The inoperability input-output model (IIM) has recently been proposed as an extension of conventional input-output analysis for assessing the vulnerability of interdependent infrastructures to various perturbations, such as natural disasters, industrial accidents, and deliberate attacks. The IIM framework makes use of a dimensionless risk metric called inoperability, which quantifies the degree of failure of a system on a scale ranging from 0 (normal state) to 1 (total failure). This inoperability is then assumed to propagate through any given industrial network after being induced by initial demand or supply-side perturbations. This work presents a fuzzy linear programming (FLP) model to allocate inoperability in a complex industrial network caused by a loss of natural resource inputs. Such losses may either be “rapid-onset” (e.g., seismic events) or “slow-onset” (e.g., climate change). The model seeks to maximize a dimensionless variable, γ, which modulates the distribution of inoperability across the sectors, as governed by input-output relationships and a priori inoperability limits for each of the sectors. We illustrate the use of this model with two illustrative cases based on scenarios of hypothetical loss of agricultural land due to climate change.