Neighborhood search procedures for single machine tardiness scheduling with sequence-dependent setups

In this paper we address the 1/s(ij)/Sigma omega T-j(j) problem, for which we improve the time complexities of searching the interchange, insertion and twist neighborhoods from O(n(3)) to O(n(2) log n). Further, we improve the time complexity of searching the insertion and twist neighborhoods in which a candidate job is selected from among k jobs nearest to the selected job from O(n(2)k) to O(nk log k + n(2)). (C) 2012 Elsevier B.V. All rights reserved.