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Single machine scheduling with precedence constraints and positionally dependent processing times

Alexandre Dolgui 1 Valery Gordon Vitaly Strusevich 2 
1 Laboratoire en Sciences et Technologies de l'Information
DEMO-ENSMSE - Département Décision en Entreprise : Modélisation, Optimisation
Abstract : 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.
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Submitted on : Wednesday, June 20, 2012 - 3:53:15 PM
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Alexandre Dolgui, Valery Gordon, Vitaly Strusevich. Single machine scheduling with precedence constraints and positionally dependent processing times. Computers and Operations Research, Elsevier, 2012, 39 (6), pp.Pages 1218-1224. ⟨10.1016/j.cor.2010.06.004⟩. ⟨emse-00710317⟩



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