Complexity analysis of integrated dynamic lot sizing and maintenance planning problems

We consider a problem where the planning decisions of producing on and maintaining a single machine are integrated. The age of the machine, and thus when maintenance should be performed, is influenced by the production decisions. Decisions are taken on a planning horizon discretized in periods. The computational complexity of several variants of the single-item problem are studied depending on whether (i) Maintenance can be performed on the machine at any point in time in a period or must be performed at the end of a period, (ii) There is a fixed aging component when starting production, and (iii) There is a minimum age before maintenance can be performed on the machine. The multi-item case is proved to be NP-hard.