Flexible flow shop scheduling with uniform parallel 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.

A constraint programming approach for resource-constrained flexible assembly flow shop scheduling problem with batch direct delivery

The flexible flow-shop scheduling problem (FFSSP) is an important branch of production scheduling, the flexible flow shop is a combination of two well-known machine environments, which are flow shops and parallel machines, and it is well known that this problem is NP-hard. The no-wait requirement is a phenomenon that may occur in flow shops, and it's prevent the jobs to wait between two successive machines (or stages), jobs must be processed from the start to finish, without any interruption on machines (or stages) or between them. Many different approaches have been applied to FFSSP with no-wait. In this research, two-stage no-wait flexible flow shop scheduling problem (NWFFSSP) has been solved using two meta-heuristics, which are Tabu Search (TS) and Particle Swarm Optimization (PSO). We solved the NWFFSSP with minimum makespan as a performance measure. The performance of the proposed algorithms are studied and compared with previous research results using the same problem data. The results of the study proposes the effective algorithm.

The paper suggests a new rule; called no-wait process. The rule has two stages, and is a flexible flow shop scheduling. The process is the subject to maximize tardiness while minimizing the makespan. This hybrid flow shop problem is known to be NP-hard. Therefore, we come to first, Non-dominated Sorting Genetic Algorithm (NSGA-II), then, Multi-Objective Imperialist Competitive Algorithm (MOICA) and finally, Pareto Archive Evolutionary Strategy (PAES) as three multi-objective Pareto based metaheuristic optimization methods. They are developed to solve the problem to approximately figure out optimal Pareto front. The method is investigated in several problems that differed in size and terms of relative percentage deviation of performance metrics. The conclusion, developed by this method is the most efficient and practicable algorithm at the end.

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

A multi-level action coupling reinforcement learning approach for online two-stage flexible assembly flow shop scheduling

Effective upper and lower bounds for a two-stage reentrant flexible flow shop scheduling problem

Effective constructive heuristics for distributed no-wait flexible flow shop scheduling problem

Objectives: In this paper, we consider the Flexible Flowshop Scheduling (FFS) problem with parallel machines. The main objective of this paper is to obtain a good schedule of jobs to minimize the makespan of FFS problem. Methods/Statistical analysis: In this study, two heuristic algorithms have been developed of FFS to reduce the makespan. First, we constructed the new heuristic algorithm based on Minimum Processing Time Selective Approach (MPTSA) and Longest Processing Times (LPT) approach to find the optimal or near optimal sequence for minimization of makespan of FFS problem with parallel machines. Next, we developed the heuristic algorithm using PALMER approach. In the PALMER approach we sequence the jobs based on Longest Slope Value (LSV) and obtained the value of objective function. Findings: We compared both the heuristic algorithms with the help of numerical illustrations. We solved the same numerical by both the heuristic algorithm and result show that our constructed heuristic algorithm has resulted in a better industrial production makespan. The percentage improvement of our constructive heuristic algorithm is also calculated. Gantt chart is also generated to verify the effectiveness of constructed heuristic algorithm. Application/Improvements: Our constructed heuristic algorithm is more effective to reduced the makespan of FFS problems as compare to classic heuristic algorithm as Palmer approach and provide an important tool for decision makers in production management. Keywords: Flexible Flowshop Scheduling, Gantt Chart, LPT Approach, Makespan, MPTSA Approach, Parallel Machines, Percentage Improvement

Bi-objective optimization of flexible flow shop scheduling problem with multi-skilled human resources

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

The cutting and sewing process is a traditional flow shop scheduling problem in the real world. This two-stage flexible flow shop is often commonly associated with manufacturing in the fashion and textiles industry. Many investigations have demonstrated that the ant colony optimization (ACO) algorithm is effective and efficient for solving scheduling problems. This work applies a novel effective ant colony optimization (EACO) algorithm to solve two-stage flexible flow shop scheduling problems and thereby minimize earliness, tardiness, and makespan. Computational results reveal that for both small and large problems, EACO is more effective and robust than both the particle swarm optimization (PSO) algorithm and the ACO algorithm. Importantly, this work demonstrates that EACO can solve complex scheduling problems in an acceptable period of time.

Flexible flow shop scheduling problem (FFSP) is recognized as an important class of problems in manufacturing systems. To consider more actual production factors, such as transportation time, setup times, blocking constraint, etc., we solved the FFSP using the improved genetic algorithm (GA) and discrete event simulation (DES). Firstly, a mathematical model for FFSP with the objective of minimizing total completion time was established. Besides, a GA mixed with Palmer heuristic algorithm was proposed to solve the mathematical model. Moreover, a DES software-plant simulation-was used to establish a more realistic production model, and an actual production workshop was modeled and optimized. After optimization, the total completion time and equipment utilization were greatly improved compared with the original scheduling. It shows the effectiveness and rationality of the proposed method to solve the actual FFSP.

We study the bicriteria scheduling of equal length jobs on uniform parallel machines. By introducing a new scheduling model, called single-machine scheduling with generated completion times (shortly, GCT-scheduling), we show that the scheduling of equal length jobs on uniform parallel machines can be polynomially transformed into the single-machine GCT-scheduling with a special setting of generated completion times. In the GCT-scheduling, a sequence of completion times is given in advance and the job scheduled at the i-th position will be assigned the i-th completion time. We present a comprehensive study on the complexities of the bicriteria single-machine GCT-scheduling problems with respect to various regular criteria. We then turn these complexity results into the forms of bicriteria scheduling of equal length jobs on uniform (or identical) parallel machines. Our research generalizes the existing results on bicriteria scheduling of equal length jobs in the literature. Particularly, one of our results solves the open problem posed by Sarin and Prakash (J Comb Optim 8:227–240, 2004), which asks for minimizing the total weighted completion time subject to the optimality of minimizing the total number of tardy jobs on identical parallel machines, and we show that this problem is solvable in polynomial time.

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.