Complexity of machine scheduling problems
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In this paper, the authors survey and extend the results on the complexity of machine scheduling problems and give a classification of scheduling problems on single, different and identical machines and study the influence of various parameters on their complexity.Abstract:
We survey and extend the results on the complexity of machine scheduling problems. After a brief review of the central concept of NP-completeness we give a classification of scheduling problems on single, different and identical machines and study the influence of various parameters on their complexity. The problems for which a polynomial-bounded algorithm is available are listed and NP-completeness is established for a large number of other machine scheduling problems. We finally discuss some questions that remain unanswered.read more
Citations
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Book ChapterDOI
Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey
TL;DR: In this article, the authors survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory, and indicate some problems for future research and include a selective bibliography.
Journal ArticleDOI
The Complexity of Flowshop and Jobshop Scheduling
TL;DR: The results are strong in that they hold whether the problem size is measured by number of tasks, number of bits required to express the task lengths, or by the sum of thetask lengths.
Journal ArticleDOI
An algorithm for solving the job-shop problem
Jacques Carlier,Eric Pinson +1 more
TL;DR: In this paper, a branch and bound method for solving the job-shop problem is proposed, which is based on one-machine scheduling problems and is made more efficient by several propositions which limit the search tree by using immediate selections.
Journal ArticleDOI
A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process
TL;DR: Several well-documented applications of no-wait and blocking scheduling models are described and some ways in which the increasing use of modern manufacturing methods gives rise to other applications are illustrated.
Journal ArticleDOI
A Review of Production Scheduling
TL;DR: The intent of this paper is to present a broad classification for various scheduling problems, to review important theoretical developments for these problem classes, and to contrast the currently available theory with the practice of production scheduling.
References
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TL;DR: A simple decision rule is obtained in this paper for the optimal scheduling of the production so that the total elapsed time is a minimum.
Journal ArticleDOI
The Complexity of Flowshop and Jobshop Scheduling
TL;DR: The results are strong in that they hold whether the problem size is measured by number of tasks, number of bits required to express the task lengths, or by the sum of thetask lengths.
Journal ArticleDOI
Some simplified NP-complete graph problems
TL;DR: This paper shows that a number of NP - complete problems remain NP -complete even when their domains are substantially restricted, and determines essentially the lowest possible upper bounds on node degree for which the problems remainNP -complete.