Time scale decomposition in production planning for unreliable flexible manufacturing systems

In this paper we consider a class of stochastic control models for the planning of operations in unreliable flexible manufacturing systems (i.e. subject to random failures or stoppages). These models are formulated in continuous time and include a representation of (i) the tracking of a fluctuating demand for different part-types, (ii) the influence of a wear process on machine breakdowns and (iii) the possibility to perform preventive maintenance or replacement. This involves a coupling between two controlled stochastic processes, a jump process and a diffusion process. They correspond to phenomena intervening at different time-scales respectively. The paper shows how these two different time-scales can be exploited in an optimal stochastic control approach. In particular, the turnpike or hedging point policies for piecewise deterministic systems or the singular perturbation techniques for switching diffusion models are shown to be efficient ways to exploit this two-time-scale structure.