Robust single machine scheduling with a flexible maintenance activity.

•A problem concerning the joint scheduling of multiple jobs and a maintenance activity on a single machine is addressed. The maintenance activity has an uncertain duration and must be processed within a given time window.•The problem is that of finding job schedules which are robust to any possible changes in the maintenance activity duration.•We investigate properties of robust schedules when minimizing makespan and total completion time objectives under four different robustness criteria.•Exact and heuristic algorithms have been designed and tested for the problem, in which we minimize total completion time under the maximum absolute regret criterion.