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Single-machine scheduling with deteriorating jobs under a series-parallel graph constraint. (English) Zbl 1180.90143
Summary: This paper considers single-machine scheduling problems with deteriorating jobs, i.e., jobs whose processing times are an increasing function of their starting times. In addition, the jobs are related by a series-parallel graph. It is shown that, for the general linear problem to minimize the makespan, polynomial algorithms exist. It is also shown that for the proportional linear problem of minimization of the total weighted completion time, polynomial algorithms exist, too.
90B35Scheduling theory, deterministic
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