The Interdependent Network Design Problem for Optimal Infrastructure System Restoration

This study introduces the Interdependent Network Design Problem (INDP), concerned with defining the minimum-cost reconstruction strategy of a partially destroyed system of infrastructure networks, subject to budget, resources, and operational constraints, while considering interdependencies between them. To solve the INDP, the authors develop an efficient Mixed Integer Programming (MIP) model, which considers different types of interdependency while exploiting efficiencies from joint restoration due to colocation for the first time. The authors also propose heuristic methodologies based on simulation and the iterative use of the INDP model, to enable studying problems with additional complexity, such as accounting for uncertainty from possible disaster scenarios, or determining not only what to reconstruct but the order of reconstruction. Such methodologies enable the analysis of expected costs and performance associated to reconstruction of the system of networks, providing an effective tool for infrastructure decision makers. To exemplify the capabilities of the presented INDP-based methodologies, the authors study the process of restoration of a set of interdependent networks after hypothetical earthquakes in Shelby County, TN, United States. Results show that the INDP-based approaches that account for time-dependent recovery converge to quasi-optimal solutions in all 16 configurations studied, considering four different resource levels and four different earthquake magnitudes. Similarly, as desired in emergency response scenarios, the rate of performance recovery is high in the early reconstruction stages, recovering more than 85% of performance in the first stage in a worst-case scenario.