Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey

@article{Graham1977OptimizationAA,
  title={Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey},
  author={Ron Graham and Eugene L. Lawler and Jan Karel Lenstra and Alexander H. G. Rinnooy Kan},
  journal={Annals of discrete mathematics},
  year={1977},
  volume={5},
  pages={287-326}
}
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References

SHOWING 1-10 OF 111 REFERENCES
Scheduling with parallel processors and linear delay costs
TLDR
The theoretical properties of this m-machine problem are explored, and the problem of determining an optimum scheduling procedure is examined; properties of the optimum schedule are given as well as the corresponding reductions in the number of schedules that must be evaluated in the search for an optimum.
On the Scheduling of Jobs on a Number of Identical Machines.
Abstract : Several theoretical results are developed to obtain an efficient branch-and-bound algorithm for the sequencing problem when all jobs are available to process at time zero and are
Algorithms for Scheduling Independent Tasks
TLDR
Three general techniques are presented to obtain approximate solutions for optimization problems solvable in this way, and polynomial time algorithms are applied to obtain “good” approximate solutions.
Job-Shop Scheduling by Implicit Enumeration
The classical combinatorial optimization problem of minimizing maximum completion time in a general job-shop has been the subject of extensive research. In this paper we review and extend this work.
Bounds for the Optimal Scheduling of n Jobs on m Processors
TLDR
Lower and upper bounds are given for the cost of an optimal schedule and a procedure is described for obtaining a schedule which costs less than the given upper bound.
Complexity of Scheduling under Precedence Constraints
TLDR
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.
Coordinating Aggregate and Detailed Scheduling Decisions in the One-Machine Job Shop: Part I. Theory
TLDR
This paper presents a formal model of the one-machine job-shop scheduling problem with variable capacity and outlines a preliminary branch-and-bound algorithm, and illustrates several interesting features of the algorithm and bounding structures by an example.
Decomposition Algorithms for Single-Machine Sequencing with Precedence Relations and Deferral Costs
TLDR
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.
Minimizing maximum lateness on one machine : Computational experience and some applications
TLDR
This work considers the problem of scheduling jobs on a single machine subject to given release dates and precedence constraints, and describes applications to the theory of job-shop scheduling and to a practical scheduling situation.
...
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