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
Fast approximation algorithms for knapsack problems
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Approximation schemes for constrained scheduling problems
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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In a scheduling problem with controllable processing times the job processing time can be compressed through incurring an additional cost. We consider the problem of scheduling n jobs on a single machine with controllable processing times. 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. We develop a polynomial time approximation scheme whose running time depends only linearly on the input size. This improves and generalizes the previous (3/2+@?)-approximation algorithm by Zdrzalka. Moreover, this linear complexity bound gives a substantial improvement of the best previously known polynomial bound obtained by Hall and Shmoys for the special case without controllable processing times.