Abstract
We investigate one-machine scheduling problems subject to generalized precedence constraints which specify that when job J j precedes job J j′ (denoted by J j → J j′ ), the time between the end J j and the beginning of job J j′ must be at least l jj′ , but no more than u jj′ , where 0⩽ l jj′ ⩽ u jj′ , The objective is to minimize makespan. For some very simple precedence relations, we present polynomial algorithms. For more complex precedence structures, we establish that the problems are NP-hard. For one of these hard problems, we provide heuristics and worst-case bounds.
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