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Scheduling with step-improving processing times. (English) Zbl 1080.90044

Summary: We consider the scheduling problem of minimizing the makespan on a single machine with step-improving job processing times around a common critical date. For this problem we give an NP-hardness proof, a fast pseudo-polynomial time algorithm, an FPTAS, and an on-line algorithm with best possible competitive ratio.

MSC:

90B35 Deterministic scheduling theory in operations research
90C27 Combinatorial optimization
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References:

[1] Cheng, T. C.E.; Ding, Q.; Lin, B. M.T., A concise survey of scheduling with time-dependent processing times, Eur. J. Oper. Res., 152, 1-13 (2004) · Zbl 1030.90023
[2] Kellerer, H.; Pferschy, U.; Pisinger, D., Knapsack Problems (2004), Springer: Springer Berlin · Zbl 1103.90003
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