Finally, decision-making under uncertainty largely impacts the optimum repair modes and schedule. Particularly, the benefits of the proposed stochastic method increase as the uncertainty associated with the restoration process grows. 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. A multi-mode restoration model is proposed that offers more flexibility than its single-mode counterpart. The inherent stochasticity is represented via a set of scenarios capturing specific realizations of repair activity durations and available resources, and their probabilities. Two-stage stochastic optimization provides insights for prioritizing the intensity and time allocation of the repair activities with the objective of maximizing system resilience. To bridge this gap, this paper investigates the effects of uncertain repair time and resources on the post-disruption restoration of critical infrastructure. LHS accomplishes this by stratifying the cumulative distribution function and randomly sampling within the strata.
Another technique that has gained popularity is the Latin hypercube sampling (LHS), a technique emphasizing uniform sampling of the univariate distributions. Thus, the solutions obtained by a deterministic approach may be suboptimal or even infeasible under specific realizations of the uncertainties. cumulative distributions to obtain variable inputs.
e.g. stemming from subjective estimates of resources and costs, are rarely considered. Latin hypercubes are essentially collections of points on a hypercube that are placed on a cubic/rectangular grid, which possess the property that no two points share any individual coordinate, and every row/column/higher-dimensional-axis is sampled once. In fact, the uncertainties faced by restoration activities, e.g. 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.
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