Abstract: This article aims to present the main published works on multi states
degradable systems, maintenance and production planning and optimization methods.
The first part focuses on the characterization of binary systems and multi-state systems
based on the work published in the literature and the presentation of optimization
models that ensure continuity of service for repairable systems that can operate in
degraded mode. In the second part we review the main models and optimization of
maintenance strategies as well as those concerning the planning and optimization of
production. We review the work that has focused only on planning models separated,
then we introduce the approach to integrated production and maintenance planning for
binary systems and ultimately for degradable multi-state systems.

Keywords: optimization, model, multi-state system, degradable, integrated planning.