natural numbers according to the workpiece processing order, and takes the reciprocal of the maximum process time as the fitness function. Through the introduction of isolation niche and other technologies, the adaptability of the immune algorithm is improved, the diversity of the population is ensured, and the premature convergence is overcome, The convergence speed is improved. The benchmark test of flow shop problem shows that the algorithm not only has good scalability in the scale of solving the problem, but also is lower than tabu search algorithm and simulated annealing algorithm in operation time, which verifies the effectiveness of the algorithm.

In this paper, a network based formulation of a permutation flow shop problem is presented. Two nuances of flow shop problems with different levels of complexity are solved using different approaches to the linear programming formulation. Key flow shop parameters inclosing makespan of the flow shop problems were obtained without recourse to the traditional approach of using Gantt charts. The linear programming models of the flow shop problems considered were solved using LINGO 7.0. The present technique has been shown to be very effective and efficient.http://dx.doi.org/10.4314/njt.v34i2.11

This article describes a heuristic algorithm which will yield an optimal or near optimal minimal makespan solution to a specific type of sequencing/scheduling problem defined as the dependent sequencing problem which includes the pure job-shop and flow-shop sequencing problems. The name ‘ dependent sequencing ’ was selected for this model since it reflects the possibility of interdependence between activities of the technological processing order graph (GTPO) not present in ‘ pure ’ job -shop or f low-shop sequencing models. There are some approaches to this class of problem which provide optimal solutions, but their time to solutions and/or theoretical approaches make them difficult to understand and apply. Recent articles in the literature have recommended that research in the sequencing/ scheduling area be directed toward developing practical approaches which can be easily understood and applied. The dependent shop algorithm utilizes extensions of PERT/CPM techniques which are widely known and therefor...

This note studies the flow shop scheduling problems with the effects of exponential learning and simple linear deterioration. The objective functions are to minimize makespan, total completion, the sum of the th power of completion times and total lateness. We show that several flow shop problems can be solved in polynomial time.

On scheduling in a GT environment