Variable neighborhood search with memory for a single-machine scheduling problem with periodic maintenance and sequence-dependent set-up times.

•A single machine scheduling problem with periodic maintenance and sequence-dependent set-up times is analyzed.•The problem has practical relevance because of its industrial applications: textile, chemical, circuit boards, etc.•A new MILP formulation is proposed. This new formulation can solve larger instances than with previous ones.•A Skewed VNS approach with memory is proposed. It improves significantly the performance of previous heuristics.