Parallel machine scheduling with nested job assignment restrictions

Muratore, Gabriella; Schwarz, Ulrich M.; Woeginger, Gerhard J.

doi:10.1016/j.orl.2009.09.010

Cited by 37 publications

(35 citation statements)

References 8 publications

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“…Thus, the time complexity of our algorithm is polynomial. Combining inequality (21) and Lemmas 13,15,18,19, and 20, we have…”

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confidence: 80%

“…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%

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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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“…Thus, the time complexity of our algorithm is polynomial. Combining inequality (21) and Lemmas 13,15,18,19, and 20, we have…”

mentioning

confidence: 80%

Section: M)mentioning

confidence: 99%

Multiple subset sum with inclusive assignment set restrictions

Kellerer

Leung

2011

Naval Research Logistics

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“…A polynomial-time approximation scheme (PTAS) is a type of polynomial-time approximation algorithm with performance guarantee 1+ε for all ε>0 [13] [14]. Muratore et al [15] considered a scheduling problem in which jobs can be performed on a certain subset of the machines, where the machine sets are nested. They developed a polynomial-time approximation scheme to minimize makespan.…”

Section: Literature Reviewmentioning

confidence: 99%

An artificial bee colony algorithm approach for unrelated parallel machine scheduling with processing set restrictions, job sequence-dependent setup times, and due date

Caniyilmaz

Benli

Ilkay

2014

Int J Adv Manuf Technol

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The problem dealt with in this study has job sequence-dependent setup times under suitable machine constraints and due date constraints. The performance criterion for this problem is to minimize the sum of makespan and total tardiness. In the literature, an application of ABC algorithm for the problems which includes all the properties that we have dealt has not been discussed. Because there is no appropriate test data, a real-life data was collected from a factory. In this study, a new approach has been proposed for the solution with meta-heuristics of unrelated parallel machine scheduling problems which is a combinatorial problem. This new neighborhood approach provides different machine assignments for every candidate job sequences. This approach is used by integrating into ABC and GA. To evaluate the performances of the algorithms, the real-life problem was solved by using ABC and GA algorithms under similar conditions. It was found that all jobs can be completed in two shifts without the need for a third shift. Computational results show that ABC algorithm has better performance than GA.

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“…Furthermore, offline problems P | M i (GoS) | C max and P | M i (nested) | C max have PTASs that are proposed by Ou et al (2008) and Muratore et al (2010), respectively. While the PTASs have very high running times, there are faster approximation algorithms with constant worst-case bounds for P | M i (GoS) | C max proposed by Ou et al (2008) and for P | M i (nested) | C max proposed by Huo and Leung (2010a), Huo and Leung (2010b).…”

Section: Makespanmentioning

confidence: 99%

Makespan minimization in online scheduling with machine eligibility

2010

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In this paper we provide a survey of online scheduling in parallel machine environments with machine eligibility constraints and the makespan as objective function. We first give a brief overview of the different parallel machine environments and then survey the various types of machine eligibility constraints, including treehierarchical processing sets, Grade of Service processing sets, interval processing sets, and nested processing sets. We furthermore describe the relationships between the various different types of processing sets. We proceed with describing two basic online scheduling paradigms, namely online over list and online over time. For each one of the two paradigms we survey all the results that have been recorded in the literature with regard to each type of machine eligibility constraints. We obtain also

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Parallel machine scheduling with nested job assignment restrictions

Cited by 37 publications

References 8 publications

Multiple subset sum with inclusive assignment set restrictions

Multiple subset sum with inclusive assignment set restrictions

An artificial bee colony algorithm approach for unrelated parallel machine scheduling with processing set restrictions, job sequence-dependent setup times, and due date

Makespan minimization in online scheduling with machine eligibility

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