This paper addresses a new model for the one-machine earliness–tardiness scheduling problem where jobs can be interrupted. Some dominance rules and a lower bound are derived. A new timing algorithm is also presented and a local search algorithm based on this timing algorithm permits the computation of good feasible solutions. We experimentally compare our timing algorithm with a previously published timing algorithm. The tests show that the execution time of the new timing algorithm is significantly faster, especially for large instances. The values of the solutions are compared to the lower bound.