Single-machine scheduling with mixed precedence constraints

Eugene Levner; Milan Vlach

doi:10.15807/jorsj.42.330

Single-machine scheduling with mixed precedence constraints

Eugene Levner
, Milan Vlach

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The paper deals with a single machine scheduling problem involving a general precedence structure that permits both ordinary and fuzzy precedence constraints. Feasible schedules are evaluated not only by their cost but also by the degree of satisfaction with their precedence structure. An O(ℳlog n+ max(n2, kn2))-time algorithm is proposed for finding nondominated solutions of the resulting bi-criteria scheduling problem where n is the number of jobs, k is the number of fuzzy constraints, and ℳ is the total number of precedence constraints.

Original language	English
Pages (from-to)	330-341
Number of pages	12
Journal	Journal of the Operations Research Society of Japan
Volume	42
Issue number	3
DOIs	https://doi.org/10.15807/jorsj.42.330
State	Published - Sep 1999
Externally published	Yes

Bibliographical note

Funding Information:
Acknowledgments This work was performed while the first author was visiting the Japan Advanced Institute of Science and Technology, Ishikawa. The support of this author by the International Information Science Foundation (grant 97.1.3.615) and by the Ministry of Science of Israel in the framework of the cooperative program with the Japan Society for the Promotion of Science (grant 8951.1.97) is gratefully acknowledged. The authors thank J.K. Lenstra for a very helpful comment.

Funding

Acknowledgments This work was performed while the first author was visiting the Japan Advanced Institute of Science and Technology, Ishikawa. The support of this author by the International Information Science Foundation (grant 97.1.3.615) and by the Ministry of Science of Israel in the framework of the cooperative program with the Japan Society for the Promotion of Science (grant 8951.1.97) is gratefully acknowledged. The authors thank J.K. Lenstra for a very helpful comment.

Funders	Funder number
International Information Science Foundation	97.1.3.615
Japan Society for the Promotion of Science	8951.1.97
Ministry of science and technology, Israel

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Cite this

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abstract = "The paper deals with a single machine scheduling problem involving a general precedence structure that permits both ordinary and fuzzy precedence constraints. Feasible schedules are evaluated not only by their cost but also by the degree of satisfaction with their precedence structure. An O(ℳlog n+ max(n2, kn2))-time algorithm is proposed for finding nondominated solutions of the resulting bi-criteria scheduling problem where n is the number of jobs, k is the number of fuzzy constraints, and ℳ is the total number of precedence constraints.",

author = "Eugene Levner and Milan Vlach",

note = "Funding Information: Acknowledgments This work was performed while the first author was visiting the Japan Advanced Institute of Science and Technology, Ishikawa. The support of this author by the International Information Science Foundation (grant 97.1.3.615) and by the Ministry of Science of Israel in the framework of the cooperative program with the Japan Society for the Promotion of Science (grant 8951.1.97) is gratefully acknowledged. The authors thank J.K. Lenstra for a very helpful comment.",

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N2 - The paper deals with a single machine scheduling problem involving a general precedence structure that permits both ordinary and fuzzy precedence constraints. Feasible schedules are evaluated not only by their cost but also by the degree of satisfaction with their precedence structure. An O(ℳlog n+ max(n2, kn2))-time algorithm is proposed for finding nondominated solutions of the resulting bi-criteria scheduling problem where n is the number of jobs, k is the number of fuzzy constraints, and ℳ is the total number of precedence constraints.

AB - The paper deals with a single machine scheduling problem involving a general precedence structure that permits both ordinary and fuzzy precedence constraints. Feasible schedules are evaluated not only by their cost but also by the degree of satisfaction with their precedence structure. An O(ℳlog n+ max(n2, kn2))-time algorithm is proposed for finding nondominated solutions of the resulting bi-criteria scheduling problem where n is the number of jobs, k is the number of fuzzy constraints, and ℳ is the total number of precedence constraints.

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Single-machine scheduling with mixed precedence constraints

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