Optimal Policies for Recovery of Multiple Systems After Disruptions
Provides theoretical insights for scheduling repairs in multi-component systems under continuous deterioration, but the explicit policies are limited to homogeneous settings.
The paper characterizes optimal control policies for maximizing weighted sum of recovered components after disruptions, providing explicit policies under homogeneous conditions: target the component with largest state when deterioration ≥ repair, or target the component with minimal state minus deterioration rate when repair rates are sufficiently larger.
We consider a scenario where a system experiences a disruption, and the states (representing health values) of its components continue to reduce over time, unless they are acted upon by a controller. Given this dynamical setting, we consider the problem of finding an optimal control (or switching) sequence to maximize the sum of the weights of the components whose states are brought back to the maximum value. We first provide several characteristics of the optimal policy for the general (fully heterogeneous) version of this problem. We then show that under certain conditions on the rates of repair and deterioration, we can explicitly characterize the optimal control policy as a function of the states. When the deterioration rate (when not being repaired) is larger than or equal to the repair rate, and the deterioration and repair rates as well as the weights are homogeneous across all the components, the optimal control policy is to target the component that has the largest state value at each time step. On the other hand, if the repair rates are sufficiently larger than the deterioration rates, the optimal control policy is to target the component whose state minus the deterioration rate is least in a particular subset of components at each time step.