Our problem considers a single machine with a health index on which jobs of different families are scheduled to minimize the sum of completion times and maintenance operations are scheduled to restore the health of the machine. The health of the machine decreases when jobs are processed. Moreover, to be scheduled, each job requires the machine to have a minimum health index which depends on the job family.
Two cases are studied: (1) The daily case with a single flexible maintenance operation, and (2) The weekly case with two flexible maintenance operations. The second case is shown to be NP-complete. Two Mixed Integer Linear Programming models are presented for each case. The first model uses ``classical'' positional variables, while the second model improves the first model by using the notion of master sequence. Different valid inequalities are also proposed. Computational experiments show that the second model is much more efficient than the first model when solved with a standard solver, and the impact of the valid inequalities is discussed.