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Single machine scheduling with step-deteriorating processing times. (English) Zbl 0984.90014
Summary: We study in this paper a scheduling model in which each task has a normal processing time which deteriorates as a step function if its starting time is beyond a given deteriorating date. We focus on problems with identical task deteriorating dates. We show that the flow time problem is NP-complete and suggest a pseudo-polynomial algorithm for the makespan problem. We also introduce a general method of solution, which facilitates the identification of solvable cases for some related problems. Finally, we provide a counterexample that invalidates the conjecture of optimality of a switching algorithm reported in the literature. Thus, we solve several unexplored or open problems and obtain a sharp boundary delineating the complexity of the considered problems.

90B35Scheduling theory, deterministic
68Q25Analysis of algorithms and problem complexity
Full Text: DOI
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