On-line Algorithms for Hybrid Flow Shop Scheduling (original) (raw)
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Scheduling a two-stage hybrid flow shop with parallel machines at the first stage
Annals of Operations Research, 1997
This paper considers a non-preemptive two-stage hybrid flow shop problem in which the first stage contains several identical machines, and the second stage contains a single machine. Each job is to be processed on one of the first-stage machines, and then on the second-stage machine. The objective is to find a schedule which minimizes the maximum completion time or makespan. The problem is NP-hard in the strong sense, even when there are two machines at the first stage. Several lower bounds are derived and are tested in a branch and bound algorithm. Also, constructive heuristics are presented, and a descent algorithm is proposed. Extensive computational tests with up to 250 jobs, and up to 10 machines in the first stage, indicate that some of the heuristics consistently generate optimal or near-optimal solutions.
The hybrid flow shop scheduling problem
2010
The scheduling of flow shops with multiple parallel machines per stage, usually referred to as the Hybrid Flow Shop (HFS), is a complex combinatorial problem encountered in many real world applications. Given its importance and complexity, the HFS problem has been intensively studied. This paper presents a literature review on exact, heuristic and metaheuristic methods that have been proposed for its solution. The paper discusses several variants of the HFS problem, each in turn considering different assumptions, constraints and objective functions. Research opportunities in HFS are also discussed.
This paper investigates a difficult scheduling problem on a specialized two-stage hybrid flow shop with multiple processors that appears in semiconductor manufacturing industry, where the first and second stages process serial jobs and parallel batches, respectively. The objective is to seek job-machine, job-batch, and batch-machine assignments such that makespan is minimized, while considering parallel batch, release time, and machine eligibility constraints. We first propose a mixed integer programming (MIP) formulation for this problem, then gives a heuristic approach for solving larger problems. In order to handle real world large-scale scheduling problems, we propose an efficient dispatching rule called BFIFO that assigns jobs or batches to machines based on first-in-first-out principle, and then give several reoptimization techniques using MIP and local search heuristics involving interchange, translocation and transposition among assigned jobs. Computational experiments indicate our proposed re-optimization techniques are efficient. In particular, our approaches can produce good solutions for scheduling up to 160 jobs on 40 machines at both stages within 10 min.
Invited Review The hybrid flow shop scheduling problem
The scheduling of flow shops with multiple parallel machines per stage, usually referred to as the hybrid flow shop (HFS), is a complex combinatorial problem encountered in many real world applications. Given its importance and complexity, the HFS problem has been intensively studied. This paper presents a literature review on exact, heuristic and metaheuristic methods that have been proposed for its solution. The paper briefly discusses and reviews several variants of the HFS problem, each in turn considering different assumptions, constraints and objective functions. Research opportunities in HFS are also discussed.
2020
This paper presents an effective memetic algorithm (MA) for a hybrid flow shop scheduling problem with multiprocessor tasks (HFSMT) to minimize the makespan. The problem is modeled as deterministic by a mixed graph. This problem has at least two production stages, each of which has several machines, operating in parallel. Two sub-problems are considered for solving this problem: determining the sequence of jobs in the first stage and reducing the idle time of the processors in the next stages. The developed algorithm uses an operator called Bad Selection Operator. This operator holds the worst chromosomes of each generation and uses them to search in the space of other problems at predetermined timescales. Besides, this algorithm uses a dynamic adjustment structure to improve the ratio of crossover and mutation operators that could reduce the execution time. The efficiency of the proposed MA is investigated by testing it on well-known benchmark instances and also compared with other...
Three Algorithms for Flexible Flow-shop Scheduling
American Journal of Applied Sciences, 2007
Scheduling is an important process widely used in manufacturing, production, management, computer science, and so on. Appropriate scheduling can reduce material handling costs and time. Finding good schedules for given sets of jobs can thus help factory supervisors effectively control job flows and provide solutions for job sequencing. 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. Flexible flow shops are thus generalization of simple flow shops. In this paper, we propose three algorithms to solve flexible flow-shop problems of more than two machine centers. The first one extends Sriskandarajah and Sethi's method by combining both the LPT and the search-and-prune approaches to get a nearly optimal makespan. It is suitable for a medium-sized number of jobs. The second one is an optimal algorithm, entirely using the search-and-prune technique. It can work only when the job number is small. The third one is similar to the first one, except that it uses Petrov's approach (PT) to deal with job sequencing instead of searchand-prune. It can get a polynomial time complexity, thus being more suitable for real applications than the other two. Experiments are also made to compare the three proposed algorithms. A trade-off can thus be achieved between accuracy and time complexity.
Dynamic set-up rules for hybrid flow shop scheduling with parallel batching machines
International Journal of Production Research, 2013
An S-stage hybrid (or flexible) flowshop, with sequence-independent uniform setup times, parallel batching machines with compatible parallel batch families (like in casting or heat treatments in furnaces, chemical or galvanic baths, painting in autoclave etc.) has been analyzed with the purpose of reducing the number of tardy jobs (and the makespan); in Graham's notation: FPB(m 1 , m 2 , … , m S )|p-batch, ST si,b |ΣU i . Jobs are sorted dynamically (at each new delivery); batches are closed within sliding (or rolling) time windows and processed in parallel by multiple identical machines. Computation experiments have shown the better performance on benchmarks of the two proposed heuristics based on new formulations of the critical ratio (CR setup ) considering the ratio of allowance setup and processing time in the scheduling horizon, which improves the weighted modified operation due date rule (WMOD).
Two-stage hybrid flow shop with precedence constraints and parallel machines at second stage
Computers & Operations Research, 2012
This study deals with the two-stage hybrid flow shop (HFS) problem with precedence constraints. Two versions are examined, the classical HFS where idle time between the operations of the same job is allowed and the no-wait HFS where idle time is not permitted. For solving these problems an adaptive randomized list scheduling heuristic is proposed. Two global bounds are also introduced so as to conservatively estimate the distance to optimality of the proposed heuristic. The evaluation is done on a set of randomly generated instances. The heuristic solutions for the classical HFS in average are provably situated below 2% from the optimal ones, and on the other hand, in the case of the no-wait HFS the average deviation is below 5%.
Minimizing makespan in a three-stage hybrid flow shop with dedicated machines
International Journal of Industrial Engineering Computations
In recent years, many studies on scheduling problems with dedicated machines have been carried out. But, few of them have considered the case of more than two stages. This paper aims at filling this gap by addressing the three-stage hybrid flow shop scheduling problem with two dedicated machines in stage 3. Each job must be processed, consecutively, on the single machines of stages 1 and 2, and depending on its type, it will be further processed on one of the two dedicated machines of stage 3. The objective is to find an optimal schedule that minimizes the maximum completion time (makespan). Since this problem is strongly NP-hard, we first provide some basic results including solutions for several variations of the problem. Then, for the general case we adapt a set of lower bounds from the literature and propose a heuristic approach that is based on the dynamic programming technique, which uses a local search procedure. Finally, various experimentations on several problems with different sizes are conducted and the computational results of the heuristic show that the mean percentage deviation value from the lower bound was lower than 0.8 percent for some instances with 40 to 200 jobs in size.