Abstract
We consider single machine scheduling problems in which the processing time of a job depends on its position in a processing sequence. The objectives are to minimize the weighted sum of completion times, to minimize the maximum lateness and to minimize the number of tardy jobs. For some special cases, we prove that the weighted shortest processing time (WSPT) rule, the earliest due date (EDD) rule and Moore’s algorithm can construct an optimal sequence for these objective functions, respectively. For the general cases, we also give the worst-case bound of these three rules.
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