Book ChapterDOI
An algorithm for the single machine sequencing problem with precedence constraints
C. N. Potts
- pp 78-87
TLDR
The single machine sequencing problem is considered, in which each job has a processing time and a weight, and there are precedence constraints on the jobs.Abstract:
The single machine sequencing problem is considered, in which each job has a processing time and a weight, and there are precedence constraints on the jobs. The objective is to find a sequence of jobs which minimises the weighted sum of completion times. A new lower bound is derived and used in a branch and bound algorithm. Computational results for up to forty jobs are given.read more
Citations
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Sequencing and scheduling: algorithms and complexity
TL;DR: This survey focuses on the area of deterministic machine scheduling, and reviews complexity results and optimization and approximation algorithms for problems involving a single machine, parallel machines, open shops, flow shops and job shops.
Journal ArticleDOI
Aggregating inconsistent information: Ranking and clustering
TL;DR: This work almost settles a long-standing conjecture of Bang-Jensen and Thomassen and shows that unless NP⊆BPP, there is no polynomial time algorithm for the problem of minimum feedback arc set in tournaments.
Book ChapterDOI
Chapter 9 Sequencing and scheduling: Algorithms and complexity
TL;DR: Different types of sequencing and scheduling problems are discussed, and different types of algorithms and the concepts of complexity theory are described.
Journal ArticleDOI
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
TL;DR: This paper introduces two general techniques for the design and analysis of approximation algorithms for NP-hard scheduling problems in which the objective is to minimize the weighted sum of the job completion times.
Book ChapterDOI
A Review of Machine Scheduling: Complexity, Algorithms and Approximability
TL;DR: This work focuses on deterministic machine scheduling for which it is assumed that all data that define a problem instance are known with certainty.
References
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Book
Theory of scheduling
TL;DR: Reading theory of scheduling as one of the reading material to finish quickly to increase the knowledge and happiness in your lonely time.
Journal ArticleDOI
Complexity of Scheduling under Precedence Constraints
TL;DR: The use of precedence constraints between jobs that have to be respected in every feasible schedule is illustrated by extending some typical NP-completeness results and simplifying their correctness proofs for scheduling problems involving precedence constraints.
Book ChapterDOI
Sequencing Jobs to Minimize Total Weighted Completion Time Subject to Precedence Constraints
TL;DR: In this paper, it was shown that the problem is NP-complete if there are arbitrary precedence constraints, but can be solved in O( n log n ) time if precedence constraints are series parallel.
Journal ArticleDOI
Decomposition Algorithms for Single-Machine Sequencing with Precedence Relations and Deferral Costs
TL;DR: It is proved that a permutation is optimal if and only if it can be generated by this algorithm, and four special network structures are considered, and specializations of the general algorithm are presented.