Parallel machine scheduling with precedence constraints

Abstract : The main problem studied in this thesis is that of parallel machine scheduling with precedence constraints. The complexity depends on the shape that the precedence graph takes and the objective function. We prove that one minimum-open problem of scheduling equal-processing-time jobs which subject to in-tree precedence constrains is NP complete while minimizing the total competition time.Then, we prove that the open problem of scheduling level-order precedence constrains is NP-complete too. We adapted the second proof to other scheduling problems as well.On the other hand, we improved an exponential algorithm designed for a specific NP-hard problem. At the end, we propose a linear programming model for the general scheduling problem with arbitrary precedence constraints and processing-time. We adapt the existing models which are originally designed for other scheduling problems to parallel scheduling problem and compare these models with ours.
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Tianyu Wang. Parallel machine scheduling with precedence constraints. Computer science. École centrale de Nantes, 2018. English. ⟨NNT : 2018ECDN0025⟩. ⟨tel-02101466⟩

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