Fast approximation algorithms for job scheduling with processing set restrictions

Huo, Yumei; Leung, Joseph Y.-T.

doi:10.1016/j.tcs.2010.08.008

Cited by 26 publications

(23 citation statements)

References 14 publications

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“…Ou et al (2008) have given a heuristic with worst-case performance ratio of 4/3. Huo and Leung (2010) gave a faster algorithm and for a more general processing set restrictions with the same worst-case bound. Our paper differs from previous studies in that we are scheduling pbatch jobs rather than traditional jobs.…”

Section: Literature Reviewmentioning

confidence: 96%

Effective heuristic for makespan minimization in parallel batch machines with non-identical capacities

Jia

Leung

2015

International Journal of Production Economics

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Section: Literature Reviewmentioning

confidence: 96%

Effective heuristic for makespan minimization in parallel batch machines with non-identical capacities

Jia

Leung

2015

International Journal of Production Economics

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“…The restricted assignment problem on intervals has been discussed in several papers, [7][8][9]12]. Here, each processing set forms a consecutive set of machines.…”

Section: Restricted Assignment On Intervalsmentioning

confidence: 99%

“…For totally ordered sets a 3/2-approximation was designed. Huo and Leung [7] improved the nested case by giving an algorithm with worst-case bound of 5/3, moreover they also studied so called tree-hierarchical processing sets. Here, machines are the nodes of a rooted tree and processing sets correspond with a path from some vertex to the root.…”

Section: Introductionmentioning

confidence: 99%

On some special cases of the restricted assignment problem

Wang

Sitters

2016

Information Processing Letters

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Available online xxxx Communicated by M. Chrobak Keywords: Scheduling Restricted assignment problem Design of algorithmsWe consider some special cases of the restricted assignment problem. In this scheduling problem on parallel machines, any job j can only be assigned to one of the machines in its given subset M j of machines. We give an LP-formulation for the problem with two job sizes and show that it has an integral optimal solution. We also present a PTAS for the case that the M j 's are intervals of the same length. Further, we give a new and very simple algorithm for the case that |M j | = 2 (known as the graph balancing problem) with ratio 11/6.

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“…A typical machine scheduling model with this kind of assignment restriction appears in parallel machine models, where some machines are more flexible and can process more jobs, while other machines are less flexible and can process fewer jobs. For example, Ou et al [13] have studied such a scheduling problem with "inclusive processing sets," while Huo and Leung [14] and Muratore et al [15] have studied a more general model with "nested processing sets." Leung and Li [16] have provided a comprehensive survey of scheduling models with job assignment restrictions in general and inclusive/nested processing set restrictions in particular.…”

Section: M)mentioning

confidence: 99%

Multiple subset sum with inclusive assignment set restrictions

Kellerer

Leung

2011

Naval Research Logistics

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Abstract:In a traditional multiple subset sum problem (MSSP), there is a given set of items and a given set of bins (or knapsacks) with identical capacities. The objective is to select a subset of the items and pack them into the bins such that the total weight of the selected items is maximized. However, in many applications of the MSSP, the bins have assignment restrictions. In this article, we study the subset sum problem with inclusive assignment set restrictions, in which the assignment set of one item (i.e., the set of bins that the item may be assigned to) must be either a subset or a superset of the assignment set of another item. We develop an efficient 0.6492-approximation algorithm and test its effectiveness via computational experiments. We also develop a polynomial time approximation scheme for this problem.

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Fast approximation algorithms for job scheduling with processing set restrictions

Cited by 26 publications

References 14 publications

Effective heuristic for makespan minimization in parallel batch machines with non-identical capacities

Effective heuristic for makespan minimization in parallel batch machines with non-identical capacities

On some special cases of the restricted assignment problem

Multiple subset sum with inclusive assignment set restrictions

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