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
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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 + ε)-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.