Optimum post-disruption restoration under uncertainty for enhancing critical infrastructure resilience

The planning of post-disruption restoration in critical infrastructure systems often relies on deterministic assumptions such as complete information on resources and known duration of the repair tasks. In fact, the uncertainties faced by restoration activities, e.g. stemming from subjective estimates of resources and costs, are rarely considered. Thus, the solutions obtained by a deterministic approach may be suboptimal or even infeasible under specific realizations of the uncertainties. To bridge this gap, this paper investigates the effects of uncertain repair time and resources on the post-disruption restoration of critical infrastructure. Two-stage stochastic optimization provides insights for prioritizing the intensity and time allocation of the repair activities with the objective of maximizing system resilience. The inherent stochasticity is represented via a set of scenarios capturing specific realizations of repair activity durations and available resources, and their probabilities. A multi-mode restoration model is proposed that offers more flexibility than its single-mode counterpart. The restoration framework is applied to the reduced British electric power system and the results demonstrate the added value of using the stochastic model as opposed to the deterministic model. Particularly, the benefits of the proposed stochastic method increase as the uncertainty associated with the restoration process grows. Finally, decision-making under uncertainty largely impacts the optimum repair modes and schedule.