The effect of machine availability on the worst-case performance of LPT

Hwang, Ho Jung; Lee, Kangbok; Chang, Soo Y.

doi:10.1016/j.dam.2004.12.002

Cited by 35 publications

(30 citation statements)

References 11 publications

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“…For the same problem, Kellerer [15] found an algorithm with a tight ratio of 5/4. Furthermore, Hwang et al briefly pointed out that this problem admits a PTAS [11]. A more general case is the setting where the at most one interval per machine may have an arbitrary position.…”

Section: Introductionmentioning

confidence: 99%

“…Hwang et al studied the ratio of LPT for the same scenario but assumed that at least m − λ machines are available simultaneously. They first obtained a ratio of 2 for λ ≤ m/2 [10] which they later refined to a ratio of 1 + 1/(1 − λ/m) /2 for λ arbitrary [11]. For λ = m − 1, this yields 1 + m/2; if ρ denotes the percentage of permanently available machines, this yields 1 + 1/ρ /2 which depends on ρ.…”

Section: Introductionmentioning

confidence: 99%

“…In parallel machine scheduling, an important issue is the scenario where either some jobs are already fixed in the system [29,30] or intervals of non-availability of some machines must be taken into account [4,11,21,23,24]. The first problem occurs since high-priority jobs are present in the system while the latter problem is due to regular maintenance of machines; both models are relevant for turnaround scheduling [26] and overlay computing where machines are donated on a volunteer basis.…”

Section: Introductionmentioning

confidence: 99%

“…Now we present the approximation algorithm for scheduling with non-availability where the ratio of permanently available machines is constant. Similar to [11], we use λ ∈ {1, . .…”

mentioning

confidence: 99%

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Improved Approximation Algorithms for Scheduling with Fixed Jobs

Diedrich¹,

Jansen²

2009

Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms

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We study two closely related problems in non-preemptive scheduling of sequential jobs on identical parallel machines. In these two settings there are either fixed jobs or nonavailability intervals during which the machines are not available; in either case, the objective is to minimize the makespan. Both formulations have different applications, e.g. in turnaround scheduling or overlay computing. For both problems we contribute approximation algorithms with an improved ratio of 3/2 + , respectively. For scheduling with fixed jobs, a lower bound of 3/2 on the approximation ratio has been obtained by Scharbrodt, Steger & Weisser; for scheduling with non-availability we provide the same lower bound. In total, our approximation ratio for both problems is essentially tight via suitable inapproximability results. We use dual approximation, creation of a gap structure and job configurations, and a PTAS for the multiple subset sum problem. However, the main feature of our algorithms is a new technique for the assignment of large jobs via flexible rounding. Our new technique is based on an interesting cyclic shifting argument in combination with a network flow model for the assignment of jobs to large gaps.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Now we present the approximation algorithm for scheduling with non-availability where the ratio of permanently available machines is constant. Similar to [11], we use λ ∈ {1, . .…”

mentioning

confidence: 99%

See 2 more Smart Citations

Improved Approximation Algorithms for Scheduling with Fixed Jobs

Diedrich¹,

Jansen²

2009

Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Five years later, the same author (1996) discussed the performance of List Scheduling (LS) and LPT heuristics for the identical parallel machine problem wherein one machine is always available and the other ones are subject to a single unavailability interval during the planning time. The effectiveness of LPT heuristic was also investigated by Hwang et al (1998) and Hwang, et al (2005) for the parallel machine scheduling problem where some workstations are planned to be shut down during a-priori known time interval. Liao et al (2005) provided an exact algorithm for a two-machine problem with one machine needing preventive maintenance or periodical repair during a fixed period.…”

Section: Introductionmentioning

confidence: 99%

Minimizing the total tardiness for the tool change scheduling problem on parallel machines

Costa¹,

Cappadonna²,

Fichera³

2016

10.5267/j.ijiec

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This paper deals with the total tardiness minimization problem in a parallel machines manufacturing environment where tool change operations have to be scheduled along with jobs. The mentioned issue belongs to the family of scheduling problems under deterministic machine availability restrictions. A new model that considers the effects of the tool wear on the quality characteristics of the worked product is proposed. Since no mathematical programming-based approach has been developed by literature so far, two distinct mixed integer linear programming models, able to schedule jobs as well as tool change activities along the provided production horizon, have been devised. The former is an adaptation of a well-known model presented by the relevant literature for the single machine scheduling problem with tool changes. The latter has been specifically developed for the issue at hand. After a theoretical analysis aimed at revealing the differences between the proposed mathematical models in terms of computational complexity, an extensive experimental campaign has been fulfilled to assess performances of the proposed methods under the CPU time viewpoint. Obtained results have been statistically analyzed through a properly arranged ANOVA analysis.

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Multiprocessor Scheduling with Availability Constraints

Grigoriu

2013

Operations Research Proceedings

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We consider the problem of scheduling a given set of tasks on multiple processors with predefined periods of unavailability, with the aim of minimizing the maximum completion time. Since this problem is strongly NP-hard, polynomial approximation algorithms are being studied for its solution. Among these, the best known are LPT (largest processing time first) and Multifit with their variants. We give a Multifit-based algorithm, FFDL Multifit, which has an optimal worstcase performance in the class of polynomial algorithms for same-speed processors with at most two downtimes on each machine, and for uniform processors with at most one downtime on each machine, assuming that P = N P. Our algorithm finishes within 3/2 the maximum between the end of the last downtime and the end of the 5 Example showing that the 3/2 bound is asymptotically tight. .. .. 22 CHAPTER I

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The effect of machine availability on the worst-case performance of LPT

Cited by 35 publications

References 11 publications

Improved Approximation Algorithms for Scheduling with Fixed Jobs

Improved Approximation Algorithms for Scheduling with Fixed Jobs

Minimizing the total tardiness for the tool change scheduling problem on parallel machines

Multiprocessor Scheduling with Availability Constraints

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