Inoperability Input-Output Modeling: Inventory Optimization and Resilience Estimation during Critical Events

Abstract

Assessing the ability of critical infrastructures to overcome shocks and optimizing their preparedness for critical events is a key factor in reducing damage, ensuring resilience, and mitigating monetary losses. When considering the problem in a broad sense, the assessment of technical dependencies among engineered systems can be supported by the analysis of economical relationships. A key tool to accomplish this objective is to exploit the input-output approach proposed by Wassily Leontief for the quantitative analysis of the relationships among different branches of an economy. Recently, the input-output approach was effectively exploited to assess the resilience of economies against critical events that may affect some sectors and ripple through neighboring economic segments as a function of their vulnerability, inertia, and centrality to the overall economy. Building on an existing approach, this paper considers a dynamic inoperability input-output model with inventories, examined according to their ability to ensure extended service continuity despite the inoperability of some sectors. Referring to this model, the authors first introduce a method for the estimation of the resilience parameter describing the elasticity of the sectors with respect to service perturbations. Furthermore, the authors study an optimization problem for the assignment of inventory levels able to enhance the overall resilience to selected critical events.