Two-Machine Flow Shop with a Dynamic Storage Space and UET Operations

Berlińska, Joanna; Kononov, Alexander; Zinder, Yakov

doi:10.1007/978-3-030-21803-4_112

Cited by 2 publications

(8 citation statements)

References 7 publications

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“…If ω j 1 < 6, then at least one unit of the resource is wasted in the interval [0, 1), and at least one unit is lost in the interval [1,2). Thus, ω j 1 = 6, j 1 = 1, and this job completes on M 2 at time C 2 1 = 2, as otherwise at least 6 units of the resource would be wasted in the interval [1,2). Similarly, let j 2 be the second job in σ .…”

Section: Lemma 3 Any Two Conjugate Instances Of the F2|storage ω J mentioning

confidence: 99%

“…Similarly, let j 2 be the second job in σ . If ω j 2 < 6, then at least one unit of the resource is wasted in the interval [1,2), and another one in the interval [2,3) or [3,4). Hence, ω j 2 = 6, j 2 = 2 and S 1 2 = 1.…”

Section: Lemma 3 Any Two Conjugate Instances Of the F2|storage ω J mentioning

confidence: 99%

“…In case (2), machine M 2 is idle in the interval [2,3), and job 2 has to be completed at time C 2 2 = 4, because at least 2 units of the resource would be wasted in the interval [2,4) otherwise. Hence, one unit of the resource is wasted in the interval [3,4), and in consequence, job 3 (whose resource requirement is 6) has to be executed on M 1 in the interval [2,3). Then, job 3 is scheduled on M 2 in the interval [4,5), which leads to losing one more unit of the resource.…”

Section: Lemma 3 Any Two Conjugate Instances Of the F2|storage ω J mentioning

confidence: 99%

“…For example, the storage space is often shared by several clients of the same transportation facility, and the computer memory is often used by several processes simultaneously. Despite this, to the best of the authors' knowledge, there are no publications except [2] that study such systems. The paper addresses this gap in the literature on scheduling by considering the two-machine flow shop with variable storage capacity.…”

Section: Introductionmentioning

confidence: 99%

“…The case where all jobs have the same processing time on one of the machines, or the same processing time on the first-stage machine and the same processing time on the second-stage machine was considered in a number of publications, including [2,9] and the mentioned above [13]. Besides the theoretical interest, this case has applications in star data gathering networks where different workstations are allocated datasetindependent time slots for data transfer, and in unloading and loading involving a crane.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Two-machine flow shop with dynamic storage space

2020

Self Cite

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The publications on two-machine flow shop scheduling problems with job dependent storage requirements, where a job seizes a portion of the storage space for the entire duration of its processing, were motivated by various applications ranging from supply chains of mineral resources to multimedia systems. In contrast to the previous publications that assumed that the availability of the storage space remains unchanged, this paper is concerned with a more general case when the availability is a function of time. It strengthens the previously published result concerning the existence of an optimal permutation schedule, shows that the variable storage space availability leads to the NP-hardness in the strong sense even for unit processing times, and presents a polynomial-time approximation scheme together with several heuristic algorithms. The heuristics are evaluated by means of computational experiments.

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Section: Lemma 3 Any Two Conjugate Instances Of the F2|storage ω J mentioning

confidence: 99%

Section: Lemma 3 Any Two Conjugate Instances Of the F2|storage ω J mentioning

confidence: 99%

Section: Lemma 3 Any Two Conjugate Instances Of the F2|storage ω J mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two-machine flow shop with dynamic storage space

2020

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Iterated Local Search and Other Algorithms for Buffered Two-Machine Permutation Flow Shops with Constant Processing Times on One Machine

Geser

Middendorf

2021

Evolutionary Computation

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The two-machine permutation flow shop scheduling problem with buffer is studied for the special case that all processing times on one of the two machines are equal to a constant c. This case is interesting because it occurs in various applications, e.g., when one machine is a packing machine or when materials have to be transported. Different types of buffers and buffer usage are considered. It is shown that all considered buffer flow shop problems remain NP-hard for the makespan criterion even with the restriction to equal processing times on one machine. However, the special case where the constant c is larger or smaller than all processing times on the other machine is shown to be polynomially solvable by presenting an algorithm (2BF-OPT) that calculates optimal schedules in [Formula: see text] steps. Two heuristics for solving the NP-hard flow shop problems are proposed: i) a modification of the commonly used NEH heuristic (mNEH) and ii) an Iterated Local Search heuristic (2BF-ILS) that uses the mNEH heuristic for computing its initial solution. It is shown experimentally that the proposed 2BF-ILS heuristic obtains better results than two state-of-the-art algorithms for buffered flow shop problems from the literature and an Ant Colony Optimization algorithm. In addition, it is shown experimentally that 2BF-ILS obtains the same solution quality as the standard NEH heuristic, however, with a smaller number of function evaluations.

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Two-Machine Flow Shop with a Dynamic Storage Space and UET Operations

Cited by 2 publications

References 7 publications

Two-machine flow shop with dynamic storage space

Two-machine flow shop with dynamic storage space

Iterated Local Search and Other Algorithms for Buffered Two-Machine Permutation Flow Shops with Constant Processing Times on One Machine

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