Dominance inequalities for scheduling around an unrestrictive common due date

The problem considered in this work consists scheduling a set of tasks on single machine, around an unrestrictive common due date to minimize the weighted sum earliness and tardiness. This can be formulated as compact mixed integer program (MIP). In article, we focus neighborhood-based dominance properties, where neighborhood is associated insert swap operations. We derive from these properties local search procedure providing very good heuristic solution. main contribution stands exact solving context: constraints eliminating non locally optimal solutions with respect propose linear inequalities translating strengthen MIP formulation. These inequalities, called are different standard reinforcement inequalities. provide numerical analysis which shows that adding significantly reduces computation time required for using solver.