In one-machine scheduling, MIP time-indexed formulations are often used to provide very good lower bounds through Lagrangian relaxations. In order to get an improved lower bound, we add valid cuts to a time-indexed formulation and show we still have a Lagrangian relaxation that can be solved as a shortest path in a graph. Two branch-and-bound algorithms are then presented for the earliness-tardiness scheduling problem with either common or general due dates. In both cases, our algorithms outperform the previously published approaches.
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LIP6 working paper
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View A new lower bound for one-machine earliness-tardiness scheduling