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