Fast approximation algorithm for job sequencing with deadlines

Gens, George; Levner, Eugene

doi:10.1016/0166-218x(81)90008-1

Cited by 87 publications

(36 citation statements)

References 3 publications

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“…Finally, we use static interval partitioning of the narrowed range in the algorithm DP to get the FPTAS. Similar techniques were used by Gens and Levner [1981] for the one-machine weighted-number-of-late-jobs problem and Brucker and Kovalyov [1996] for the one-machine weighted-number-of-latejobs batching problem without delivery costs . The range algorithm is very similar to the algorithm DP with a certain variation of the The Range Algorithm R(u, ) [Initialization] The same as that in the algorithm DP.…”

Section: The Fully Polynomial Time Approximation Schemementioning

confidence: 99%

“…Next, we show how to narrow the range of these bounds. Similarly to Gens and Levner [1981], we use the algorithm R(u, ) with = 1/4 in a binary search to narrow the range [v', nv'] Finally, to get an FPTAS, we need to run a slightly modified version of the algorithm DP with static interval partitioning. We describe this below.…”

Section: The Fully Polynomial Time Approximation Schemementioning

confidence: 99%

“…Gens and Levner [1979] developed an FPTAS solving the minimization version of the weighted problem in O(n 3 / ) time. Later on, they developed another FPTAS that improved the time complexity to O(n 2 logn + n 2 / ) [Gens and Levner, 1981]. In the batching version of the problem, denoted by , jobs are processed in batches which require setup time s, and every job's completion time is the completion time of the last job in its batch.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Minimizing the Weighted Number of Late Jobs with Batch Setup Times and Delivery Costs on a Single Machine

Steiner¹,

Zhang²

2007

Multiprocessor Scheduling, Theory and Applications

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Section: The Fully Polynomial Time Approximation Schemementioning

confidence: 99%

Section: The Fully Polynomial Time Approximation Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Minimizing the Weighted Number of Late Jobs with Batch Setup Times and Delivery Costs on a Single Machine

Steiner¹,

Zhang²

2007

Multiprocessor Scheduling, Theory and Applications

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“…In what follows, we suggest a general three-stage technique, which follows and extends an earlier computational scheme suggested by Gens and Levner [22,23] and by Elalouf and Levner [13] for the Knapsack and routing problems, respectively.…”

Section: Related Workmentioning

confidence: 99%

Efficient Routing of Mobile Agents in a Stochastic Network

Elalouf¹,

Levner²,

Cheng³

2013

Polibits

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Abstract-Mobile agents are autonomous programs that may be dispatched through computer networks. Using a mobile agent is a potentially efficient method to perform transactions and retrieve information in networks. Unknown congestion in a network causes uncertainty in the routing times of mobile agents so the routing of mobile agents cannot rely solely on the average travel time. In this paper we deal with a given stochastic network in which the mobile agent routing time is a random variable. Given pre-specified values R and PR, the objective is to find the path with the minimum expected time under the constraint that the probability that the path time is less than R is at least PR. We show that this problem is NP-hard, and construct an exact pseudo-polynomial algorithm and an ε-approximation algorithm (FPTAS) for the problem.Index Terms-Agent-based architecture, fast routing algorithm, FPTAS, stochastic routing.

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“…It is noteworthy that during the last decades numerous scheduling problems have been addressed by applying such an approach. A sample of these papers includes Gens and Levner (1981), Kacem (2009), Kacem (2010), Kacem and Kellerer (2011), Kacem and Mahjoub (2009), Haouari (2009), Sahni (1976), Kovalyov and Kubiak (1999a), Kellerer and Strusevich (2006) and Woeginger (2000).…”

Section: Descriptionmentioning

confidence: 99%

Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem

Kacem¹,

Lanuel²,

Sahnoune³

2011

IJPS

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Abstract:We study the n-job two-parallel machines scheduling problem with the aim of minimising the total flow-time. In this problem, instead of allowing both machines to be continuously available as it is often assumed in the literature, we consider that one of the machines is available for a specified period of time after which it can no longer process any job. On the basis of the modification of an exact algorithm execution, we establish the existence of a strongly Fully Polynomial Time Approximation Scheme (FPTAS) for the above-mentioned problem.

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Fast approximation algorithm for job sequencing with deadlines

Cited by 87 publications

References 3 publications

Minimizing the Weighted Number of Late Jobs with Batch Setup Times and Delivery Costs on a Single Machine

Minimizing the Weighted Number of Late Jobs with Batch Setup Times and Delivery Costs on a Single Machine

Efficient Routing of Mobile Agents in a Stochastic Network

Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem

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