Optimal sequencing by modular decomposition: Polynomial algorithms
Operations Research
Optimal sequencing via modular decomposition: characterization of sequencing functions
Mathematics of Operations Research
Incremental modular decomposition
Journal of the ACM (JACM)
Earliness penalties on a single machine subject to precedence constraints
Computers and Operations Research
Efficient and practical algorithms for sequential modular decomposition
Journal of Algorithms
A survey of scheduling with controllable processing times
Discrete Applied Mathematics
Single-machine scheduling with deteriorating jobs under a series-parallel graph constraint
Computers and Operations Research
Minimizing the makespan in a single machine scheduling problem with a time-based learning effect
Information Processing Letters
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In many real-life situations the processing conditions in scheduling models cannot be viewed as given constants since they vary over time thereby affecting actual durations of jobs. We consider single machine scheduling problems of minimizing the makespan in which the processing time of a job depends on its position (with either cumulative deterioration or exponential learning). It is often found in practice that some products are manufactured in a certain order implied, for example, by technological, marketing or assembly requirements. This can be modeled by imposing precedence constraints on the set of jobs. We consider scheduling models with positional deterioration or learning under precedence constraints that are built up iteratively from the prime partially ordered sets of a bounded width (this class of precedence constraints includes, in particular, series-parallel precedence constraints). We show that objective functions of the considered problems satisfy the job module property and possess the recursion property. As a result, the problems under consideration are solvable in polynomial time.