Jackson's rule for single-machine scheduling: making a good heuristic better
Mathematics of Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Near-Optimal Sequencing with Precedence Constraints
Proceedings of the 1st Integer Programming and Combinatorial Optimization Conference
Approximation schemes for constrained scheduling problems
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
A PTAS for the Single Machine Scheduling Problem with Controllable Processing Times
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
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We consider the problem of scheduling n jobs on a single machine. Each job has a release date, when it becomes available for processing, and, after completing its processing, requires an additional delivery time. Feasible schedules are further restricted by job precedence constraints, and the objective is to minimize the time by which all jobs are delivered. In the notation of Graham et al. [2], this problem is noted 1|rj, prec|Lmax. We develop a polynomial time approximation scheme whose running time depends only linearly on the input size. This linear complexity bound gives a substantial improvement of the best previously known polynomial bound [4].