2018
DOI: 10.1007/978-3-319-78825-8_26
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Efficient Lagrangian Heuristics for the Two-Stage Flow Shop with Job Dependent Buffer Requirements

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Cited by 4 publications
(4 citation statements)
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“…Examples for methods from the literature for this flow shop type are a Variable Neighborhood Search by Kononova and Kochetov (2013), where Integer Linear Programming was also used to solve small instances, a Branch-and-Bound algorithm used to calculate lower bounds and optimally solve small instances with up to 18 jobs (Lin et al, 2009) as well as a heuristic based on Lagrangian relaxation and bin packing (Kononov et al, 2019). This buffer type is also analyzed by Gu et al (2018) Figure 1: Overview of works containing comparisons between algorithms for buffered flow shops with intermediate buffers. The notation A ← B indicates that algorithm A is outperformed by algorithm B in the given reference.…”
Section: Related Workmentioning
confidence: 99%
“…Examples for methods from the literature for this flow shop type are a Variable Neighborhood Search by Kononova and Kochetov (2013), where Integer Linear Programming was also used to solve small instances, a Branch-and-Bound algorithm used to calculate lower bounds and optimally solve small instances with up to 18 jobs (Lin et al, 2009) as well as a heuristic based on Lagrangian relaxation and bin packing (Kononov et al, 2019). This buffer type is also analyzed by Gu et al (2018) Figure 1: Overview of works containing comparisons between algorithms for buffered flow shops with intermediate buffers. The notation A ← B indicates that algorithm A is outperformed by algorithm B in the given reference.…”
Section: Related Workmentioning
confidence: 99%
“…Proof Let n = 6, and let the resource requirements of the jobs be (ω j ) 6 j=1 = (6, 6, 6, 5, 5, 2). Let the resource availability be described by a function Ω(t) given by the sequence (6,12,6,7,7,11,6,6,6,6,6,6). An optimal schedule of length 8 is presented in Fig.…”
Section: Lemma 3 Any Two Conjugate Instances Of the F2|storage ω J mentioning
confidence: 99%
“…It is known that the two-machine flow shop problem with limited storage and the objective of makespan is NP-hard in the strong sense [14]. Moreover, it remains NPhard in the strong sense even under the restriction that the order in which the jobs should be processed on one of the machines is given [12]. According to [13] the makespan minimisation problem is also NP-hard in the following two cases: when all jobs have the same processing time on the second-stage machine and the buffer requirement of a job is proportional to its processing time on the first-stage machine, and in the case when all jobs have the same processing time on the second-stage machine and the same buffer requirements.…”
Section: Introductionmentioning
confidence: 99%
“…The PP-problem is NP-hard in the strong sense [19]. The problem remains NP-hard in the strong sense even under the restriction that, on one of the machines, the jobs are to be processed in a given sequence [11]. Furthermore, it has been proven in [10] that there are instances for which the set of all optimal schedules does not contain a permutation schedule, that is, a schedule in which both machines process the jobs in the same order.…”
mentioning
confidence: 99%